sbplib: +scheme/Heat2dCurvilinear.m annotate

annotate +scheme/Heat2dCurvilinear.m @ 1031:2ef20d00b386 feature/advectionRV

For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Thu, 17 Jan 2019 10:25:06 +0100
parents	08f3ffe63f48
children	78db023a7fe3

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
742 08f3ffe63f48 Add metric scale factors to properties in heat and elastic curvilinear Martin Almquist <malmquist@stanford.edu> parents: 741 diff changeset	39 beta % Cell array of scale factors
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	40
5a9acf282b34 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 % 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	42 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	43
5a9acf282b34 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 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	45
5a9acf282b34 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 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	47
5a9acf282b34 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 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	49 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	50 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	51 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	52
5a9acf282b34 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 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	54 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	55 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	56
5a9acf282b34 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 % 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	58 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	59 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	60 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	61 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	62
5a9acf282b34 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 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	64 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	65 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	66 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	67 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	68 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	69 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	70 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	71 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	72
5a9acf282b34 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 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	74 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	75 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	76 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	77 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	78 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	79 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	80 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	81 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	82 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	83 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	84
5a9acf282b34 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 %====== 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	86 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	87 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	88
5a9acf282b34 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 % 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	90 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	91 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	92 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	93 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	94 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	95 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	96
5a9acf282b34 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 % 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	98 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	99 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	100
5a9acf282b34 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 % -- 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	102 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	103 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	104 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	105
5a9acf282b34 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 % 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	107 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	108 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	109 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	110 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	111 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	112 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	113
5a9acf282b34 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_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	115 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	116 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	117 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	118
5a9acf282b34 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 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	120
5a9acf282b34 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 = 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	122 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	123 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	124 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	125 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	126
5a9acf282b34 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 % 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	128 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	129 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	130 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	131
5a9acf282b34 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 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	133 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	134 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	135 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	136 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	137 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	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 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	140 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	141 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	142 obj.b = b;
742 08f3ffe63f48 Add metric scale factors to properties in heat and elastic curvilinear Martin Almquist <malmquist@stanford.edu> parents: 741 diff changeset	143 obj.beta = beta;
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	144 %----------------------------
5a9acf282b34 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
5a9acf282b34 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 % 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	147 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	148 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	149 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	150 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	151
5a9acf282b34 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_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	153 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	154 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	155 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	156
5a9acf282b34 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 % 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	158 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	159 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	160 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	161 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	162 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	163 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	164 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	165 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	166 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	167
5a9acf282b34 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 % 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	169 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	170 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	171 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	172
5a9acf282b34 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 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	174 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	175 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	176
5a9acf282b34 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 % 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	178 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	179 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	180 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	181
5a9acf282b34 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 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	183 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	184 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	185
5a9acf282b34 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 % 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	187 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	188 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	189 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	190 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	191 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	192 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	193 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	194 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	195
5a9acf282b34 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 %=== 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	197 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	198 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	199 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	200
5a9acf282b34 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 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	202 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	203
5a9acf282b34 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 % 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	205 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	206 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	207 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	208
5a9acf282b34 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 % 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	210 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	211 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	212 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	213 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	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 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	216 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	217 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	218 %=========================================%
5a9acf282b34 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
5a9acf282b34 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 % 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	221 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	222 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	223
5a9acf282b34 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 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	225 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	226 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	227 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	228
5a9acf282b34 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 % 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	230 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	231 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	232 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	233
5a9acf282b34 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 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	236 % 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	237 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	238 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	239 - 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	240
5a9acf282b34 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 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	242 + 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	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
5a9acf282b34 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 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	246 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	247 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	248 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	249
5a9acf282b34 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 % 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	251 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	252 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	253 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	254 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	255 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	256 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	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 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	259
5a9acf282b34 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
5a9acf282b34 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 % 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	262 % 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	263 % 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	264 % 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	265 % 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	266 % 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	267 % 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	268 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	269 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	270 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	271 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	272
5a9acf282b34 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 % 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	274 % 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	275 % 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	276 % 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	277 [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	278 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	279 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	280 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	281 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	282 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	283 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	284 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	285 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	286 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	287 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	288
5a9acf282b34 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 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	290 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	291 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	292 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	293 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	294 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	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 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	297
5a9acf282b34 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 % 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	299 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	300
5a9acf282b34 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 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	302 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	303 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	304 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	305 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	306 -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	307 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	308 +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	309 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	310
5a9acf282b34 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 % 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	312 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	313 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	314 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	315
5a9acf282b34 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 % 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	317 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	318 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	319 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	320 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	321
5a9acf282b34 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 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	323 % 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	324 % 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	325 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	326 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	327
5a9acf282b34 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 % 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	329 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	330
5a9acf282b34 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 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	332 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	333 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	334 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	335 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	336 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	337 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	338 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	339
5a9acf282b34 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 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	341 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	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 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	344 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	345 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	346 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	347
5a9acf282b34 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 % 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	349 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	350
5a9acf282b34 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 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	352 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	353 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	354 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	355 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	356 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	357 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	358 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	359
5a9acf282b34 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 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	361 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	362 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	363 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	364 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	365 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	366 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	367 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	368 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	369 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	370 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	371 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	372 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	373 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	374 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	375 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	376 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	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 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	380
5a9acf282b34 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 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	382 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	383 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	384 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	385 end

Mercurial > repos > public > sbplib

annotate +scheme/Heat2dCurvilinear.m @ 1031:2ef20d00b386 feature/advectionRV