sbplib: +scheme/LaplaceCurvilinearNewCorner.m annotate

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1085:49c0b8c7330a feature/laplace_curvilinear_test

Clean up Dirichlet BC code in LaplaceCurvilinearNew.

author	Martin Almquist <malmquist@stanford.edu>
date	Fri, 29 Mar 2019 14:24:39 -0700
parents	d5290a056049
children

rev	line source
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearNewCorner < scheme.Scheme
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5 dim % Number of spatial dimensions
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7 grid
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9 order % Order of accuracy for the approximation
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11 a,b % Parameters of the operator
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 % Inner products and operators for physical coordinates
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 D % Laplace operator
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 H, Hi % Inner product
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 e_w, e_e, e_s, e_n
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 H_w, H_e, H_s, H_n % Boundary inner products
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 Dx, Dy % Physical derivatives
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21 M % Gradient inner product
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 % Metric coefficients
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 J, Ji
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 a11, a12, a22
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 K
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 x_u
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 x_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29 y_u
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 y_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 % Inner product and operators for logical coordinates
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 H_u, H_v % Norms in the x and y directions
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 Hi_u, Hi_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 Hiu, Hiv
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_w, dv_w
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 du_e, dv_e
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	40 du_s, dv_s
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 du_n, dv_n
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_M_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	45 theta_R_u, theta_R_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 theta_H_u, theta_H_v
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	48 % Temporary
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	49 lambda
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	50 gamm_u, gamm_v
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	51
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 end
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 methods
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 % Implements adiv(bgrad(u)) as a SBP scheme
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 function obj = LaplaceCurvilinearNewCorner(g, order, a, b, opSet)
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 default_arg('opSet',@sbp.D2Variable);
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60 default_arg('a', 1);
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	61 default_arg('b', @(x,y) 0*x + 1);
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	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
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	69 if isa(b, 'function_handle')
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	70 b = grid.evalOn(g, b);
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	71 b = spdiag(b);
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	72 end
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	73
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	74 % If b is scalar
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	75 if length(b) == 1
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	76 b = b*speye(g.N(), g.N());
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	77 end
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	78
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	79 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	80 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	81 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	82 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	83 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	84
c2bd7f15da48 Add scheme where only corner 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 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	86 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	87 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	88
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	91 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	92 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	93
c2bd7f15da48 Add scheme where only corner 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 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	95 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	96
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 D1_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	98 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	99 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	100 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	101 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	102 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	103 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	104 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	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 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	107 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	108 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	109 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	110 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	111 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	112 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	113 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	114
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	117 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	118 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	119 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	120 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	121 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	122 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	123
c2bd7f15da48 Add scheme where only corner 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 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	125 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	126 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	127 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	128 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	129 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	130 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	131 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	132 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	133 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	134 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	135 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	136
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137
c2bd7f15da48 Add scheme where only corner 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 % 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	139 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	140 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	141 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	142
c2bd7f15da48 Add scheme where only corner 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 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	144 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	145 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	146 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	147
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 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	149 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	150 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	151 a22 = 1./J .* (x_u.^2 + y_u.^2);
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	152 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153
c2bd7f15da48 Add scheme where only corner 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 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	155 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	156 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	157 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	158 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	159 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	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 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	162 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	163 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	164 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	165
c2bd7f15da48 Add scheme where only corner 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 % 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	167 L_12 = spdiag(a12);
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	168 Duv = DubL_12*Dv;
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	169 Dvu = DvbL_12*Du;
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	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 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	172 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	173 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	174
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 for i = 1:m_v
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	176 b_a11 = b*a11;
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	177 D = D2_u(b_a11(ind(:,i)));
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	178 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	179 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	180 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	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 for i = 1:m_u
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	183 b_a22 = b*a22;
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	184 D = D2_v(b_a22(ind(i,:)));
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	185 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	186 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	187 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	188
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 % 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	191 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	192 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	193
c2bd7f15da48 Add scheme where only corner 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 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	195 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	196 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	197
c2bd7f15da48 Add scheme where only corner 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 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	199 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	200 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	201 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	202
c2bd7f15da48 Add scheme where only corner 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 %% 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	204 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	205 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	206 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	207 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	208
c2bd7f15da48 Add scheme where only corner 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 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	210 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	211 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	212 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	213 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	214 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	215 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	216 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	217
c2bd7f15da48 Add scheme where only corner 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 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	219 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	220 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	221 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	222
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 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	224 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	225 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	226 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	227
c2bd7f15da48 Add scheme where only corner 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.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	229 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	230
