sbplib: +scheme/LaplaceCurvilinearNew.m annotate

annotate +scheme/LaplaceCurvilinearNew.m @ 1065:c2bd7f15da48 feature/laplace_curvilinear_test

Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable.

author	Martin Almquist <malmquist@stanford.edu>
date	Thu, 17 Jan 2019 18:57:54 -0800
parents	1341c6cea9c1
children	7a55a72729e6

rev	line source
1063 e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearNew < scheme.Scheme
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 % Inner products and operators for physical coordinates
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 D % Laplace operator
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 H, Hi % Inner product
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 e_w, e_e, e_s, e_n
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 H_w, H_e, H_s, H_n % Boundary inner products
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 Dx, Dy % Physical derivatives
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 M % Gradient inner product
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Metric coefficients
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 J, Ji
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 a11, a12, a22
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 K
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 x_u
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 y_u
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Inner product and operators for logical coordinates
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H_u, H_v % Norms in the x and y directions
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 Hi_u, Hi_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hiu, Hiv
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_w, dv_w
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_e, dv_e
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_s, dv_s
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_n, dv_n
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_M_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_R_u, theta_R_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_H_u, theta_H_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 methods
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51 % Implements adiv(bgrad(u)) as a SBP scheme
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 function obj = LaplaceCurvilinearNew(g, order, a, b, opSet)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 default_arg('opSet',@sbp.D2Variable);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 default_arg('a', 1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 default_arg('b', 1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 if b ~=1
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 error('Not implemented yet')
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 % assert(isa(g, 'grid.Curvilinear'))
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 if isa(a, 'function_handle')
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 a = grid.evalOn(g, a);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66 a = spdiag(a);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 dim = 2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 m = g.size();
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 m_u = m(1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 m_v = m(2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 m_tot = g.N();
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 h = g.scaling();
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 h_u = h(1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 h_v = h(2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 % 1D operators
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 ops_u = opSet(m_u, {0, 1}, order);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 ops_v = opSet(m_v, {0, 1}, order);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 I_u = speye(m_u);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 I_v = speye(m_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 D1_u = ops_u.D1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 D2_u = ops_u.D2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 H_u = ops_u.H;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90 Hi_u = ops_u.HI;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 e_l_u = ops_u.e_l;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 e_r_u = ops_u.e_r;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 d1_l_u = ops_u.d1_l;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 d1_r_u = ops_u.d1_r;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 D1_v = ops_v.D1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 D2_v = ops_v.D2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 H_v = ops_v.H;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 Hi_v = ops_v.HI;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 e_l_v = ops_v.e_l;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 e_r_v = ops_v.e_r;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 d1_l_v = ops_v.d1_l;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 d1_r_v = ops_v.d1_r;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 % Logical operators
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 Du = kr(D1_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 Dv = kr(I_u,D1_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 obj.Hu = kr(H_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 obj.Hv = kr(I_u,H_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 obj.Hiu = kr(Hi_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 obj.Hiv = kr(I_u,Hi_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 e_w = kr(e_l_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 e_e = kr(e_r_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 e_s = kr(I_u,e_l_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 e_n = kr(I_u,e_r_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 obj.du_w = kr(d1_l_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 obj.dv_w = (e_w'*Dv)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 obj.du_e = kr(d1_r_u,I_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 obj.dv_e = (e_e'*Dv)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 obj.du_s = (e_s'*Du)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 obj.dv_s = kr(I_u,d1_l_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 obj.du_n = (e_n'*Du)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 obj.dv_n = kr(I_u,d1_r_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 % Metric coefficients
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 coords = g.points();
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 x = coords(:,1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 y = coords(:,2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 x_u = Du*x;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 x_v = Dv*x;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 y_u = Du*y;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 y_v = Dv*y;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 J = x_u.y_v - x_v.y_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 a11 = 1./J .* (x_v.^2 + y_v.^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 a12 = -1./J .* (x_u.x_v + y_u.y_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 a22 = 1./J .* (x_u.^2 + y_u.^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 % lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 K = cell(dim, dim);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 K{1,1} = spdiag(y_v./J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 K{1,2} = spdiag(-y_u./J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 K{2,1} = spdiag(-x_v./J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 K{2,2} = spdiag(x_u./J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 obj.K = K;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 obj.x_u = x_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 obj.x_v = x_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 obj.y_u = y_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 obj.y_v = y_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 % Assemble full operators
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 L_12 = spdiag(a12);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 Duv = DuL_12Dv;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 Dvu = DvL_12Du;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 Duu = sparse(m_tot);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 Dvv = sparse(m_tot);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 ind = grid.funcToMatrix(g, 1:m_tot);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 for i = 1:m_v
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 D = D2_u(a11(ind(:,i)));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 p = ind(:,i);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 Duu(p,p) = D;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 for i = 1:m_u
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 D = D2_v(a22(ind(i,:)));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 p = ind(i,:);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 Dvv(p,p) = D;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 % Physical operators
