sbplib: +scheme/Heat2dCurvilinear.m annotate

author	Martin Almquist <malmquist@stanford.edu>
date	Wed, 09 May 2018 19:29:12 -0700
parents
children	08f3ffe63f48

rev	line source
741 5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef Heat2dCurvilinear < scheme.Scheme
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 % Discretizes the Laplacian with variable coefficent, curvilinear,
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 % in the Heat equation way (i.e., the discretization matrix is not necessarily
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 % symmetric)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 % u_t = div * (kappa * grad u )
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 % opSet should be cell array of opSets, one per dimension. This
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 % is useful if we have periodic BC in one direction.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 properties
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 m % Number of points in each direction, possibly a vector
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12 h % Grid spacing
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 grid
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 order % Order of accuracy for the approximation
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 % Diagonal matrix for variable coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 KAPPA % Variable coefficient
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 D % Total operator
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 D1 % First derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 % Second derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 D2_kappa
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 H, Hi % Inner products
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 e_l, e_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 d1_l, d1_r % Normal derivatives at the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 alpha % Vector of borrowing constants
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Boundary inner products
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H_boundary_l, H_boundary_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 % Metric coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 b % Cell matrix of size dim x dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 J, Ji
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 % Numerical boundary flux operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 flux_l, flux_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 methods
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 function obj = Heat2dCurvilinear(g ,order, kappa_fun, opSet)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 default_arg('kappa_fun', @(x,y) 0*x+1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 dim = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 kappa = grid.evalOn(g, kappa_fun);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 m = g.size();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 m_tot = g.N();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % 1D operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 ops = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 ops{i} = opSet{i}(m(i), {0, 1}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 I = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 D1 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 D2 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 H = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 Hi = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 e_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 e_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 d1_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 d1_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 I{i} = speye(m(i));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 D1{i} = ops{i}.D1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 D2{i} = ops{i}.D2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 H{i} = ops{i}.H;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 Hi{i} = ops{i}.HI;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 e_l{i} = ops{i}.e_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 e_r{i} = ops{i}.e_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 d1_l{i} = ops{i}.d1_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 d1_r{i} = ops{i}.d1_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 %====== Assemble full operators ========
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 KAPPA = spdiag(kappa);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 obj.KAPPA = KAPPA;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 % Allocate
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 obj.D1 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 obj.D2_kappa = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 obj.e_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 obj.e_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 obj.d1_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 obj.d1_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 % D1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 obj.D1{1} = kron(D1{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 obj.D1{2} = kron(I{1},D1{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 % -- Metric coefficients ----
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 coords = g.points();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 x = coords(:,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 y = coords(:,2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 % Use non-periodic difference operators for metric even if opSet is periodic.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 xmax = max(ops{1}.x);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 ymax = max(ops{2}.x);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 opSetMetric{1} = sbp.D2Variable(m(1), {0, xmax}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 opSetMetric{2} = sbp.D2Variable(m(2), {0, ymax}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 D1Metric{1} = kron(opSetMetric{1}.D1, I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 D1Metric{2} = kron(I{1}, opSetMetric{2}.D1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 x_xi = D1Metric{1}*x;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 x_eta = D1Metric{2}*x;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 y_xi = D1Metric{1}*y;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 y_eta = D1Metric{2}*y;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 J = x_xi.y_eta - x_eta.y_xi;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 b = cell(dim,dim);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 b{1,1} = y_eta./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 b{1,2} = -x_eta./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 b{2,1} = -y_xi./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 b{2,2} = x_xi./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 % Scale factors for boundary integrals
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 beta = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 beta{1} = sqrt(x_eta.^2 + y_eta.^2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 beta{2} = sqrt(x_xi.^2 + y_xi.^2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 J = spdiag(J);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 Ji = inv(J);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 beta{i} = spdiag(beta{i});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 b{i,j} = spdiag(b{i,j});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 obj.J = J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 obj.Ji = Ji;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 obj.b = b;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 %----------------------------
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 % Boundary operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 obj.e_l{1} = kron(e_l{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 obj.e_l{2} = kron(I{1},e_l{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 obj.e_r{1} = kron(e_r{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 obj.e_r{2} = kron(I{1},e_r{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 obj.d1_l{1} = kron(d1_l{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 obj.d1_l{2} = kron(I{1},d1_l{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 obj.d1_r{1} = kron(d1_r{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 obj.d1_r{2} = kron(I{1},d1_r{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 % D2 coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 kappa_coeff = cell(dim,dim);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 obj.D2_kappa{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 kappa_coeff{j} = sparse(m_tot,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 kappa_coeff{j} = kappa_coeff{j} + b{i,j}Jb{i,j}*kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 ind = grid.funcToMatrix(g, 1:m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 % x-dir
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 for col = 1:m(2)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 D_kappa = D2{1}(kappa_coeff{j}(ind(:,col)));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 p = ind(:,col);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 obj.D2_kappa{j}(p,p) = D_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 % y-dir