c2bd7f15da48 Add scheme where only corner 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 %% 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	232 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	233 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	234 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	235 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	236
c2bd7f15da48 Add scheme where only corner 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 % 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	238 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	239 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	240 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	241 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	242 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	243
c2bd7f15da48 Add scheme where only corner 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.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	245 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	246 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	247 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	248 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	249 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	250 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	251 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	252 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	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 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	255 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	256
c2bd7f15da48 Add scheme where only corner 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 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	258 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	259
c2bd7f15da48 Add scheme where only corner 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 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	261 obj.theta_H_v = h_v*ops_v.borrowing.H11;
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	262
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	263 % Temporary
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	264 obj.lambda = lambda;
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	265 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	266 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	267 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	268
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	271 % 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	272 % 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	273 % 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	274 % 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	275 % 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	276 % 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	277 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	278 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	279 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	280
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	281 e = obj.getBoundaryOperator('e', boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	282 d = obj.getBoundaryOperator('d', boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283 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	284 s_b = obj.getBoundaryScaling(boundary);
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	285 [th_H, ~, th_R] = obj.getBoundaryBorrowing(boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 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	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 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	289 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	290 Hi = obj.Hi;
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	291 a = obj.a;
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	292 b_b = e'obj.be;
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	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 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	295 % 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	296 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	297 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	298
1084 d5290a056049 Fix bug in new implementations that made matrices non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1068 diff changeset	299 sigma = 0*b_b;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300 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	301 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	302 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	303 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	304 % 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	305
c2bd7f15da48 Add scheme where only corner 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 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	307
c2bd7f15da48 Add scheme where only corner 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 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	309 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	310 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	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 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	313
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	314 closure = aHidb_bH_b*e' ...
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	315 -aHietaub_bH_be';
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	316
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	317 penalty = -aHidb_bH_b ...
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	318 +aHietaub_b*H_b;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319
c2bd7f15da48 Add scheme where only corner 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
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	321 % Neumann boundary condition. Note that the penalty is for du/dn and not b*du/dn.
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	322 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	323 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	324 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	325 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	326
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	327 closure = aHitaub_bd';
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	328 penalty = -aHitau*b_b;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	329
c2bd7f15da48 Add scheme where only corner 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 % 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	332 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	333 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	334 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	335 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	336
c2bd7f15da48 Add scheme where only corner 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 % 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	338 % 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	339 % -- 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	340 % -- 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	341 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	342
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	343 % error('Not implemented')
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	345 defaultType.tuning = 1.0;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 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	347 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	348
c2bd7f15da48 Add scheme where only corner 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 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	350 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	351 [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	352 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	353 [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	354 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	355 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	356 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	357 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	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 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	360 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	361
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	362 dim = obj.dim;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	363 % 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	364 % 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	365 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	366 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	367
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	368 % Boundary operators, u
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	369 e_u = u.getBoundaryOperator('e', boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	370 d_u = u.getBoundaryOperator('d', boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	371 gamm_u = u.getBoundaryBorrowing(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	372 s_b_u = u.getBoundaryScaling(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	373 [th_H_u, ~, th_R_u] = u.getBoundaryBorrowing(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	374 m_u = u.getBoundaryNumber(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	375
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	376 % Coefficients, u
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	377 K_u = u.K;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	378 J_u = u.J;
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	379 b_b_u = e_u'u.be_u;
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	380
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	381 % Boundary operators, v
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	382 e_v = v.getBoundaryOperator('e', neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	383 d_v = v.getBoundaryOperator('d', neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	384 gamm_v = v.getBoundaryBorrowing(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	385 s_b_v = v.getBoundaryScaling(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	386 [th_H_v, ~, th_R_v] = v.getBoundaryBorrowing(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	387 m_v = v.getBoundaryNumber(neighbour_boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	388
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	389 % Coefficients, v
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	390 K_v = v.K;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	391 J_v = v.J;
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	392 b_b_v = e_v'v.be_v;
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	393
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	394 %--- Penalty strength tau -------------
1084 d5290a056049 Fix bug in new implementations that made matrices non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1068 diff changeset	395 sigma_u = 0*b_b_u;
d5290a056049 Fix bug in new implementations that made matrices non-sparse. Martin Almquist <malmquist@stanford.edu> parents: 1068 diff changeset	396 sigma_v = 0*b_b_v;
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	397 for i = 1:obj.dim
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	398 sigma_u = sigma_u + e_u'J_uK_u{i,m_u}K_u{i,m_u}e_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	399 sigma_v = sigma_v + e_v'J_vK_v{i,m_v}K_v{i,m_v}e_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	400 end
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	401 sigma_u = sigma_u/s_b_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	402 sigma_v = sigma_v/s_b_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	403
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	404 tau_R_u = 1/th_R_u*sigma_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	405 tau_R_v = 1/th_R_v*sigma_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	406
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	407 tau_H_u = 1/th_H_u*sigma_u;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	408 tau_H_u(1,1) = dim*tau_H_u(1,1);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	409 tau_H_u(end,end) = dim*tau_H_u(end,end);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	411 tau_H_v = 1/th_H_v*sigma_v;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	412 tau_H_v(1,1) = dim*tau_H_v(1,1);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	413 tau_H_v(end,end) = dim*tau_H_v(end,end);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	414
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	415 tau = 1/4tuning(b_b_u(tau_R_u + tau_H_u) + b_b_v(tau_R_v + tau_H_v));
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	416 %--------------------------------------
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	417
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	418 % Operators/coefficients that are only required from this side
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	419 Hi = u.Hi;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	420 H_b = u.getBoundaryQuadrature(boundary);
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	421 a = u.a;
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	422
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	423 closure = 1/2aHid_ub_b_uH_be_u' ...
