sbplib: +scheme/LaplaceCurvilinearMin.m annotate

annotate +scheme/LaplaceCurvilinearMin.m @ 1210:5e7692ed7c7c feature/laplace_curvilinear_test

Add CG interface coupling

author	Martin Almquist <malmquist@stanford.edu>
date	Sun, 22 Sep 2019 19:05:17 -0700
parents	6bc93c091682
children

rev	line source
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearMin < scheme.Scheme
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 % Inner products and operators for physical coordinates
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 D % Laplace operator
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 H, Hi % Inner product
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 e_w, e_e, e_s, e_n
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 H_w, H_e, H_s, H_n % Boundary inner products
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 Dx, Dy % Physical derivatives
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 M % Gradient inner product
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Metric coefficients
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 J, Ji
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 a11, a12, a22
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 K
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 x_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 y_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Inner product and operators for logical coordinates
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H_u, H_v % Norms in the x and y directions
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 Hi_u, Hi_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hiu, Hiv
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_w, dv_w
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_e, dv_e
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_s, dv_s
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_n, dv_n
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_M_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_R_u, theta_R_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_H_u, theta_H_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 % Temporary, only used for nonconforming interfaces but should be removed.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 lambda
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	50
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	51 % Number of boundary points in minumum check
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	52 bp
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 methods
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % Implements adiv(bgrad(u)) as a SBP scheme
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 function obj = LaplaceCurvilinearMin(g, order, a, b, opSet)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('opSet',@sbp.D2Variable);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('a', 1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 default_arg('b', @(x,y) 0*x + 1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	64 % Number of boundary points in minimum check
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	65 switch order
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	66 case 2
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	67 obj.bp = 2;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	68 case 4
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	69 obj.bp = 4;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	70 case 6
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	71 obj.bp = 7;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	72 end
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	73
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 % assert(isa(g, 'grid.Curvilinear'))
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 if isa(a, 'function_handle')
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 a = grid.evalOn(g, a);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 a = spdiag(a);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 if isa(b, 'function_handle')
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 b = grid.evalOn(g, b);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 % If b is scalar
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 if length(b) == 1
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 % b = b*speye(g.N(), g.N());
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 b = b*ones(g.N(), 1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 b = spdiag(b);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 dim = 2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 m = g.size();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 m_u = m(1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 m_v = m(2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 m_tot = g.N();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 % 1D operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 ops_u = opSet(m_u, {0, 1}, order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 ops_v = opSet(m_v, {0, 1}, order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 h_u = ops_u.h;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 h_v = ops_v.h;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 I_u = speye(m_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 I_v = speye(m_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 D1_u = ops_u.D1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 D2_u = ops_u.D2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 H_u = ops_u.H;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 Hi_u = ops_u.HI;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 e_l_u = ops_u.e_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 e_r_u = ops_u.e_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 d1_l_u = ops_u.d1_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 d1_r_u = ops_u.d1_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 D1_v = ops_v.D1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 D2_v = ops_v.D2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 H_v = ops_v.H;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 Hi_v = ops_v.HI;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 e_l_v = ops_v.e_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 e_r_v = ops_v.e_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 d1_l_v = ops_v.d1_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 d1_r_v = ops_v.d1_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 % Logical operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 Du = kr(D1_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 Dv = kr(I_u,D1_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 obj.Hu = kr(H_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 obj.Hv = kr(I_u,H_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 obj.Hiu = kr(Hi_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 obj.Hiv = kr(I_u,Hi_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 e_w = kr(e_l_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 e_e = kr(e_r_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 e_s = kr(I_u,e_l_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 e_n = kr(I_u,e_r_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 obj.du_w = kr(d1_l_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 obj.dv_w = (e_w'*Dv)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 obj.du_e = kr(d1_r_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 obj.dv_e = (e_e'*Dv)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 obj.du_s = (e_s'*Du)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 obj.dv_s = kr(I_u,d1_l_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 obj.du_n = (e_n'*Du)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 obj.dv_n = kr(I_u,d1_r_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 % Metric coefficients
