sbplib: +scheme/LaplaceCurvilinearNewCorner.m annotate

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1067:9a858436f8fa feature/laplace_curvilinear_test

Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty.

author	Martin Almquist <malmquist@stanford.edu>
date	Tue, 22 Jan 2019 18:17:01 -0800
parents	d64062bed5fb
children	e0ecce90f8cf

rev	line source
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearNewCorner < scheme.Scheme
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 % Inner products and operators for physical coordinates
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 D % Laplace operator
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 H, Hi % Inner product
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 e_w, e_e, e_s, e_n
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 H_w, H_e, H_s, H_n % Boundary inner products
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 Dx, Dy % Physical derivatives
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 M % Gradient inner product
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Metric coefficients
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 J, Ji
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 a11, a12, a22
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 K
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 x_u
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 y_u
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Inner product and operators for logical coordinates
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H_u, H_v % Norms in the x and y directions
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 Hi_u, Hi_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hiu, Hiv
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_w, dv_w
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_e, dv_e
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_s, dv_s
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_n, dv_n
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_M_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_R_u, theta_R_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_H_u, theta_H_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	48 % Temporary
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	49 lambda
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	50 gamm_u, gamm_v
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	51
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 % Implements adiv(bgrad(u)) as a SBP scheme
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 function obj = LaplaceCurvilinearNewCorner(g, order, a, b, opSet)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 default_arg('opSet',@sbp.D2Variable);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('a', 1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 default_arg('b', 1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	62
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	63 if b ~=1
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	64 error('Not implemented yet')
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	65 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	66
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 % assert(isa(g, 'grid.Curvilinear'))
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	68 if isa(a, 'function_handle')
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	69 a = grid.evalOn(g, a);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	70 a = spdiag(a);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 dim = 2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 m = g.size();
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 m_u = m(1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76 m_v = m(2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 m_tot = g.N();
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 h = g.scaling();
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 h_u = h(1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81 h_v = h(2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 % 1D operators
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85 ops_u = opSet(m_u, {0, 1}, order);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86 ops_v = opSet(m_v, {0, 1}, order);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 I_u = speye(m_u);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 I_v = speye(m_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 D1_u = ops_u.D1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 D2_u = ops_u.D2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93 H_u = ops_u.H;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 Hi_u = ops_u.HI;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 e_l_u = ops_u.e_l;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 e_r_u = ops_u.e_r;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 d1_l_u = ops_u.d1_l;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 d1_r_u = ops_u.d1_r;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 D1_v = ops_v.D1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 D2_v = ops_v.D2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102 H_v = ops_v.H;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 Hi_v = ops_v.HI;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 e_l_v = ops_v.e_l;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 e_r_v = ops_v.e_r;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 d1_l_v = ops_v.d1_l;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 d1_r_v = ops_v.d1_r;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 % Logical operators
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111 Du = kr(D1_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112 Dv = kr(I_u,D1_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 obj.Hu = kr(H_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 obj.Hv = kr(I_u,H_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 obj.Hiu = kr(Hi_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 obj.Hiv = kr(I_u,Hi_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 e_w = kr(e_l_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 e_e = kr(e_r_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120 e_s = kr(I_u,e_l_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 e_n = kr(I_u,e_r_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 obj.du_w = kr(d1_l_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 obj.dv_w = (e_w'*Dv)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 obj.du_e = kr(d1_r_u,I_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 obj.dv_e = (e_e'*Dv)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 obj.du_s = (e_s'*Du)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 obj.dv_s = kr(I_u,d1_l_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 obj.du_n = (e_n'*Du)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 obj.dv_n = kr(I_u,d1_r_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 % Metric coefficients
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133 coords = g.points();
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134 x = coords(:,1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 y = coords(:,2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 x_u = Du*x;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 x_v = Dv*x;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139 y_u = Du*y;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 y_v = Dv*y;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 J = x_u.y_v - x_v.y_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 a11 = 1./J .* (x_v.^2 + y_v.^2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144 a12 = -1./J .* (x_u.x_v + y_u.y_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 a22 = 1./J .* (x_u.^2 + y_u.^2);
