sbplib: +scheme/LaplaceCurvilinearNew.m annotate

annotate +scheme/LaplaceCurvilinearNew.m @ 1302:a0d615bde7f8 feature/poroelastic

Add the hollow option to the anisotropic diffops

author	Martin Almquist <malmquist@stanford.edu>
date	Fri, 10 Jul 2020 20:24:23 -0700
parents	5c5815af4b7a
children

rev	line source
1212 5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearNew < scheme.Scheme
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12 weight % Parameter in front of time derivative (e.g. u_tt in wave equation) here: 1/a.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 % Inner products and operators for physical coordinates
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 D % Laplace operator
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 H, Hi % Inner product
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 e_w, e_e, e_s, e_n
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 H_w, H_e, H_s, H_n % Boundary inner products
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 Dx, Dy % Physical derivatives
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 M % Gradient inner product
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 % Metric coefficients
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 J, Ji
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 a11, a12, a22
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 K
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_u
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 x_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_u
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 y_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 s_w, s_e, s_s, s_n % Boundary integral scale factors
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 % Inner product and operators for logical coordinates
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 H_u, H_v % Norms in the x and y directions
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hi_u, Hi_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 Hiu, Hiv
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_w, dv_w
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_e, dv_e
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_s, dv_s
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42 du_n, dv_n
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 % Borrowing constants
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_M_u, theta_M_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_R_u, theta_R_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47 theta_H_u, theta_H_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 % Temporary, only used for nonconforming interfaces but should be removed.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 lambda
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 methods
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 % Implements adiv(bgrad(u)) as a SBP scheme
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 function obj = LaplaceCurvilinearNew(g, order, a, b, opSet)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 default_arg('opSet',@sbp.D2Variable);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 default_arg('a', 1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('b', @(x,y) 0*x + 1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62 % assert(isa(g, 'grid.Curvilinear'))
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 if isa(a, 'function_handle')
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 a = grid.evalOn(g, a);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 % If a is scalar
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 if length(a) == 1
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 a = a*ones(g.N(), 1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 a = spdiag(a);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 if isa(b, 'function_handle')
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 b = grid.evalOn(g, b);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 % If b is scalar
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 if length(b) == 1
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 % b = b*speye(g.N(), g.N());
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 b = b*ones(g.N(), 1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 b = spdiag(b);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 dim = 2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 m = g.size();
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 m_u = m(1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 m_v = m(2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 m_tot = g.N();
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 % 1D operators
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 ops_u = opSet(m_u, {0, 1}, order);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 ops_v = opSet(m_v, {0, 1}, order);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 h_u = ops_u.h;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 h_v = ops_v.h;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 I_u = speye(m_u);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 I_v = speye(m_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 D1_u = ops_u.D1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 D2_u = ops_u.D2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 H_u = ops_u.H;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 Hi_u = ops_u.HI;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 e_l_u = ops_u.e_l;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 e_r_u = ops_u.e_r;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 d1_l_u = ops_u.d1_l;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 d1_r_u = ops_u.d1_r;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 D1_v = ops_v.D1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 D2_v = ops_v.D2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 H_v = ops_v.H;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 Hi_v = ops_v.HI;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 e_l_v = ops_v.e_l;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 e_r_v = ops_v.e_r;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 d1_l_v = ops_v.d1_l;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 d1_r_v = ops_v.d1_r;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 % Logical operators
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 Du = kr(D1_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 Dv = kr(I_u,D1_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 obj.Hu = kr(H_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 obj.Hv = kr(I_u,H_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 obj.Hiu = kr(Hi_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 obj.Hiv = kr(I_u,Hi_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 e_w = kr(e_l_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 e_e = kr(e_r_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 e_s = kr(I_u,e_l_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 e_n = kr(I_u,e_r_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 obj.du_w = kr(d1_l_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 obj.dv_w = (e_w'*Dv)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 obj.du_e = kr(d1_r_u,I_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 obj.dv_e = (e_e'*Dv)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 obj.du_s = (e_s'*Du)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 obj.dv_s = kr(I_u,d1_l_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 obj.du_n = (e_n'*Du)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 obj.dv_n = kr(I_u,d1_r_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 % Metric coefficients
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 coords = g.points();
