sbplib: +scheme/LaplaceCurvilinearNewCorner.m annotate

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1339:bcdb14b05d03 feature/D2_boundary_opt

Fix comment

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Fri, 22 Jul 2022 16:31:18 +0200
parents	27019aca2f17
children

rev	line source
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearNewCorner < scheme.Scheme
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 % Inner products and operators for physical coordinates
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 D % Laplace operator
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 H, Hi % Inner product
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 e_w, e_e, e_s, e_n
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 H_w, H_e, H_s, H_n % Boundary inner products
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 Dx, Dy % Physical derivatives
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 M % Gradient inner product
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Metric coefficients
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 J, Ji
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 a11, a12, a22
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 K
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 x_u
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 y_u
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Inner product and operators for logical coordinates
1080 753de514ae77 Add H_1D to LaplaceCurvilinearNewCorner Martin Almquist <malmquist@stanford.edu> parents: 1055 diff changeset	34 H_u, H_v, H_1D % Norms in the x and y directions
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 Hi_u, Hi_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hiu, Hiv
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_w, dv_w
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_e, dv_e
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_s, dv_s
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_n, dv_n
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_M_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_R_u, theta_R_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_H_u, theta_H_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 % Temporary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 lambda
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 gamm_u, gamm_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 % Implements adiv(bgrad(u)) as a SBP scheme
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 function obj = LaplaceCurvilinearNewCorner(g, order, a, b, opSet)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 default_arg('opSet',@sbp.D2Variable);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('a', 1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('b', @(x,y) 0*x + 1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 % assert(isa(g, 'grid.Curvilinear'))
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 if isa(a, 'function_handle')
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 a = grid.evalOn(g, a);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 end
1117 27019aca2f17 Fix bug in LaplCurveNewCorner that makes bc matrix non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1080 diff changeset	67 a = spdiag(a);
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 if isa(b, 'function_handle')
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 b = grid.evalOn(g, b);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 end
1117 27019aca2f17 Fix bug in LaplCurveNewCorner that makes bc matrix non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1080 diff changeset	72 b = spdiag(b);
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 % If b is scalar
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 if length(b) == 1
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 b = b*speye(g.N(), g.N());
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 dim = 2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 m = g.size();
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 m_u = m(1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 m_v = m(2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 m_tot = g.N();
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 if isa(g, 'grid.Curvilinear')
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 h = g.scaling();
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 h_u = h(1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 h_v = h(2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 else
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 h_u = 1/(m_u - 1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 h_v = 1/(m_v - 1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 h = [h_u, h_v];
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 % 1D operators
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 ops_u = opSet(m_u, {0, 1}, order);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 ops_v = opSet(m_v, {0, 1}, order);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 I_u = speye(m_u);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 I_v = speye(m_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 D1_u = ops_u.D1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 D2_u = ops_u.D2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 H_u = ops_u.H;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 Hi_u = ops_u.HI;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 e_l_u = ops_u.e_l;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 e_r_u = ops_u.e_r;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 d1_l_u = ops_u.d1_l;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 d1_r_u = ops_u.d1_r;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 D1_v = ops_v.D1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 D2_v = ops_v.D2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 H_v = ops_v.H;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 Hi_v = ops_v.HI;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 e_l_v = ops_v.e_l;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 e_r_v = ops_v.e_r;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 d1_l_v = ops_v.d1_l;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 d1_r_v = ops_v.d1_r;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 % Logical operators
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 Du = kr(D1_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 Dv = kr(I_u,D1_v);
1080 753de514ae77 Add H_1D to LaplaceCurvilinearNewCorner Martin Almquist <malmquist@stanford.edu> parents: 1055 diff changeset	124 obj.H_u = H_u;
753de514ae77 Add H_1D to LaplaceCurvilinearNewCorner Martin Almquist <malmquist@stanford.edu> parents: 1055 diff changeset	125 obj.H_v = H_v;
753de514ae77 Add H_1D to LaplaceCurvilinearNewCorner Martin Almquist <malmquist@stanford.edu> parents: 1055 diff changeset	126 obj.H_1D = {H_u, H_v};
753de514ae77 Add H_1D to LaplaceCurvilinearNewCorner Martin Almquist <malmquist@stanford.edu> parents: 1055 diff changeset	127
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 obj.Hu = kr(H_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 obj.Hv = kr(I_u,H_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 obj.Hiu = kr(Hi_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 obj.Hiv = kr(I_u,Hi_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 e_w = kr(e_l_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 e_e = kr(e_r_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 e_s = kr(I_u,e_l_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 e_n = kr(I_u,e_r_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 obj.du_w = kr(d1_l_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 obj.dv_w = (e_w'*Dv)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 obj.du_e = kr(d1_r_u,I_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 obj.dv_e = (e_e'*Dv)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 obj.du_s = (e_s'*Du)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 obj.dv_s = kr(I_u,d1_l_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 obj.du_n = (e_n'*Du)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 obj.dv_n = kr(I_u,d1_r_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 % Metric coefficients