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	146 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 K = cell(dim, dim);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 K{1,1} = spdiag(y_v./J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150 K{1,2} = spdiag(-y_u./J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 K{2,1} = spdiag(-x_v./J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 K{2,2} = spdiag(x_u./J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 obj.K = K;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155 obj.x_u = x_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156 obj.x_v = x_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 obj.y_u = y_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 obj.y_v = y_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 % Assemble full operators
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161 L_12 = spdiag(a12);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 Duv = DuL_12Dv;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 Dvu = DvL_12Du;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165 Duu = sparse(m_tot);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 Dvv = sparse(m_tot);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 ind = grid.funcToMatrix(g, 1:m_tot);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 for i = 1:m_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 D = D2_u(a11(ind(:,i)));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171 p = ind(:,i);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 Duu(p,p) = D;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 for i = 1:m_u
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 D = D2_v(a22(ind(i,:)));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177 p = ind(i,:);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178 Dvv(p,p) = D;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182 % Physical operators
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 obj.J = spdiag(J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 obj.Ji = spdiag(1./J);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 obj.H = obj.J*kr(H_u,H_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 obj.e_w = e_w;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191 obj.e_e = e_e;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 obj.e_s = e_s;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 obj.e_n = e_n;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 %% normal derivatives
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 I_w = ind(1,:);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197 I_e = ind(end,:);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 I_s = ind(:,1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 I_n = ind(:,end);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 a11_w = spdiag(a11(I_w));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 a12_w = spdiag(a12(I_w));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 a11_e = spdiag(a11(I_e));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 a12_e = spdiag(a12(I_e));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 a22_s = spdiag(a22(I_s));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206 a12_s = spdiag(a12(I_s));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 a22_n = spdiag(a22(I_n));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 a12_n = spdiag(a12(I_n));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 %% Boundary inner products
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 obj.H_w = H_v*spdiag(s_w);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225 obj.H_e = H_v*spdiag(s_e);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 obj.H_s = H_u*spdiag(s_s);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 obj.H_n = H_u*spdiag(s_n);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 % Misc.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 obj.m = m;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231 obj.h = [h_u h_v];
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.order = order;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.grid = g;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.dim = dim;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 obj.a = a;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 obj.b = b;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238 obj.a11 = a11;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 obj.a12 = a12;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 obj.a22 = a22;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 obj.s_w = spdiag(s_w);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	242 obj.s_e = spdiag(s_e);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	243 obj.s_s = spdiag(s_s);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 obj.s_n = spdiag(s_n);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246 obj.theta_M_u = h_u*ops_u.borrowing.M.d1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 obj.theta_M_v = h_v*ops_v.borrowing.M.d1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_D;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_D;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 obj.theta_H_u = h_u*ops_u.borrowing.H11;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 obj.theta_H_v = h_v*ops_v.borrowing.H11;
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	254
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	255 % Temporary
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	256 obj.lambda = lambda;
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	257 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	258 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	262 % Closure functions return the opertors applied to the own doamin to close the boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	263 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 % type is a string specifying the type of boundary condition if there are several.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	266 % data is a function returning the data that should be applied at the boundary.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 % neighbour_scheme is an instance of Scheme that should be interfaced to.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	268 % neighbour_boundary is a string specifying which boundary to interface to.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	269 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	270 default_arg('type','neumann');
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	271 default_arg('parameter', []);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	272
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	273 e = obj.getBoundaryOperator('e', boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	274 d = obj.getBoundaryOperator('d', boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	275 H_b = obj.getBoundaryQuadrature(boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 s_b = obj.getBoundaryScaling(boundary);
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	277 [th_H, ~, th_R] = obj.getBoundaryBorrowing(boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	278 m = obj.getBoundaryNumber(boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	279
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	280 K = obj.K;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	281 J = obj.J;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	282 Hi = obj.Hi;
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	283 a = obj.a;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 switch type
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 % Dirichlet boundary condition
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 case {'D','d','dirichlet'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288 tuning = 1.0;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	290 sigma = 0;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	291 for i = 1:obj.dim