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 for row = 1:m(1)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 D_kappa = D2{2}(kappa_coeff{j}(ind(row,:)));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 p = ind(row,:);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 obj.D2_kappa{j}(p,p) = D_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 % Quadratures
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 obj.H = kron(H{1},H{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 obj.Hi = inv(obj.H);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 obj.H_boundary_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 obj.H_boundary_l{1} = obj.e_l{1}'beta{1}obj.e_l{1}*H{2};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 obj.H_boundary_l{2} = obj.e_l{2}'beta{2}obj.e_l{2}*H{1};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 obj.H_boundary_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 obj.H_boundary_r{1} = obj.e_r{1}'beta{1}obj.e_r{1}*H{2};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 obj.H_boundary_r{2} = obj.e_r{2}'beta{2}obj.e_r{2}*H{1};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 %=== Differentiation matrix D (without SAT) ===
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 D2_kappa = obj.D2_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 D1 = obj.D1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 D = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 d = @kroneckerDelta; % Kronecker delta
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 % 2nd derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 D = D + Ji*D2_kappa{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 % Mixed terms
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 for k = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 D = D + db(i,j)JiD1{j}b{i,j}JKAPPAb{i,k}*D1{k};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 obj.D = D;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 %=========================================%
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 % Normal flux operators for BC.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 flux_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 flux_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 d1_l = obj.d1_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 d1_r = obj.d1_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 e_l = obj.e_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 e_r = obj.e_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 % Loop over boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 flux_l{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 flux_r{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 % Loop over dummy index
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 % Loop over dummy index
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 for k = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 flux_l{j} = flux_l{j} ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 - beta{j}\b{i,j}JKAPPAb{i,k}( d(j,k)e_l{k}d1_l{k}' + db(j,k)*D1{k} );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 flux_r{j} = flux_r{j} ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 + beta{j}\b{i,j}JKAPPAb{i,k}( d(j,k)e_r{k}d1_r{k}' + db(j,k)*D1{k} );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 obj.flux_l = flux_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 obj.flux_r = flux_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 % Misc.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.m = m;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.h = g.scaling();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 obj.order = order;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 obj.grid = g;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 obj.dim = dim;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 obj.alpha = [ops{1}.borrowing.M.d1, ops{2}.borrowing.M.d1];
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 % Closure functions return the operators applied to the own domain to close the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 % type is a string specifying the type of boundary condition.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 % data is a function returning the data that should be applied at the boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 % neighbour_scheme is an instance of Scheme that should be interfaced to.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 % neighbour_boundary is a string specifying which boundary to interface to.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 function [closure, penalty] = boundary_condition(obj, boundary, type, symmetric, tuning)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 default_arg('type','Neumann');
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 default_arg('symmetric', false);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 default_arg('tuning',1.2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 % j is the coordinate direction of the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 % nj: outward unit normal component.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 % nj = -1 for west, south, bottom boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 % nj = 1 for east, north, top boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 [j, nj] = obj.get_boundary_number(boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 switch nj
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 case 1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 e = obj.e_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 flux = obj.flux_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 H_gamma = obj.H_boundary_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 case -1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 e = obj.e_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 flux = obj.flux_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 H_gamma = obj.H_boundary_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 Hi = obj.Hi;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 Ji = obj.Ji;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 KAPPA = obj.KAPPA;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 kappa_gamma = e'KAPPAe;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 h = obj.h(j);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 alpha = h*obj.alpha(j);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 switch type
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 % Dirichlet boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 case {'D','d','dirichlet','Dirichlet'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 if ~symmetric
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 closure = -JiHiflux'eH_gamma*(e' );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 penalty = JiHiflux'eH_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 else
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 closure = JiHiflux'eH_gamma*(e' )...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 -tuning2/alphaJiHiekappa_gammaH_gamma*(e' ) ;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 penalty = -JiHiflux'eH_gamma ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 +tuning2/alphaJiHiekappa_gammaH_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 % Normal flux boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310 case {'N','n','neumann','Neumann'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 closure = -JiHieH_gamma(e'*flux );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 penalty = JiHie*H_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 % Unknown boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 error('No such boundary condition: type = %s',type);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 % u denotes the solution in the own domain
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 % v denotes the solution in the neighbour domain
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 error('Interface not implemented');
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 function [j, nj] = get_boundary_number(obj, boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 error('No such boundary: boundary = %s',boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 nj = -1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 nj = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 function [return_op] = get_boundary_operator(obj, op, boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 error('No such boundary: boundary = %s',boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 switch op
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 case 'e'
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 return_op = obj.e_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 return_op = obj.e_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 case 'd'
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 return_op = obj.d1_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 return_op = obj.d1_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 error(['No such operator: operatr = ' op]);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 function N = size(obj)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 N = prod(obj.m);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 end