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 coords = g.points();
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 x = coords(:,1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 y = coords(:,2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 x_u = Du*x;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 x_v = Dv*x;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 y_u = Du*y;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 y_v = Dv*y;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 J = x_u.y_v - x_v.y_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 a11 = 1./J .* (x_v.^2 + y_v.^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 a12 = -1./J .* (x_u.x_v + y_u.y_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 a22 = 1./J .* (x_u.^2 + y_u.^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 K = cell(dim, dim);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 K{1,1} = spdiag(y_v./J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 K{1,2} = spdiag(-y_u./J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 K{2,1} = spdiag(-x_v./J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 K{2,2} = spdiag(x_u./J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 obj.K = K;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 obj.x_u = x_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 obj.x_v = x_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 obj.y_u = y_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 obj.y_v = y_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 % Assemble full operators
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 L_12 = spdiag(a12);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 Duv = DubL_12*Dv;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 Dvu = DvbL_12*Du;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 Duu = sparse(m_tot);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 Dvv = sparse(m_tot);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 ind = grid.funcToMatrix(g, 1:m_tot);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 for i = 1:m_v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 b_a11 = b*a11;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 D = D2_u(b_a11(ind(:,i)));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 p = ind(:,i);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 Duu(p,p) = D;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 for i = 1:m_u
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 b_a22 = b*a22;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 D = D2_v(b_a22(ind(i,:)));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 p = ind(i,:);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 Dvv(p,p) = D;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 % Physical operators
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 obj.J = spdiag(J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 obj.Ji = spdiag(1./J);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 obj.H = obj.J*kr(H_u,H_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 obj.e_w = e_w;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 obj.e_e = e_e;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 obj.e_s = e_s;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 obj.e_n = e_n;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 %% normal derivatives
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 I_w = ind(1,:);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 I_e = ind(end,:);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 I_s = ind(:,1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 I_n = ind(:,end);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 a11_w = spdiag(a11(I_w));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 a12_w = spdiag(a12(I_w));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 a11_e = spdiag(a11(I_e));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 a12_e = spdiag(a12(I_e));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 a22_s = spdiag(a22(I_s));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 a12_s = spdiag(a12(I_s));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 a22_n = spdiag(a22(I_n));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 a12_n = spdiag(a12(I_n));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 %% Boundary inner products
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 obj.H_w = H_v*spdiag(s_w);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 obj.H_e = H_v*spdiag(s_e);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 obj.H_s = H_u*spdiag(s_s);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 obj.H_n = H_u*spdiag(s_n);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 % Misc.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 obj.m = m;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 obj.h = [h_u h_v];
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.order = order;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.grid = g;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 obj.dim = dim;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 obj.a = a;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 obj.b = b;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 obj.a11 = a11;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 obj.a12 = a12;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 obj.a22 = a22;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 obj.s_w = spdiag(s_w);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 obj.s_e = spdiag(s_e);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 obj.s_s = spdiag(s_s);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 obj.s_n = spdiag(s_n);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 obj.theta_M_u = h_u*ops_u.borrowing.M.d1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 obj.theta_M_v = h_v*ops_v.borrowing.M.d1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_D;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_D;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 obj.theta_H_u = h_u*ops_u.borrowing.H11;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 obj.theta_H_v = h_v*ops_v.borrowing.H11;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 % Temporary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 obj.lambda = lambda;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 % Closure functions return the opertors applied to the own doamin to close the boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 % type is a string specifying the type of boundary condition if there are several.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 % data is a function returning the data that should be applied at the boundary.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 % neighbour_scheme is an instance of Scheme that should be interfaced to.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 % neighbour_boundary is a string specifying which boundary to interface to.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 default_arg('type','neumann');
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 default_arg('parameter', []);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 e = obj.getBoundaryOperator('e', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 d = obj.getBoundaryOperator('d', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 H_b = obj.getBoundaryQuadrature(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 s_b = obj.getBoundaryScaling(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 [th_H, ~, th_R] = obj.getBoundaryBorrowing(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 m = obj.getBoundaryNumber(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 K = obj.K;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 J = obj.J;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 Hi = obj.Hi;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 a = obj.a;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 b_b = e'obj.be;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 switch type