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 obj.J = spdiag(J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 obj.Ji = spdiag(1./J);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 obj.H = obj.J*kr(H_u,H_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 obj.e_w = e_w;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 obj.e_e = e_e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 obj.e_s = e_s;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 obj.e_n = e_n;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 %% normal derivatives
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 I_w = ind(1,:);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 I_e = ind(end,:);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 I_s = ind(:,1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 I_n = ind(:,end);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 a11_w = spdiag(a11(I_w));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 a12_w = spdiag(a12(I_w));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 a11_e = spdiag(a11(I_e));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 a12_e = spdiag(a12(I_e));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 a22_s = spdiag(a22(I_s));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 a12_s = spdiag(a12(I_s));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 a22_n = spdiag(a22(I_n));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 a12_n = spdiag(a12(I_n));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219 %% Boundary inner products
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 obj.H_w = H_v*spdiag(s_w);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 obj.H_e = H_v*spdiag(s_e);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 obj.H_s = H_u*spdiag(s_s);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 obj.H_n = H_u*spdiag(s_n);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 % Misc.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 obj.m = m;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 obj.h = [h_u h_v];
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 obj.order = order;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 obj.grid = g;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 obj.dim = dim;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.a = a;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.b = b;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.a11 = a11;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.a12 = a12;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 obj.a22 = a22;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 % obj.lambda = lambda;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.s_w = spdiag(s_w);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 obj.s_e = spdiag(s_e);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 obj.s_s = spdiag(s_s);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 obj.s_n = spdiag(s_n);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 obj.theta_M_u = h_u*ops_u.borrowing.M.d1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 obj.theta_M_v = h_v*ops_v.borrowing.M.d1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_D;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_D;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.theta_H_u = h_u*ops_u.borrowing.H11;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.theta_H_v = h_v*ops_v.borrowing.H11;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 % Closure functions return the opertors applied to the own doamin to close the boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 % type is a string specifying the type of boundary condition if there are several.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 % data is a function returning the data that should be applied at the boundary.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 % neighbour_scheme is an instance of Scheme that should be interfaced to.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 % neighbour_boundary is a string specifying which boundary to interface to.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 default_arg('type','neumann');
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 default_arg('parameter', []);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 H_b = obj.getBoundaryQuadrature(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 s_b = obj.getBoundaryScaling(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 [th_H, th_M, th_R] = obj.getBoundaryBorrowing(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 m = obj.getBoundaryNumber(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 K = obj.K;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272 J = obj.J;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	273 Hi = obj.Hi;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	274 a_b = e'obj.ae;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 switch type
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	277 % Dirichlet boundary condition
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 case {'D','d','dirichlet'}
1064 1341c6cea9c1 Set tuning to 1.0 in both old and new Dirichlet. Martin Almquist <malmquist@stanford.edu> parents: 1063 diff changeset	279 tuning = 1.0;
1063 e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 sigma = 0;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 for i = 1:obj.dim
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 sigma = sigma + e'JK{i,m}K{i,m}e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 sigma = sigma/s_b;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 tau = tuning(1/th_R + obj.dim/th_H)sigma;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 closure = Hida_bH_be' ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 -HietauH_be';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 penalty = -Hida_b*H_b ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 +Hietau*H_b;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 % Neumann boundary condition
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 case {'N','n','neumann'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 tau1 = -1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298 tau2 = 0;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 tau = (tau1e + tau2d)*H_b;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 closure = obj.aHitau*d';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302 penalty = -obj.aHitau;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305 % Unknown, boundary condition
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 error('No such boundary condition: type = %s',type);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 % type Struct that specifies the interface coupling.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 % Fields:
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 % -- tuning: penalty strength, defaults to 1.2
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 % -- interpolation: type of interpolation, default 'none'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 error('Not implemented')
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 defaultType.tuning = 1.2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 defaultType.interpolation = 'none';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 default_struct('type', defaultType);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 switch type.interpolation
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 case {'none', ''}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 case {'op','OP'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 error('Unknown type of interpolation: %s ', type.interpolation);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 tuning = type.tuning;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 % u denotes the solution in the own domain
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 % v denotes the solution in the neighbour domain
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 H_b_u = obj.getBoundaryQuadrature(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 I_u = obj.getBoundaryIndices(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 gamm_u = obj.getBoundaryBorrowing(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 u = obj;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 v = neighbour_scheme;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 tau1 = -1./(4b1_u) -1./(4b1_v) -1./(4b2_u) -1./(4b2_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 tau1 = tuning * spdiag(tau1);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 tau2 = 1/2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360 sig1 = -1/2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	361 sig2 = 0;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 tau = (e_utau1 + tau2d_u)*H_b_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 sig = (sig1e_u + sig2d_u)*H_b_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	365
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 closure = obj.aobj.Hi( taue_u' + sigd_u');
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 penalty = obj.aobj.Hi(-taue_v' + sigd_v');
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	369