741

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

1 classdef Heat2dCurvilinear < scheme.Scheme

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

2

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

3 % Discretizes the Laplacian with variable coefficent, curvilinear,

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

4 % in the Heat equation way (i.e., the discretization matrix is not necessarily

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

5 % symmetric)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

6 % u_t = div * (kappa * grad u )

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

7 % opSet should be cell array of opSets, one per dimension. This

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

8 % is useful if we have periodic BC in one direction.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

9

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

10 properties

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

11 m % Number of points in each direction, possibly a vector

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

12 h % Grid spacing

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

13

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

14 grid

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

15 dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

16

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

17 order % Order of accuracy for the approximation

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

18

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

19 % Diagonal matrix for variable coefficients

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

20 KAPPA % Variable coefficient

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

21

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

22 D % Total operator

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

23 D1 % First derivatives

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

24

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

25 % Second derivatives

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

26 D2_kappa

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

27

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

28 H, Hi % Inner products

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

29 e_l, e_r

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

30 d1_l, d1_r % Normal derivatives at the boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

31 alpha % Vector of borrowing constants

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

32

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

33 % Boundary inner products

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

34 H_boundary_l, H_boundary_r

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

35

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

36 % Metric coefficients

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

37 b % Cell matrix of size dim x dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

38 J, Ji

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

39

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

40 % Numerical boundary flux operators

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

41 flux_l, flux_r

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

42

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

43 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

44

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

45 methods

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

46

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

47 function obj = Heat2dCurvilinear(g ,order, kappa_fun, opSet)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

48 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

49 default_arg('kappa_fun', @(x,y) 0*x+1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

50 dim = 2;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

51

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

52 kappa = grid.evalOn(g, kappa_fun);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

53 m = g.size();

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

54 m_tot = g.N();

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

55

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

56 % 1D operators

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

57 ops = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

58 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

59 ops{i} = opSet{i}(m(i), {0, 1}, order);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