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 x = coords(:,1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 y = coords(:,2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 x_u = Du*x;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 x_v = Dv*x;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 y_u = Du*y;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 y_v = Dv*y;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 J = x_u.y_v - x_v.y_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 a11 = 1./J .* (x_v.^2 + y_v.^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 a12 = -1./J .* (x_u.x_v + y_u.y_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 a22 = 1./J .* (x_u.^2 + y_u.^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 K = cell(dim, dim);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 K{1,1} = spdiag(y_v./J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 K{1,2} = spdiag(-y_u./J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 K{2,1} = spdiag(-x_v./J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 K{2,2} = spdiag(x_u./J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 obj.K = K;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 obj.x_u = x_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 obj.x_v = x_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 obj.y_u = y_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 obj.y_v = y_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 % Assemble full operators
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 L_12 = spdiag(a12);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 Duv = DubL_12*Dv;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 Dvu = DvbL_12*Du;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 Duu = sparse(m_tot);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 Dvv = sparse(m_tot);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 ind = grid.funcToMatrix(g, 1:m_tot);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 for i = 1:m_v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 b_a11 = b*a11;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 D = D2_u(b_a11(ind(:,i)));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 p = ind(:,i);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 Duu(p,p) = D;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 for i = 1:m_u
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 b_a22 = b*a22;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 D = D2_v(b_a22(ind(i,:)));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 p = ind(i,:);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 Dvv(p,p) = D;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 % Physical operators
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 obj.J = spdiag(J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 obj.Ji = spdiag(1./J);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 obj.H = obj.J*kr(H_u,H_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 obj.e_w = e_w;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 obj.e_e = e_e;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 obj.e_s = e_s;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 obj.e_n = e_n;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 %% normal derivatives
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 I_w = ind(1,:);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 I_e = ind(end,:);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 I_s = ind(:,1);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 I_n = ind(:,end);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 a11_w = spdiag(a11(I_w));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 a12_w = spdiag(a12(I_w));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 a11_e = spdiag(a11(I_e));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 a12_e = spdiag(a12(I_e));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 a22_s = spdiag(a22(I_s));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 a12_s = spdiag(a12(I_s));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 a22_n = spdiag(a22(I_n));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 a12_n = spdiag(a12(I_n));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 %% Boundary inner products
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.H_w = H_v*spdiag(s_w);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 obj.H_e = H_v*spdiag(s_e);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 obj.H_s = H_u*spdiag(s_s);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.H_n = H_u*spdiag(s_n);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 % Misc.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 obj.m = m;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 obj.h = [h_u h_v];
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 obj.order = order;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 obj.grid = g;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245 obj.dim = dim;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 obj.a = a;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 obj.weight = inv(a);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.b = b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.a11 = a11;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 obj.a12 = a12;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 obj.a22 = a22;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 obj.s_w = spdiag(s_w);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 obj.s_e = spdiag(s_e);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 obj.s_s = spdiag(s_s);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 obj.s_n = spdiag(s_n);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 obj.theta_M_u = h_u*ops_u.borrowing.M.d1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 obj.theta_M_v = h_v*ops_v.borrowing.M.d1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_D;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_D;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 obj.theta_H_u = h_u*ops_u.borrowing.H11;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 obj.theta_H_v = h_v*ops_v.borrowing.H11;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 % Temporary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 obj.lambda = lambda;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 % Closure functions return the opertors applied to the own doamin to close the boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 % type is a string specifying the type of boundary condition if there are several.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 % data is a function returning the data that should be applied at the boundary.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 % neighbour_scheme is an instance of Scheme that should be interfaced to.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 % neighbour_boundary is a string specifying which boundary to interface to.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 default_arg('type','neumann');
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 default_arg('parameter', []);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 e = obj.getBoundaryOperator('e', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 d = obj.getBoundaryOperator('d', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 H_b = obj.getBoundaryQuadrature(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 s_b = obj.getBoundaryScaling(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 [th_H, ~, th_R] = obj.getBoundaryBorrowing(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 m = obj.getBoundaryNumber(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 K = obj.K;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 J = obj.J;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 Hi = obj.Hi;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 a = obj.a;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 b_b = e'obj.be;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 switch type
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 % Dirichlet boundary condition
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 case {'D','d','dirichlet'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 tuning = 1.0;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 sigma = 0*b_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 for i = 1:obj.dim