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	292 sigma = sigma + e'JK{i,m}K{i,m}e;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	293 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 sigma = sigma/s_b;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	295 % tau = tuning(1/th_R + obj.dim/th_H)sigma;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297 tau_R = 1/th_R*sigma;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	298
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 tau_H = 1/th_H*sigma;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 tau_H(1,1) = obj.dim*tau_H(1,1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 tau_H(end,end) = obj.dim*tau_H(end,end);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 tau = tuning*(tau_R + tau_H);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	305 closure = aHidH_be' ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	306 -aHietauH_b*e';
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	308 penalty = -aHid*H_b ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	309 +aHietauH_b;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312 % Neumann boundary condition
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 case {'N','n','neumann'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 tau1 = -1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315 tau2 = 0;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316 tau = (tau1e + tau2d)*H_b;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	318 closure = aHitau*d';
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	319 penalty = -aHitau;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322 % Unknown, boundary condition
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 otherwise
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 error('No such boundary condition: type = %s',type);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328 % type Struct that specifies the interface coupling.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329 % Fields:
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 % -- tuning: penalty strength, defaults to 1.2
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 % -- interpolation: type of interpolation, default 'none'
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	334 % error('Not implemented')
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	336 defaultType.tuning = 1.0;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 defaultType.interpolation = 'none';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 default_struct('type', defaultType);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 switch type.interpolation
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 case {'none', ''}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 case {'op','OP'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345 otherwise
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 error('Unknown type of interpolation: %s ', type.interpolation);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	351 tuning = type.tuning;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	353 dim = obj.dim;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 % u denotes the solution in the own domain
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 % v denotes the solution in the neighbour domain
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	356 u = obj;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357 v = neighbour_scheme;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	359 % Boundary operators, u
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	360 e_u = u.getBoundaryOperator('e', boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	361 d_u = u.getBoundaryOperator('d', boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	362 gamm_u = u.getBoundaryBorrowing(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	363 s_b_u = u.getBoundaryScaling(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	364 [th_H_u, ~, th_R_u] = u.getBoundaryBorrowing(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	365 m_u = u.getBoundaryNumber(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	366
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	367 % Coefficients, u
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	368 K_u = u.K;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	369 J_u = u.J;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	370
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	371 % Boundary operators, v
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	372 e_v = v.getBoundaryOperator('e', neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	373 d_v = v.getBoundaryOperator('d', neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	374 gamm_v = v.getBoundaryBorrowing(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	375 s_b_v = v.getBoundaryScaling(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	376 [th_H_v, ~, th_R_v] = v.getBoundaryBorrowing(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	377 m_v = v.getBoundaryNumber(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	378
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	379 % Coefficients, v
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	380 K_v = v.K;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	381 J_v = v.J;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	382
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	383 %--- Penalty strength tau -------------
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	384 sigma_u = 0;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	385 sigma_v = 0;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	386 for i = 1:obj.dim
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	387 sigma_u = sigma_u + e_u'J_uK_u{i,m_u}K_u{i,m_u}e_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	388 sigma_v = sigma_v + e_v'J_vK_v{i,m_v}K_v{i,m_v}e_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	389 end
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	390 sigma_u = sigma_u/s_b_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	391 sigma_v = sigma_v/s_b_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	392
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	393 tau_R_u = 1/th_R_u*sigma_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	394 tau_R_v = 1/th_R_v*sigma_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	395
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	396 tau_H_u = 1/th_H_u*sigma_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	397 tau_H_u(1,1) = dim*tau_H_u(1,1);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	398 tau_H_u(end,end) = dim*tau_H_u(end,end);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	400 tau_H_v = 1/th_H_v*sigma_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	401 tau_H_v(1,1) = dim*tau_H_v(1,1);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	402 tau_H_v(end,end) = dim*tau_H_v(end,end);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	403
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	404 tau = 1/4tuning(tau_R_u + tau_H_u + tau_R_v + tau_H_v);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	405 %--------------------------------------
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	407 % Operators/coefficients that are only required from this side
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	408 Hi = u.Hi;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	409 H_b = u.getBoundaryQuadrature(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	410 a = u.a;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	411
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	412 closure = 1/2aHid_uH_b*e_u' ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	413 -1/2aHie_uH_b*d_u' ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	414 -aHie_utauH_b*e_u';
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	415
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	416 penalty = -1/2aHid_uH_b*e_v' ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	417 -1/2aHie_uH_b*d_v' ...