60 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

61

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

62 I = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

63 D1 = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

64 D2 = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

65 H = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

66 Hi = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

67 e_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

68 e_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

69 d1_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

70 d1_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

71

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

72 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

73 I{i} = speye(m(i));

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

74 D1{i} = ops{i}.D1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

75 D2{i} = ops{i}.D2;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

76 H{i} = ops{i}.H;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

77 Hi{i} = ops{i}.HI;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

78 e_l{i} = ops{i}.e_l;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

79 e_r{i} = ops{i}.e_r;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

80 d1_l{i} = ops{i}.d1_l;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

81 d1_r{i} = ops{i}.d1_r;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

82 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

83

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

84 %====== Assemble full operators ========

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

85 KAPPA = spdiag(kappa);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

86 obj.KAPPA = KAPPA;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

87

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

88 % Allocate

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

89 obj.D1 = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

90 obj.D2_kappa = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

91 obj.e_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

92 obj.e_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

93 obj.d1_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

94 obj.d1_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

95

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

96 % D1

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

97 obj.D1{1} = kron(D1{1},I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

98 obj.D1{2} = kron(I{1},D1{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

99

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

100 % -- Metric coefficients ----

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

101 coords = g.points();

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

102 x = coords(:,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

103 y = coords(:,2);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

104

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

105 % Use non-periodic difference operators for metric even if opSet is periodic.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

106 xmax = max(ops{1}.x);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

107 ymax = max(ops{2}.x);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

108 opSetMetric{1} = sbp.D2Variable(m(1), {0, xmax}, order);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

109 opSetMetric{2} = sbp.D2Variable(m(2), {0, ymax}, order);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

110 D1Metric{1} = kron(opSetMetric{1}.D1, I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

111 D1Metric{2} = kron(I{1}, opSetMetric{2}.D1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

112

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

113 x_xi = D1Metric{1}*x;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

114 x_eta = D1Metric{2}*x;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

115 y_xi = D1Metric{1}*y;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

116 y_eta = D1Metric{2}*y;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

117

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

118 J = x_xi.*y_eta - x_eta.*y_xi;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

119

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

120 b = cell(dim,dim);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

121 b{1,1} = y_eta./J;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

122 b{1,2} = -x_eta./J;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

123 b{2,1} = -y_xi./J;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

124 b{2,2} = x_xi./J;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

125

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

126 % Scale factors for boundary integrals

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

127 beta = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

128 beta{1} = sqrt(x_eta.^2 + y_eta.^2);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

129 beta{2} = sqrt(x_xi.^2 + y_xi.^2);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

130

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

131 J = spdiag(J);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

132 Ji = inv(J);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

133 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

134 beta{i} = spdiag(beta{i});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

135 for j = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

136 b{i,j} = spdiag(b{i,j});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

137 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

138 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

139 obj.J = J;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

140 obj.Ji = Ji;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

141 obj.b = b;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

142 %----------------------------

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

143

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

144 % Boundary operators

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

145 obj.e_l{1} = kron(e_l{1},I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

146 obj.e_l{2} = kron(I{1},e_l{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

147 obj.e_r{1} = kron(e_r{1},I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

148 obj.e_r{2} = kron(I{1},e_r{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

149

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

150 obj.d1_l{1} = kron(d1_l{1},I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

151 obj.d1_l{2} = kron(I{1},d1_l{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

152 obj.d1_r{1} = kron(d1_r{1},I{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

153 obj.d1_r{2} = kron(I{1},d1_r{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

154

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

155 % D2 coefficients

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

156 kappa_coeff = cell(dim,dim);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

157 for j = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

158 obj.D2_kappa{j} = sparse(m_tot,m_tot);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

159 kappa_coeff{j} = sparse(m_tot,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

160 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

161 kappa_coeff{j} = kappa_coeff{j} + b{i,j}*J*b{i,j}*kappa;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

162 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

163 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

164 ind = grid.funcToMatrix(g, 1:m_tot);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

165

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

166 % x-dir

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

167 j = 1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

168 for col = 1:m(2)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

169 D_kappa = D2{1}(kappa_coeff{j}(ind(:,col)));

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

170

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

171 p = ind(:,col);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

172 obj.D2_kappa{j}(p,p) = D_kappa;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