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 coords = g.points();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 x = coords(:,1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 y = coords(:,2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 x_u = Du*x;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 x_v = Dv*x;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 y_u = Du*y;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 y_v = Dv*y;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 J = x_u.y_v - x_v.y_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 a11 = 1./J .* (x_v.^2 + y_v.^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 a12 = -1./J .* (x_u.x_v + y_u.y_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 a22 = 1./J .* (x_u.^2 + y_u.^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 K = cell(dim, dim);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 K{1,1} = spdiag(y_v./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 K{1,2} = spdiag(-y_u./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 K{2,1} = spdiag(-x_v./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 K{2,2} = spdiag(x_u./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 obj.K = K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 obj.x_u = x_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 obj.x_v = x_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 obj.y_u = y_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 obj.y_v = y_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 % Assemble full operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 L_12 = spdiag(a12);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 Duv = DubL_12*Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 Dvu = DvbL_12*Du;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 Duu = sparse(m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 Dvv = sparse(m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 ind = grid.funcToMatrix(g, 1:m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 for i = 1:m_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 b_a11 = b*a11;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 D = D2_u(b_a11(ind(:,i)));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 p = ind(:,i);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 Duu(p,p) = D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 for i = 1:m_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 b_a22 = b*a22;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 D = D2_v(b_a22(ind(i,:)));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 p = ind(i,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 Dvv(p,p) = D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 % Physical operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 obj.J = spdiag(J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 obj.Ji = spdiag(1./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 obj.H = obj.J*kr(H_u,H_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 obj.e_w = e_w;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 obj.e_e = e_e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 obj.e_s = e_s;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 obj.e_n = e_n;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 %% normal derivatives
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 I_w = ind(1,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 I_e = ind(end,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 I_s = ind(:,1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 I_n = ind(:,end);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 a11_w = spdiag(a11(I_w));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 a12_w = spdiag(a12(I_w));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 a11_e = spdiag(a11(I_e));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 a12_e = spdiag(a12(I_e));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 a22_s = spdiag(a22(I_s));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 a12_s = spdiag(a12(I_s));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 a22_n = spdiag(a22(I_n));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 a12_n = spdiag(a12(I_n));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 %% Boundary inner products
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 obj.H_w = H_v*spdiag(s_w);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 obj.H_e = H_v*spdiag(s_e);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 obj.H_s = H_u*spdiag(s_s);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 obj.H_n = H_u*spdiag(s_n);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 % Misc.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 obj.m = m;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.h = [h_u h_v];
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.order = order;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 obj.grid = g;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 obj.dim = dim;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 obj.a = a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 obj.b = b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 obj.a11 = a11;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 obj.a12 = a12;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 obj.a22 = a22;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 obj.s_w = spdiag(s_w);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 obj.s_e = spdiag(s_e);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 obj.s_s = spdiag(s_s);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 obj.s_n = spdiag(s_n);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 obj.theta_M_u = h_u*ops_u.borrowing.M.d1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 obj.theta_M_v = h_v*ops_v.borrowing.M.d1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 obj.theta_H_u = h_u*ops_u.borrowing.H11;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 obj.theta_H_v = h_v*ops_v.borrowing.H11;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 % Temporary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 obj.lambda = lambda;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 % Closure functions return the opertors applied to the own doamin to close the boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 % type is a string specifying the type of boundary condition if there are several.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 % data is a function returning the data that should be applied at the boundary.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 % neighbour_scheme is an instance of Scheme that should be interfaced to.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 % neighbour_boundary is a string specifying which boundary to interface to.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 default_arg('type','neumann');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 default_arg('parameter', []);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 e = obj.getBoundaryOperator('e', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 d = obj.getBoundaryOperator('d', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 H_b = obj.getBoundaryQuadrature(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 s_b = obj.getBoundaryScaling(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 [th_H, ~, th_R] = obj.getBoundaryBorrowing(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 m = obj.getBoundaryNumber(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 K = obj.K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 J = obj.J;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 Hi = obj.Hi;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 a = obj.a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 b_b = e'obj.be;