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	418 +aHie_utauH_b*e_v';
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	420
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	422
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	423 % TODO: Make this work for curvilinear grids
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	425 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 % User can request special interpolation operators by specifying type.interpOpSet
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 interpOpSet = type.interpOpSet;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 tuning = type.tuning;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 % u denotes the solution in the own domain
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434 % v denotes the solution in the neighbour domain
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	435 e_u = obj.getBoundaryOperator('e', boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	436 d_u = obj.getBoundaryOperator('d', boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 H_b_u = obj.getBoundaryQuadrature(boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438 I_u = obj.getBoundaryIndices(boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 gamm_u = obj.getBoundaryBorrowing(boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	441 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	442 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448 % Find the number of grid points along the interface
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 m_u = size(e_u, 2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 m_v = size(e_v, 2);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 Hi = obj.Hi;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 a = obj.a;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 u = obj;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456 v = neighbour_scheme;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 tau_u = -1./(4b1_u) -1./(4b2_u);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 tau_v = -1./(4b1_v) -1./(4b2_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466 tau_u = tuning * spdiag(tau_u);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467 tau_v = tuning * spdiag(tau_v);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 beta_u = tau_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 % Build interpolation operators
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472 Iu2v = intOps.Iu2v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 Iv2u = intOps.Iv2u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 closure = aHie_utau_uH_b_u*e_u' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477 a1/2Hid_uH_b_u*e_u' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 -a1/2Hie_uH_b_u*d_u';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 -a1/2Hie_uH_b_uIv2u.badd_v';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 % Returns the boundary operator op for the boundary specified by the string boundary.
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	488 % op -- string
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489 % boundary -- string
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	490 function o = getBoundaryOperator(obj, op, boundary)
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	491 assertIsMember(op, {'e', 'd'})
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	492 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	494 o = obj.([op, '_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 % Returns square boundary quadrature matrix, of dimension
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 % corresponding to the number of boundary points
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499 %
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500 % boundary -- string
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 function H_b = getBoundaryQuadrature(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	502 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	504 H_b = obj.(['H_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 % Returns square boundary quadrature scaling matrix, of dimension
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 % corresponding to the number of boundary points
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 %
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510 % boundary -- string
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 function s_b = getBoundaryScaling(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	512 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	514 s_b = obj.(['s_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 % Returns the coordinate number corresponding to the boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 %
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 % boundary -- string
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 function m = getBoundaryNumber(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	521 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 switch boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 case {'w', 'e'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 m = 1;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 case {'s', 'n'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 m = 2;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 % Returns the indices of the boundary points in the grid matrix
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 % boundary -- string
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 function I = getBoundaryIndices(obj, boundary)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 switch boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 case 'w'
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 I = ind(1,:);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 case 'e'
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 I = ind(end,:);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 case 's'
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 I = ind(:,1)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 case 'n'
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 I = ind(:,end)';
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 otherwise
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545 error('No such boundary: boundary = %s',boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549 % Returns borrowing constant gamma
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 % boundary -- string
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551 function [theta_H, theta_M, theta_R] = getBoundaryBorrowing(obj, boundary)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 switch boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553 case {'w','e'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 theta_H = obj.theta_H_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 theta_M = obj.theta_M_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556 theta_R = obj.theta_R_u;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557 case {'s','n'}
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 theta_H = obj.theta_H_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559 theta_M = obj.theta_M_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 theta_R = obj.theta_R_v;
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 otherwise
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 error('No such boundary: boundary = %s',boundary);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566 function N = size(obj)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567 N = prod(obj.m);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1067:9a858436f8fa feature/laplace_curvilinear_test