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 % Dirichlet boundary condition
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 case {'D','d','dirichlet'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 tuning = 1.0;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307
1117 27019aca2f17 Fix bug in LaplCurveNewCorner that makes bc matrix non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1080 diff changeset	308 sigma = 0*b_b;
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 for i = 1:obj.dim
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310 sigma = sigma + e'JK{i,m}K{i,m}e;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 sigma = sigma/s_b;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 % tau = tuning(1/th_R + obj.dim/th_H)sigma;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 tau_R = 1/th_R*sigma;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 tau_H = 1/th_H*sigma;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 tau_H(1,1) = obj.dim*tau_H(1,1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 tau_H(end,end) = obj.dim*tau_H(end,end);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 tau = tuning*(tau_R + tau_H);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 closure = aHidb_bH_b*e' ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 -aHietaub_bH_be';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 penalty = -aHidb_bH_b ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 +aHietaub_b*H_b;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 % Neumann boundary condition. Note that the penalty is for du/dn and not b*du/dn.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 case {'N','n','neumann'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 tau1 = -1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 tau2 = 0;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 tau = (tau1e + tau2d)*H_b;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 closure = aHitaub_bd';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 penalty = -aHitau*b_b;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 % Unknown boundary condition
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 otherwise
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 error('No such boundary condition: type = %s',type);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % type Struct that specifies the interface coupling.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 % Fields:
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 % -- tuning: penalty strength, defaults to 1.2
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 % -- interpolation: type of interpolation, default 'none'
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 % error('Not implemented')
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 defaultType.tuning = 1.0;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 defaultType.interpolation = 'none';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 default_struct('type', defaultType);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 switch type.interpolation
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 case {'none', ''}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 case {'op','OP'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 otherwise
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 error('Unknown type of interpolation: %s ', type.interpolation);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 tuning = type.tuning;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 dim = obj.dim;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 % u denotes the solution in the own domain
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 % v denotes the solution in the neighbour domain
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 u = obj;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 v = neighbour_scheme;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 % Boundary operators, u
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 e_u = u.getBoundaryOperator('e', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379 d_u = u.getBoundaryOperator('d', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 gamm_u = u.getBoundaryBorrowing(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 s_b_u = u.getBoundaryScaling(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 [th_H_u, ~, th_R_u] = u.getBoundaryBorrowing(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 m_u = u.getBoundaryNumber(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 % Coefficients, u
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 K_u = u.K;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 J_u = u.J;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 b_b_u = e_u'u.be_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 % Boundary operators, v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 e_v = v.getBoundaryOperator('e', neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 d_v = v.getBoundaryOperator('d', neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393 gamm_v = v.getBoundaryBorrowing(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 s_b_v = v.getBoundaryScaling(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 [th_H_v, ~, th_R_v] = v.getBoundaryBorrowing(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 m_v = v.getBoundaryNumber(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 % Coefficients, v
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 K_v = v.K;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 J_v = v.J;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 b_b_v = e_v'v.be_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 %--- Penalty strength tau -------------
1117 27019aca2f17 Fix bug in LaplCurveNewCorner that makes bc matrix non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1080 diff changeset	404 sigma_u = 0*b_b_u;
27019aca2f17 Fix bug in LaplCurveNewCorner that makes bc matrix non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1080 diff changeset	405 sigma_v = 0*b_b_v;
1055 b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 for i = 1:obj.dim
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 sigma_u = sigma_u + e_u'J_uK_u{i,m_u}K_u{i,m_u}e_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408 sigma_v = sigma_v + e_v'J_vK_v{i,m_v}K_v{i,m_v}e_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 sigma_u = sigma_u/s_b_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411 sigma_v = sigma_v/s_b_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 tau_R_u = 1/th_R_u*sigma_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 tau_R_v = 1/th_R_v*sigma_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 tau_H_u = 1/th_H_u*sigma_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 tau_H_u(1,1) = dim*tau_H_u(1,1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 tau_H_u(end,end) = dim*tau_H_u(end,end);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 tau_H_v = 1/th_H_v*sigma_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 tau_H_v(1,1) = dim*tau_H_v(1,1);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 tau_H_v(end,end) = dim*tau_H_v(end,end);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 tau = 1/4tuning(b_b_u(tau_R_u + tau_H_u) + b_b_v(tau_R_v + tau_H_v));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 %--------------------------------------
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 % Operators/coefficients that are only required from this side
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 Hi = u.Hi;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 H_b = u.getBoundaryQuadrature(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 a = u.a;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 closure = 1/2aHid_ub_b_uH_be_u' ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 -1/2aHie_uH_bb_b_ud_u' ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 -aHie_utauH_b*e_u';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436 penalty = -1/2aHid_ub_b_uH_be_v' ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 -1/2aHie_uH_bb_b_vd_v' ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438 +aHie_utauH_b*e_v';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 % TODO: Make this work for curvilinear grids