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	424 -1/2aHie_uH_bb_b_ud_u' ...
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	425 -aHie_utauH_b*e_u';
9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	426
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	427 penalty = -1/2aHid_ub_b_uH_be_v' ...
e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	428 -1/2aHie_uH_bb_b_vd_v' ...
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	429 +aHie_utauH_b*e_v';
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 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	431
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 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	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 % 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	435 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
1067 9a858436f8fa Implement new penalty strength for interface. Bugfix missing coeff a in Dirichlet penalty. Martin Almquist <malmquist@stanford.edu> parents: 1066 diff changeset	436 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
1068 e0ecce90f8cf Add variable b. Tested for interface and Dirichlet, but not Neumann yet. Martin Almquist <malmquist@stanford.edu> parents: 1067 diff changeset	437 warning('LaplaceCurvilinear: Non-conforming interface assumes that b is constant');
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	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 % 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	440 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	441 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	442 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	443
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	446 % v denotes the solution in the neighbour domain
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	447 e_u = obj.getBoundaryOperator('e', boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	448 d_u = obj.getBoundaryOperator('d', boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449 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	450 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	451 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	452
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	453 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary);
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	454 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 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	456 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	457 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	458
c2bd7f15da48 Add scheme where only corner 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
c2bd7f15da48 Add scheme where only corner 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 % 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	461 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	462 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	463
c2bd7f15da48 Add scheme where only corner 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 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	465 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	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 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	468 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	469
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 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	471 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	472 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	473 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	474
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 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	476 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	477
c2bd7f15da48 Add scheme where only corner 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 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	479 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	480 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	481
c2bd7f15da48 Add scheme where only corner 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 % 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	483 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	484 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	485 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	486
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 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	488 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	489 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	490 -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	491
c2bd7f15da48 Add scheme where only corner 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 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	493 -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	494 -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	495 -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	496
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 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	498
c2bd7f15da48 Add scheme where only corner 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 % Returns the boundary operator op for the boundary specified by the string boundary.
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	500 % op -- string
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501 % boundary -- string
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	502 function o = getBoundaryOperator(obj, op, boundary)
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	503 assertIsMember(op, {'e', 'd'})
d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	504 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	506 o = obj.([op, '_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 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	508
c2bd7f15da48 Add scheme where only corner 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 % 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	510 % 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	511 %
c2bd7f15da48 Add scheme where only corner 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 % 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	513 function H_b = getBoundaryQuadrature(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	514 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	516 H_b = obj.(['H_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 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	518
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 % 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	520 % 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	521 %
c2bd7f15da48 Add scheme where only corner 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 % 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	523 function s_b = getBoundaryScaling(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	524 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	526 s_b = obj.(['s_', boundary]);
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527 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	528
c2bd7f15da48 Add scheme where only corner 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 % 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	530 %
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 % 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	532 function m = getBoundaryNumber(obj, boundary)
1066 d64062bed5fb Clean up getBoundarOperator/Quadrature as was done on feature/getBoundaryOp. Temporarily re-add lambda so that old interface method works. Martin Almquist <malmquist@stanford.edu> parents: 1065 diff changeset	533 assertIsMember(boundary, {'w', 'e', 's', 'n'})
1065 c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 switch boundary
c2bd7f15da48 Add scheme where only corner points are multiplied by dim. Does not seem to decrease spectral radius much, but is stable. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 case {'w', '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	537 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	538 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	539 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	540 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	541 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	542
c2bd7f15da48 Add scheme where only corner 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 % 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	544 % 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	545 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	546 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	547 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	548 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	549 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	550 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	551 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	552 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	553 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	554 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	555 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	556 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	557 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	558 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	559 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	560
c2bd7f15da48 Add scheme where only corner 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 % 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	562 % 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	563 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	564 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	565 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	566 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	567 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	568 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	569 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	570 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	571 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	572 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	573 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	574 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	575 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	576 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	577
c2bd7f15da48 Add scheme where only corner 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 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	579 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	580 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	581 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	582 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearNewCorner.m @ 1085:49c0b8c7330a feature/laplace_curvilinear_test