173 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

174

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

175 % y-dir

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

176 j = 2;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

177 for row = 1:m(1)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

178 D_kappa = D2{2}(kappa_coeff{j}(ind(row,:)));

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

179

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

180 p = ind(row,:);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

181 obj.D2_kappa{j}(p,p) = D_kappa;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

182 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

183

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

184 % Quadratures

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

185 obj.H = kron(H{1},H{2});

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

186 obj.Hi = inv(obj.H);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

187 obj.H_boundary_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

188 obj.H_boundary_l{1} = obj.e_l{1}'*beta{1}*obj.e_l{1}*H{2};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

189 obj.H_boundary_l{2} = obj.e_l{2}'*beta{2}*obj.e_l{2}*H{1};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

190 obj.H_boundary_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

191 obj.H_boundary_r{1} = obj.e_r{1}'*beta{1}*obj.e_r{1}*H{2};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

192 obj.H_boundary_r{2} = obj.e_r{2}'*beta{2}*obj.e_r{2}*H{1};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

193

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

194 %=== Differentiation matrix D (without SAT) ===

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

195 D2_kappa = obj.D2_kappa;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

196 D1 = obj.D1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

197 D = sparse(m_tot,m_tot);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

198

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

199 d = @kroneckerDelta; % Kronecker delta

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

200 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

201

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

202 % 2nd derivatives

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

203 for j = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

204 D = D + Ji*D2_kappa{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

205 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

206

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

207 % Mixed terms

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

208 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

209 for j = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

210 for k = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

211 D = D + db(i,j)*Ji*D1{j}*b{i,j}*J*KAPPA*b{i,k}*D1{k};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

212 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

213 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

214 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

215 obj.D = D;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

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parents:

diff changeset

216 %=========================================%

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

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parents:

diff changeset

217

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

218 % Normal flux operators for BC.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

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parents:

diff changeset

219 flux_l = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

220 flux_r = cell(dim,1);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

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parents:

diff changeset

221

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

222 d1_l = obj.d1_l;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

223 d1_r = obj.d1_r;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

224 e_l = obj.e_l;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

225 e_r = obj.e_r;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

226

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

227 % Loop over boundaries

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

228 for j = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

229 flux_l{j} = sparse(m_tot,m_tot);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

230 flux_r{j} = sparse(m_tot,m_tot);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

231

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

232 % Loop over dummy index

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

233 for i = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

234 % Loop over dummy index

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

235 for k = 1:dim

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

236 flux_l{j} = flux_l{j} ...

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

237 - beta{j}\b{i,j}*J*KAPPA*b{i,k}*( d(j,k)*e_l{k}*d1_l{k}' + db(j,k)*D1{k} );

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

238

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

239 flux_r{j} = flux_r{j} ...

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

240 + beta{j}\b{i,j}*J*KAPPA*b{i,k}*( d(j,k)*e_r{k}*d1_r{k}' + db(j,k)*D1{k} );

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

241 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

242

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

243 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

244 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

245 obj.flux_l = flux_l;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

246 obj.flux_r = flux_r;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

247

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

248 % Misc.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

249 obj.m = m;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

250 obj.h = g.scaling();

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

251 obj.order = order;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

252 obj.grid = g;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

253 obj.dim = dim;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

254 obj.alpha = [ops{1}.borrowing.M.d1, ops{2}.borrowing.M.d1];

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

255

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

256 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

257

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

258

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

259 % Closure functions return the operators applied to the own domain to close the boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

260 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

261 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

262 % type is a string specifying the type of boundary condition.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

263 % data is a function returning the data that should be applied at the boundary.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

264 % neighbour_scheme is an instance of Scheme that should be interfaced to.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

265 % neighbour_boundary is a string specifying which boundary to interface to.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

266 function [closure, penalty] = boundary_condition(obj, boundary, type, symmetric, tuning)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

267 default_arg('type','Neumann');

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

268 default_arg('symmetric', false);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