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 warning('LaplaceCurvilinear: Non-conforming interface assumes that b is constant');
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 % User can request special interpolation operators by specifying type.interpOpSet
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 interpOpSet = type.interpOpSet;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 tuning = type.tuning;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 % u denotes the solution in the own domain
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 % v denotes the solution in the neighbour domain
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456 e_u = obj.getBoundaryOperator('e', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 d_u = obj.getBoundaryOperator('d', boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 H_b_u = obj.getBoundaryQuadrature(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 I_u = obj.getBoundaryIndices(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 gamm_u = obj.getBoundaryBorrowing(boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 % Find the number of grid points along the interface
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 m_u = size(e_u, 2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 m_v = size(e_v, 2);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 Hi = obj.Hi;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 a = obj.a;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476 u = obj;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 v = neighbour_scheme;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 tau_u = -1./(4b1_u) -1./(4b2_u);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 tau_v = -1./(4b1_v) -1./(4b2_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 tau_u = tuning * spdiag(tau_u);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 tau_v = tuning * spdiag(tau_v);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489 beta_u = tau_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 % Build interpolation operators
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 Iu2v = intOps.Iu2v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494 Iv2u = intOps.Iv2u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496 closure = aHie_utau_uH_b_u*e_u' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 a1/2Hid_uH_b_u*e_u' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 -a1/2Hie_uH_b_u*d_u';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504 -a1/2Hie_uH_b_uIv2u.badd_v';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 % Returns the boundary operator op for the boundary specified by the string boundary.
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 % op -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 function o = getBoundaryOperator(obj, op, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 assertIsMember(op, {'e', 'd'})
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 assertIsMember(boundary, {'w', 'e', 's', 'n'})
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 o = obj.([op, '_', boundary]);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 % Returns square boundary quadrature matrix, of dimension
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 % corresponding to the number of boundary points
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 %
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 function H_b = getBoundaryQuadrature(obj, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 assertIsMember(boundary, {'w', 'e', 's', 'n'})
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 H_b = obj.(['H_', boundary]);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 % Returns square boundary quadrature scaling matrix, of dimension
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 % corresponding to the number of boundary points
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 %
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 function s_b = getBoundaryScaling(obj, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 assertIsMember(boundary, {'w', 'e', 's', 'n'})
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 s_b = obj.(['s_', boundary]);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 % Returns the coordinate number corresponding to the boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 %
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 function m = getBoundaryNumber(obj, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 assertIsMember(boundary, {'w', 'e', 's', 'n'})
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 switch boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 case {'w', 'e'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 m = 1;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 case {'s', 'n'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548 m = 2;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 % Returns the indices of the boundary points in the grid matrix
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 function I = getBoundaryIndices(obj, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556 switch boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557 case 'w'
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 I = ind(1,:);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559 case 'e'
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 I = ind(end,:);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 case 's'
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 I = ind(:,1)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 case 'n'
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564 I = ind(:,end)';
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565 otherwise
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566 error('No such boundary: boundary = %s',boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570 % Returns borrowing constant gamma
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	571 % boundary -- string
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	572 function [theta_H, theta_M, theta_R] = getBoundaryBorrowing(obj, boundary)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	573 switch boundary
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	574 case {'w','e'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	575 theta_H = obj.theta_H_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	576 theta_M = obj.theta_M_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	577 theta_R = obj.theta_R_u;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	578 case {'s','n'}
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	579 theta_H = obj.theta_H_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	580 theta_M = obj.theta_M_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	581 theta_R = obj.theta_R_v;
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	582 otherwise
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	583 error('No such boundary: boundary = %s',boundary);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	584 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	585 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	586
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	587 function N = size(obj)
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	588 N = prod(obj.m);
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	589 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	590 end
b828e589d540 Copy-paste LaplCurviNewCorner from laplace branch. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	591 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1339:bcdb14b05d03 feature/D2_boundary_opt