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 sigma = sigma + e'JK{i,m}K{i,m}e;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 sigma = sigma/s_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 tau = tuning(1/th_R + obj.dim/th_H)sigma;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 closure = aHidb_bH_b*e' ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 -aHietaub_bH_be';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 penalty = -aHidb_bH_b ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 +aHietaub_b*H_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 % Neumann boundary condition. Note that the penalty is for du/dn and not b*du/dn.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 case {'N','n','neumann'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 tau1 = -1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 tau2 = 0;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 tau = (tau1e + tau2d)*H_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 closure = aHitaub_bd';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 penalty = -aHitau*b_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 % Unknown, boundary condition
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 otherwise
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 error('No such boundary condition: type = %s',type);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 % type Struct that specifies the interface coupling.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 % Fields:
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 % -- tuning: penalty strength, defaults to 1.2
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 % -- interpolation: type of interpolation, default 'none'
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 defaultType.coupling = 'sat';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 defaultType.tuning = 1.0;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 defaultType.interpolation = 'none';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 default_struct('type', defaultType);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 switch type.coupling
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 case {'cg', 'CG'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 [closure, penalty] = interfaceCG(obj,boundary,neighbour_scheme,neighbour_boundary,type);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 case {'sat', 'SAT'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 switch type.interpolation
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 case {'none', ''}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 case {'op','OP'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 otherwise
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 error('Unknown type of interpolation: %s ', type.interpolation);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 otherwise
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 error('Unknown type of coupling: %s ', type.coupling);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 tuning = type.tuning;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 dim = obj.dim;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 % u denotes the solution in the own domain
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 % v denotes the solution in the neighbour domain
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365 u = obj;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 v = neighbour_scheme;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 % Boundary operators, u
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369 e_u = u.getBoundaryOperator('e', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 d_u = u.getBoundaryOperator('d', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 s_b_u = u.getBoundaryScaling(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 [th_H_u, ~, th_R_u] = u.getBoundaryBorrowing(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 m_u = u.getBoundaryNumber(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 % Coefficients, u
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 K_u = u.K;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 J_u = u.J;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 b_b_u = e_u'u.be_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 % Boundary operators, v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 e_v = v.getBoundaryOperator('e', neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 d_v = v.getBoundaryOperator('d', neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 s_b_v = v.getBoundaryScaling(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 [th_H_v, ~, th_R_v] = v.getBoundaryBorrowing(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 m_v = v.getBoundaryNumber(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 % BUGFIX?!?!?
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) \|\| (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s'))
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 e_v = fliplr(e_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 d_v = fliplr(d_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 s_b_v = rot90(s_b_v,2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 % Coefficients, v
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 K_v = v.K;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 J_v = v.J;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397 b_b_v = e_v'v.be_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 %--- Penalty strength tau -------------
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400 sigma_u = 0*b_b_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 sigma_v = 0*b_b_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 for i = 1:obj.dim
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403 sigma_u = sigma_u + e_u'J_uK_u{i,m_u}K_u{i,m_u}e_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 sigma_v = sigma_v + e_v'J_vK_v{i,m_v}K_v{i,m_v}e_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 sigma_u = sigma_u/s_b_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 sigma_v = sigma_v/s_b_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 tau_R_u = 1/th_R_u*sigma_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 tau_R_v = 1/th_R_v*sigma_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 tau_H_u = dim1/th_H_usigma_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 tau_H_v = dim1/th_H_vsigma_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415 tau = 1/4tuning(b_b_u(tau_R_u + tau_H_u) + b_b_v(tau_R_v + tau_H_v));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 %--------------------------------------
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 % Operators/coefficients that are only required from this side
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 Hi = u.Hi;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420 H_b = u.getBoundaryQuadrature(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 a = u.a;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 closure = 1/2aHid_ub_b_uH_be_u' ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 -1/2aHie_uH_bb_b_ud_u' ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 -aHie_utauH_b*e_u';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 penalty = -1/2aHid_ub_b_uH_be_v' ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 -1/2aHie_uH_bb_b_vd_v' ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 +aHie_utauH_b*e_v';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 function [closure, penalty] = interfaceCG(obj,boundary,neighbour_scheme,neighbour_boundary,type)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 % There is no penalty, only a closure. And the closure is the same as for Neumann BC
