sbplib: +scheme/LaplaceCurvilinearNewCorner.m annotate

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

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

author	Martin Almquist <malmquist@stanford.edu>
date	Thu, 17 Jan 2019 18:57:54 -0800
parents
children	d64062bed5fb

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
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 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	49
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 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	51 % 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	52 % 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	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 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	55 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	56 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	57 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	58
c2bd7f15da48 Add scheme where only corner 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 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	60 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	61 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	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 % 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	64 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	65 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	66 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	67 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	68
c2bd7f15da48 Add scheme where only corner 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 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	70 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	71 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	72 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	73 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	74
c2bd7f15da48 Add scheme where only corner 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 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	76 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	77 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	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
c2bd7f15da48 Add scheme where only corner 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 % 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	81 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	82 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	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 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	85 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	86
c2bd7f15da48 Add scheme where only corner 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 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	88 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	89 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	90 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	91 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	92 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	93 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	94 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	95
c2bd7f15da48 Add scheme where only corner 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 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	97 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	98 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	99 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	100 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	101 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	102 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	103 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	104
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	107 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	108 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	109 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	110 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	111 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	112 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	113
c2bd7f15da48 Add scheme where only corner 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 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	115 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	116 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	117 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	118 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	119 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	120 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	121 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	122 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	123 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	124 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	125 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	126
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	129 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	130 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	131 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	132
c2bd7f15da48 Add scheme where only corner 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 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	134 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	135 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	136 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	137
c2bd7f15da48 Add scheme where only corner 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 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	139 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	140 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	141 a22 = 1./J .* (x_u.^2 + 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	142 % lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^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	143
c2bd7f15da48 Add scheme where only corner 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 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	145 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	146 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	147 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	148 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	149 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	150
c2bd7f15da48 Add scheme where only corner 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 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	152 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	153 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	154 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	155
c2bd7f15da48 Add scheme where only corner 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 % 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	157 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	158 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	159 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	160
c2bd7f15da48 Add scheme where only corner 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 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	162 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	163 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	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 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	166 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	167 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	168 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	169 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	170
c2bd7f15da48 Add scheme where only corner 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 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	172 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	173 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	174 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	175 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	176
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	179 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	180 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	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 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	183 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	184 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	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.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	187 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	188 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	189 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	190
c2bd7f15da48 Add scheme where only corner 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 %% 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	192 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	193 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	194 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	195 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	196
c2bd7f15da48 Add scheme where only corner 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 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	198 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	199 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	200 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	201 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	202 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	203 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	204 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	205
c2bd7f15da48 Add scheme where only corner 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 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	207 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	208 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	209 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	210
c2bd7f15da48 Add scheme where only corner 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 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	212 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	213 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	214 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	215
c2bd7f15da48 Add scheme where only corner 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.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	217 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	218
c2bd7f15da48 Add scheme where only corner 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 %% 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	220 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	221 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	222 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	223 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	224
c2bd7f15da48 Add scheme where only corner 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 % 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	226 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	227 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	228 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	229 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	230 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	231
c2bd7f15da48 Add scheme where only corner 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.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	233 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	234 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	235 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	236 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	237 % obj.lambda = lambda;
c2bd7f15da48 Add scheme where only corner 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.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	239 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	240 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	241 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	242
c2bd7f15da48 Add scheme where only corner 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.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	244 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	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_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	247 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	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_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	250 obj.theta_H_v = h_v*ops_v.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	251 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	252
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 % 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	255 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257 % 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	258 % 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	259 % 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	260 % 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	261 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	262 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	263 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	264
c2bd7f15da48 Add scheme where only corner 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 [e, d] = obj.getBoundaryOperator({'e', 'd'}, 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	266 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	267 s_b = obj.getBoundaryScaling(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	268 [th_H, th_M, th_R] = 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	269 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	270
c2bd7f15da48 Add scheme where only corner 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 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	272 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	273 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	274 a_b = e'obj.ae;
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 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	277 % 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	278 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	279 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	280
c2bd7f15da48 Add scheme where only corner 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 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	282 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	283 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	284 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	285 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	286 % 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	287
c2bd7f15da48 Add scheme where only corner 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 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	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 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	291 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	292 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	293
c2bd7f15da48 Add scheme where only corner 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 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	295
c2bd7f15da48 Add scheme where only corner 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 closure = Hida_bH_be' ...
c2bd7f15da48 Add scheme where only corner 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 -HietauH_be';
c2bd7f15da48 Add scheme where only corner 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 penalty = -Hida_b*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	300 +Hietau*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	301
c2bd7f15da48 Add scheme where only corner 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 % 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	304 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	305 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	306 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	307 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	308
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 closure = obj.aHitau*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	310 penalty = -obj.aHitau;
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	314 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	315 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	316 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	317 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	318