269 default_arg('tuning',1.2);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

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parents:

diff changeset

270

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

271 % j is the coordinate direction of the boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

272 % nj: outward unit normal component.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

273 % nj = -1 for west, south, bottom boundaries

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

274 % nj = 1 for east, north, top boundaries

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

275 [j, nj] = obj.get_boundary_number(boundary);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

276 switch nj

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

277 case 1

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

278 e = obj.e_r{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

279 flux = obj.flux_r{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

280 H_gamma = obj.H_boundary_r{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

281 case -1

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

282 e = obj.e_l{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

283 flux = obj.flux_l{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

284 H_gamma = obj.H_boundary_l{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

285 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

286

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

287 Hi = obj.Hi;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

288 Ji = obj.Ji;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

289 KAPPA = obj.KAPPA;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

290 kappa_gamma = e'*KAPPA*e;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

291 h = obj.h(j);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

292 alpha = h*obj.alpha(j);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

293

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

294 switch type

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

295

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

296 % Dirichlet boundary condition

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

297 case {'D','d','dirichlet','Dirichlet'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

298

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

299 if ~symmetric

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

300 closure = -Ji*Hi*flux'*e*H_gamma*(e' );

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

301 penalty = Ji*Hi*flux'*e*H_gamma;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

302 else

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

303 closure = Ji*Hi*flux'*e*H_gamma*(e' )...

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

304 -tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma*(e' ) ;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

305 penalty = -Ji*Hi*flux'*e*H_gamma ...

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

306 +tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

307 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

308

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

309 % Normal flux boundary condition

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

310 case {'N','n','neumann','Neumann'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

311 closure = -Ji*Hi*e*H_gamma*(e'*flux );

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

312 penalty = Ji*Hi*e*H_gamma;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

313

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

314 % Unknown boundary condition

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

315 otherwise

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

316 error('No such boundary condition: type = %s',type);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

317 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

318 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

319

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

320 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

321 % u denotes the solution in the own domain

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

322 % v denotes the solution in the neighbour domain

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

323 error('Interface not implemented');

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

324 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

325

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

326 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

327 function [j, nj] = get_boundary_number(obj, boundary)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

328

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

329 switch boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

330 case {'w','W','west','West', 'e', 'E', 'east', 'East'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

331 j = 1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

332 case {'s','S','south','South', 'n', 'N', 'north', 'North'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

333 j = 2;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

334 otherwise

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

335 error('No such boundary: boundary = %s',boundary);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

336 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

337

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

338 switch boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

339 case {'w','W','west','West','s','S','south','South'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

340 nj = -1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

341 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

342 nj = 1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

343 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

344 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

345

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

346 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

347 function [return_op] = get_boundary_operator(obj, op, boundary)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

348

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

349 switch boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

350 case {'w','W','west','West', 'e', 'E', 'east', 'East'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

351 j = 1;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

352 case {'s','S','south','South', 'n', 'N', 'north', 'North'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

353 j = 2;

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

354 otherwise

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

355 error('No such boundary: boundary = %s',boundary);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

356 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

357

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

358 switch op

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

359 case 'e'

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

360 switch boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

361 case {'w','W','west','West','s','S','south','South'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

362 return_op = obj.e_l{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

363 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

364 return_op = obj.e_r{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

365 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

366 case 'd'

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

367 switch boundary

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

368 case {'w','W','west','West','s','S','south','South'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

369 return_op = obj.d1_l{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

370 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

371 return_op = obj.d1_r{j};

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

372 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

373 otherwise

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

374 error(['No such operator: operatr = ' op]);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

375 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

376

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

377 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

378

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

379 function N = size(obj)

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

380 N = prod(obj.m);

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

381 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

382 end

5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.

Martin Almquist <malmquist@stanford.edu>

parents:

diff changeset

383 end

Mercurial > repos > public > sbplib

annotate +scheme/Heat2dCurvilinear.m @ 741:5a9acf282b34 feature/poroelastic