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	301 b = obj.b;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 switch type
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 % Dirichlet boundary condition
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 case {'D','d','dirichlet'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 tuning = 1.0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	308 sigma = 0*b;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 for i = 1:obj.dim
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	310 sigma = sigma + bJK{i,m}*K{i,m};
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 end
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	312
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	313 % Minimum check on sigma
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	314 mx = obj.m(1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	315 my = obj.m(2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	316 bp = obj.bp;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	317 sigma_mat = reshape(diag(sigma), my, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	318 switch boundary
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	319 case 'w'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	320 sigma_min = min(sigma_mat(:,1:bp), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	321 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	322 case 'e'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	323 sigma_min = min(sigma_mat(:,end-bp+1:end), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	324 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	325 case 's'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	326 sigma_min = min(sigma_mat(1:bp,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	327 sigma_mat = repmat(sigma_min, my, 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	328 case 'n'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	329 sigma_min = min(sigma_mat(end-bp+1:end,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	330 sigma_mat = repmat(sigma_min, my, 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	331 end
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	332 sigma_min = sigma_mat(:);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	333 sigma_min = spdiag(sigma_min);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	334
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	335 % Window
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	336 sigma = e'sigmae;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	337 sigma_min = e'sigma_mine;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	338
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 sigma = sigma/s_b;
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	340 sigma_min = sigma_min/s_b;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	341
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	342 tau = tuning(1/th_Rsigma/sigma_minsigma + obj.dim/th_Hsigma);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 closure = aHidb_bH_b*e' ...
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	345 -aHietauH_b*e';
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 penalty = -aHidb_bH_b ...
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	348 +aHietauH_b;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 % Neumann boundary condition. Note that the penalty is for du/dn and not b*du/dn.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 case {'N','n','neumann'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 tau1 = -1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 tau2 = 0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 tau = (tau1e + tau2d)*H_b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 closure = aHitaub_bd';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 penalty = -aHitau*b_b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 % Unknown, boundary condition
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 error('No such boundary condition: type = %s',type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 % type Struct that specifies the interface coupling.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 % Fields:
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 % -- tuning: penalty strength, defaults to 1.2
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 % -- interpolation: type of interpolation, default 'none'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 % error('Not implemented')
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 defaultType.tuning = 1.0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 defaultType.interpolation = 'none';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 default_struct('type', defaultType);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 switch type.interpolation
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 case {'none', ''}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 case {'op','OP'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 error('Unknown type of interpolation: %s ', type.interpolation);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 tuning = type.tuning;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 dim = obj.dim;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 % u denotes the solution in the own domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 % v denotes the solution in the neighbour domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 u = obj;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 v = neighbour_scheme;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 % Boundary operators, u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 e_u = u.getBoundaryOperator('e', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 d_u = u.getBoundaryOperator('d', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 s_b_u = u.getBoundaryScaling(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 [th_H_u, ~, th_R_u] = u.getBoundaryBorrowing(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 m_u = u.getBoundaryNumber(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 % Coefficients, u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 K_u = u.K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 J_u = u.J;
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	408 b_u = u.b;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 b_b_u = e_u'u.be_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 % Boundary operators, v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 e_v = v.getBoundaryOperator('e', neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 d_v = v.getBoundaryOperator('d', neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 s_b_v = v.getBoundaryScaling(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 [th_H_v, ~, th_R_v] = v.getBoundaryBorrowing(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 m_v = v.getBoundaryNumber(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 % BUGFIX?!?!?