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 % 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	320 % 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	321 % -- 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	322 % -- 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	323 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	324
c2bd7f15da48 Add scheme where only corner 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 error('Not implemented')
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 defaultType.tuning = 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	328 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	329 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	330
c2bd7f15da48 Add scheme where only corner 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 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	332 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	333 [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	334 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	335 [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	336 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	337 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	338 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	339 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	340
c2bd7f15da48 Add scheme where only corner 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 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	342 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	343
c2bd7f15da48 Add scheme where only corner 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 % 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	345 % 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	346 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, 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	347 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	348 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	349 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	350
c2bd7f15da48 Add scheme where only corner 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 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, 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	352 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	353 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	354 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	355
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 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	360 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	361 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	362 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	363
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 tau1 = -1./(4b1_u) -1./(4b1_v) -1./(4b2_u) -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	365 tau1 = tuning * spdiag(tau1);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	366 tau2 = 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	367
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	368 sig1 = -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	369 sig2 = 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	370
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	371 tau = (e_utau1 + tau2d_u)*H_b_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	372 sig = (sig1e_u + sig2d_u)*H_b_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	373
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 closure = obj.aobj.Hi( taue_u' + sigd_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	375 penalty = obj.aobj.Hi(-taue_v' + sigd_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	376 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	377
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	378 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	379
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	380 % 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	381 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian 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	382
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 % 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	384 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	385 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	386 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	387
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	388
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	389 % 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	390 % 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	391 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, 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	392 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	393 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	394 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	395
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, 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	397 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	398 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	399 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	400
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	401
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 % 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	403 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	404 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	405
c2bd7f15da48 Add scheme where only corner 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 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	407 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	408
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	409 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	410 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	411
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	412 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	413 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	414 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	415 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	416
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	417 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	418 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	419
c2bd7f15da48 Add scheme where only corner 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 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	421 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	422 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	423
c2bd7f15da48 Add scheme where only corner 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 % 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	425 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	426 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	427 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	428
c2bd7f15da48 Add scheme where only corner 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 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	430 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	431 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	432 -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	433
c2bd7f15da48 Add scheme where only corner 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 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	435 -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	436 -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	437 -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	438
c2bd7f15da48 Add scheme where only corner 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 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	440
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 % Returns the boundary operator op for the boundary specified by the string 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	442 % op -- string or a cell array of strings
c2bd7f15da48 Add scheme where only corner 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 % 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	444 function varargout = getBoundaryOperator(obj, op, 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
c2bd7f15da48 Add scheme where only corner 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 if ~iscell(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	447 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	448 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	449
c2bd7f15da48 Add scheme where only corner 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 for i = 1:numel(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	451 switch op{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	452 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	453 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	454 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	455 e = obj.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	456 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	457 e = obj.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	458 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	459 e = obj.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	460 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	461 e = obj.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	462 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	463 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	464 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	465 varargout{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	466
c2bd7f15da48 Add scheme where only corner 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 case '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	468 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	469 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	470 d = obj.d_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	471 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	472 d = obj.d_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	473 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	474 d = obj.d_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	475 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	476 d = obj.d_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	477 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	478 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	479 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	480 varargout{i} = 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	481 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	482 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	483 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	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 % 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	486 % 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	487 %
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 % 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	489 function H_b = getBoundaryQuadrature(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	490
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 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	492 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	493 H_b = obj.H_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	494 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	495 H_b = obj.H_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	496 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	497 H_b = obj.H_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	498 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	499 H_b = obj.H_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	500 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	501 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	502 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	503 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	504
c2bd7f15da48 Add scheme where only corner 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 % 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	506 % 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	507 %
c2bd7f15da48 Add scheme where only corner 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 % 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	509 function s_b = getBoundaryScaling(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	510
c2bd7f15da48 Add scheme where only corner 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 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	512 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	513 s_b = obj.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	514 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	515 s_b = obj.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	516 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	517 s_b = obj.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	518 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	519 s_b = obj.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	520 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	521 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	522 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	523 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	524
c2bd7f15da48 Add scheme where only corner 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 % 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	526 %
c2bd7f15da48 Add scheme where only corner 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 % 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	528 function m = getBoundaryNumber(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	529
c2bd7f15da48 Add scheme where only corner 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 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	531 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	532 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	533 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	534 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	535 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	536 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	537 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	538 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	539
c2bd7f15da48 Add scheme where only corner 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 % 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	541 % 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	542 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	543 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	544 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	545 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	546 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	547 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	548 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	549 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	550 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	551 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	552 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	553 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	554 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	555 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	556 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	557
c2bd7f15da48 Add scheme where only corner 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 % 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	559 % 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	560 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	561 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	562 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	563 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	564 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	565 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	566 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	567 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	568 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	569 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	570 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	571 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	572 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	573 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	574
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	575 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	576 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	577 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	578 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	579 end

Mercurial > repos > public > sbplib

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