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435 e = obj.getBoundaryOperator('e', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436 d = obj.getBoundaryOperator('d', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 H_b = obj.getBoundaryQuadrature(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 Hi = obj.Hi;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442 a = obj.a;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 b_b = e'obj.be;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 tau1 = -1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 tau2 = 0;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 tau = (tau1e + tau2d)*H_b;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 closure = aHitaub_bd';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 % Zero penalty of correct dimensions
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 penalty = 0ee_v';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 % TODO: Make this work for curvilinear grids
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 warning('LaplaceCurvilinear: Non-conforming interface assumes that b is constant');
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462 % User can request special interpolation operators by specifying type.interpOpSet
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 interpOpSet = type.interpOpSet;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 tuning = type.tuning;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 % u denotes the solution in the own domain
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 % v denotes the solution in the neighbour domain
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 e_u = obj.getBoundaryOperator('e', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 d_u = obj.getBoundaryOperator('d', boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472 H_b_u = obj.getBoundaryQuadrature(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 I_u = obj.getBoundaryIndices(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 [~, gamm_u] = obj.getBoundaryBorrowing(boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480 [~, gamm_v] = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 % Find the number of grid points along the interface
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 m_u = size(e_u, 2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 m_v = size(e_v, 2);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 Hi = obj.Hi;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 a = obj.a;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490 u = obj;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 v = neighbour_scheme;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 tau_u = -1./(4b1_u) -1./(4b2_u);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 tau_v = -1./(4b1_v) -1./(4b2_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 tau_u = tuning * spdiag(tau_u);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 tau_v = tuning * spdiag(tau_v);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 beta_u = tau_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505 % Build interpolation operators
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 Iu2v = intOps.Iu2v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 Iv2u = intOps.Iv2u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 closure = aHie_utau_uH_b_u*e_u' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 a1/2Hid_uH_b_u*e_u' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 -a1/2Hie_uH_b_u*d_u';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 -a1/2Hie_uH_b_uIv2u.badd_v';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 % Returns the boundary operator op for the boundary specified by the string boundary.
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 % op -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 function o = getBoundaryOperator(obj, op, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 assertIsMember(op, {'e', 'd'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 o = obj.([op, '_', boundary]);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 % Returns square boundary quadrature matrix, of dimension
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 % corresponding to the number of boundary points
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 %
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 function H_b = getBoundaryQuadrature(obj, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 H_b = obj.(['H_', boundary]);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 % Returns square boundary quadrature scaling matrix, of dimension
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 % corresponding to the number of boundary points
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 %
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 function s_b = getBoundaryScaling(obj, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549 s_b = obj.(['s_', boundary]);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 % Returns the coordinate number corresponding to the boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553 %
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 function m = getBoundaryNumber(obj, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 switch boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559 case {'w', 'e'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 m = 1;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 case {'s', 'n'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 m = 2;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566 % Returns the indices of the boundary points in the grid matrix
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 function I = getBoundaryIndices(obj, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	571 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	572 switch boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	573 case 'w'
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	574 I = ind(1,:);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	575 case 'e'
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	576 I = ind(end,:);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	577 case 's'
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	578 I = ind(:,1)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	579 case 'n'
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	580 I = ind(:,end)';
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	581 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	582 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	583
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	584 % Returns borrowing constant gamma
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	585 % boundary -- string
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	586 function [theta_H, theta_M, theta_R] = getBoundaryBorrowing(obj, boundary)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	587 assertIsMember(boundary, {'w', 'e', 's', 'n'})
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	588
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	589 switch boundary
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	590 case {'w','e'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	591 theta_H = obj.theta_H_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	592 theta_M = obj.theta_M_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	593 theta_R = obj.theta_R_u;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	594 case {'s','n'}
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	595 theta_H = obj.theta_H_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	596 theta_M = obj.theta_M_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	597 theta_R = obj.theta_R_v;
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	598 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	599 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	600
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	601 function N = size(obj)
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	602 N = prod(obj.m);
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	603 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	604 end
5c5815af4b7a Add new implementation of Laplace curvilinear Martin Almquist <malmquist@stanford.edu> parents: diff changeset	605 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearNew.m @ 1302:a0d615bde7f8 feature/poroelastic