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	372 % TODO: Make this work for curvilinear grids
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	373 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 % User can request special interpolation operators by specifying type.interpOpSet
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	376 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	377 interpOpSet = type.interpOpSet;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 tuning = type.tuning;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	379
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 % u denotes the solution in the own domain
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382 % v denotes the solution in the neighbour domain
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	384 H_b_u = obj.getBoundaryQuadrature(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	385 I_u = obj.getBoundaryIndices(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 gamm_u = obj.getBoundaryBorrowing(boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	391 gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	392
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	394 % Find the number of grid points along the interface
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	395 m_u = size(e_u, 2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 m_v = size(e_v, 2);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	397
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	398 Hi = obj.Hi;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 a = obj.a;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	400
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401 u = obj;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 v = neighbour_scheme;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	403
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	407 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	408
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 tau_u = -1./(4b1_u) -1./(4b2_u);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 tau_v = -1./(4b1_v) -1./(4b2_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	411
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 tau_u = tuning * spdiag(tau_u);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	413 tau_v = tuning * spdiag(tau_v);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 beta_u = tau_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	415
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	416 % Build interpolation operators
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	418 Iu2v = intOps.Iu2v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 Iv2u = intOps.Iv2u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 closure = aHie_utau_uH_b_u*e_u' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 a1/2Hid_uH_b_u*e_u' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 -a1/2Hie_uH_b_u*d_u';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 -a1/2Hie_uH_b_uIv2u.badd_v';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 % Returns the boundary operator op for the boundary specified by the string boundary.
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 % op -- string or a cell array of strings
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436 function varargout = getBoundaryOperator(obj, op, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438 if ~iscell(op)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 op = {op};
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442 for i = 1:numel(op)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 switch op{i}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 case 'w'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 e = obj.e_w;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 e = obj.e_e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 case 's'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 e = obj.e_s;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 case 'n'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 e = obj.e_n;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 varargout{i} = e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 case 'd'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 case 'w'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462 d = obj.d_w;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 d = obj.d_e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 case 's'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 d = obj.d_s;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467 case 'n'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 d = obj.d_n;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472 varargout{i} = d;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 % Returns square boundary quadrature matrix, of dimension
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 % corresponding to the number of boundary points
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 %
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 function H_b = getBoundaryQuadrature(obj, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484 case 'w'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 H_b = obj.H_w;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 H_b = obj.H_e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 case 's'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489 H_b = obj.H_s;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490 case 'n'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 H_b = obj.H_n;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 % Returns square boundary quadrature scaling matrix, of dimension
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 % corresponding to the number of boundary points
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 %
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 function s_b = getBoundaryScaling(obj, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504 case 'w'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505 s_b = obj.s_w;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 s_b = obj.s_e;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 case 's'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 s_b = obj.s_s;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 case 'n'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 s_b = obj.s_n;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 % Returns the coordinate number corresponding to the boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 %
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 function m = getBoundaryNumber(obj, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 case {'w', 'e'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 m = 1;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 case {'s', 'n'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 m = 2;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 % Returns the indices of the boundary points in the grid matrix
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 function I = getBoundaryIndices(obj, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 case 'w'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 I = ind(1,:);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 case 'e'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 I = ind(end,:);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 case 's'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 I = ind(:,1)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 case 'n'
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 I = ind(:,end)';
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 % Returns borrowing constant gamma
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551 % boundary -- string
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 function [theta_H, theta_M, theta_R] = getBoundaryBorrowing(obj, boundary)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553 switch boundary
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 case {'w','e'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 theta_H = obj.theta_H_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556 theta_M = obj.theta_M_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557 theta_R = obj.theta_R_u;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 case {'s','n'}
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559 theta_H = obj.theta_H_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 theta_M = obj.theta_M_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 theta_R = obj.theta_R_v;
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 otherwise
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 error('No such boundary: boundary = %s',boundary);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567 function N = size(obj)
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 N = prod(obj.m);
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570 end
e913cdb34dcb Add LaplaceCurvilinearNew and implement Dirichlet BC using new borrowing. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	571 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearNew.m @ 1065:c2bd7f15da48 feature/laplace_curvilinear_test