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) \|\| (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s'))
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 e_v = fliplr(e_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 d_v = fliplr(d_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 s_b_v = rot90(s_b_v,2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 % Coefficients, v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 K_v = v.K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 J_v = v.J;
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	428 b_v = v.b;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 b_b_v = e_v'v.be_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 %--- Penalty strength tau -------------
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	432 sigma_u = 0*b_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	433 sigma_v = 0*b_v;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 for i = 1:obj.dim
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	435 sigma_u = sigma_u + b_uJ_uK_u{i,m_u}*K_u{i,m_u};
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	436 sigma_v = sigma_v + b_vJ_vK_v{i,m_v}*K_v{i,m_v};
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	437 end
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	438
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	439 %--- Minimum check on sigma_u ----
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	440 mx = u.m(1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	441 my = u.m(2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	442 bp = u.bp;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	443 sigma_mat = reshape(diag(sigma_u), my, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	444 switch boundary
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	445 case 'w'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	446 sigma_min = min(sigma_mat(:,1:bp), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	447 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	448 case 'e'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	449 sigma_min = min(sigma_mat(:,end-bp+1:end), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	450 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	451 case 's'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	452 sigma_min = min(sigma_mat(1:bp,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	453 sigma_mat = repmat(sigma_min, my, 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	454 case 'n'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	455 sigma_min = min(sigma_mat(end-bp+1:end,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	456 sigma_mat = repmat(sigma_min, my, 1);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 end
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	458 sigma_min_u = sigma_mat(:);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	459 sigma_min_u = spdiag(sigma_min_u);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	460
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	461 % Window
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	462 sigma_u = e_u'sigma_ue_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	463 sigma_min_u = e_u'sigma_min_ue_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	464 % -------------------------------
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	466 %--- Minimum check on sigma_v ----
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	467 mx = v.m(1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	468 my = v.m(2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	469 bp = v.bp;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	470 sigma_mat = reshape(diag(sigma_v), my, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	471 switch neighbour_boundary
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	472 case 'w'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	473 sigma_min = min(sigma_mat(:,1:bp), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	474 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	475 case 'e'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	476 sigma_min = min(sigma_mat(:,end-bp+1:end), [], 2);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	477 sigma_mat = repmat(sigma_min, 1, mx);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	478 case 's'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	479 sigma_min = min(sigma_mat(1:bp,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	480 sigma_mat = repmat(sigma_min, my, 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	481 case 'n'
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	482 sigma_min = min(sigma_mat(end-bp+1:end,:), [], 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	483 sigma_mat = repmat(sigma_min, my, 1);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	484 end
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	485 sigma_min_v = sigma_mat(:);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	486 sigma_min_v = spdiag(sigma_min_v);
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	487
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	488 % Window
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	489 sigma_v = e_v'sigma_ve_v;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	490 sigma_min_v = e_v'sigma_min_ve_v;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	491 % -------------------------------
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	492
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	493 sigma_u = sigma_u/s_b_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	494 sigma_min_u = sigma_min_u/s_b_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	495
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	496 sigma_v = sigma_v/s_b_v;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	497 sigma_min_v = sigma_min_v/s_b_v;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	498
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	499 tau_R_u = 1/th_R_usigma_u/sigma_min_usigma_u;
6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	500 tau_R_v = 1/th_R_vsigma_v/sigma_min_vsigma_v;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 tau_H_u = dim1/th_H_usigma_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 tau_H_v = dim1/th_H_vsigma_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504
1139 6bc93c091682 Implement minimum check in new scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	505 tau = 1/4tuning((tau_R_u + tau_H_u) + (tau_R_v + tau_H_v));
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 %--------------------------------------
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 % Operators/coefficients that are only required from this side
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 Hi = u.Hi;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 H_b = u.getBoundaryQuadrature(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 a = u.a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 closure = 1/2aHid_ub_b_uH_be_u' ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514 -1/2aHie_uH_bb_b_ud_u' ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 -aHie_utauH_b*e_u';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 penalty = -1/2aHid_ub_b_uH_be_v' ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 -1/2aHie_uH_bb_b_vd_v' ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 +aHie_utauH_b*e_v';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 % TODO: Make this work for curvilinear grids
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 warning('LaplaceCurvilinear: Non-conforming interface assumes that b is constant');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 % User can request special interpolation operators by specifying type.interpOpSet
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 interpOpSet = type.interpOpSet;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 tuning = type.tuning;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 % u denotes the solution in the own domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 % v denotes the solution in the neighbour domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 e_u = obj.getBoundaryOperator('e', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 d_u = obj.getBoundaryOperator('d', boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 H_b_u = obj.getBoundaryQuadrature(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 I_u = obj.getBoundaryIndices(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 [~, gamm_u] = obj.getBoundaryBorrowing(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 [~, gamm_v] = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 % Find the number of grid points along the interface
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551 m_u = size(e_u, 2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 m_v = size(e_v, 2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 Hi = obj.Hi;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 a = obj.a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557 u = obj;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 v = neighbour_scheme;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565 tau_u = -1./(4b1_u) -1./(4b2_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566 tau_v = -1./(4b1_v) -1./(4b2_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 tau_u = tuning * spdiag(tau_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569 tau_v = tuning * spdiag(tau_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570 beta_u = tau_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	571
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	572 % Build interpolation operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	573 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	574 Iu2v = intOps.Iu2v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	575 Iv2u = intOps.Iv2u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	576
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	577 closure = aHie_utau_uH_b_u*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	578 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	579 a1/2Hid_uH_b_u*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	580 -a1/2Hie_uH_b_u*d_u';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	581
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	582 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	583 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	584 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	585 -a1/2Hie_uH_b_uIv2u.badd_v';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	586
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	587 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	588
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	589 % Returns the boundary operator op for the boundary specified by the string boundary.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	590 % op -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	591 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	592 function o = getBoundaryOperator(obj, op, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	593 assertIsMember(op, {'e', 'd'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	594 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	595
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	596 o = obj.([op, '_', boundary]);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	597 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	598
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	599 % Returns square boundary quadrature matrix, of dimension
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	600 % corresponding to the number of boundary points
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	601 %
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	602 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	603 function H_b = getBoundaryQuadrature(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	604 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	605
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	606 H_b = obj.(['H_', boundary]);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	607 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	608
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	609 % Returns square boundary quadrature scaling matrix, of dimension
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	610 % corresponding to the number of boundary points
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	611 %
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	612 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	613 function s_b = getBoundaryScaling(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	614 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	615
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	616 s_b = obj.(['s_', boundary]);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	617 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	618
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	619 % Returns the coordinate number corresponding to the boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	620 %
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	621 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	622 function m = getBoundaryNumber(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	623 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	624
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	625 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	626 case {'w', 'e'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	627 m = 1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	628 case {'s', 'n'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	629 m = 2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	630 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	631 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	632
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	633 % Returns the indices of the boundary points in the grid matrix
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	634 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	635 function I = getBoundaryIndices(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	636 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	637
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	638 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	639 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	640 case 'w'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	641 I = ind(1,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	642 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	643 I = ind(end,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	644 case 's'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	645 I = ind(:,1)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	646 case 'n'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	647 I = ind(:,end)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	648 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	649 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	650
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	651 % Returns borrowing constant gamma
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	652 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	653 function [theta_H, theta_M, theta_R] = getBoundaryBorrowing(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	654 assertIsMember(boundary, {'w', 'e', 's', 'n'})
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	655
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	656 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	657 case {'w','e'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	658 theta_H = obj.theta_H_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	659 theta_M = obj.theta_M_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	660 theta_R = obj.theta_R_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	661 case {'s','n'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	662 theta_H = obj.theta_H_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	663 theta_M = obj.theta_M_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	664 theta_R = obj.theta_R_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	665 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	666 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	667
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	668 function N = size(obj)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	669 N = prod(obj.m);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	670 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	671 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	672 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearMin.m @ 1210:5e7692ed7c7c feature/laplace_curvilinear_test