sbplib: +scheme/LaplaceCurvilinearVirtaMin.m annotate

annotate +scheme/LaplaceCurvilinearVirtaMin.m @ 1210:5e7692ed7c7c feature/laplace_curvilinear_test

Add CG interface coupling

author	Martin Almquist <malmquist@stanford.edu>
date	Sun, 22 Sep 2019 19:05:17 -0700
parents	91058813b6e7
children

rev	line source
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	1 classdef LaplaceCurvilinearVirtaMin < scheme.Scheme
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	2 properties
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	4 h % Grid spacing
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	5
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	6 grid
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	7
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	8 order % Order accuracy for the approximation
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	9
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	10 a,b % Parameters of the operator
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	11
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	12
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	13 % Inner products and operators for physical coordinates
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	14 D % Laplace operator
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	15 H, Hi % Inner product
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	16 e_w, e_e, e_s, e_n
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	17 d_w, d_e, d_s, d_n % Normal derivatives at the boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	18 H_w, H_e, H_s, H_n % Boundary inner products
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	19 Dx, Dy % Physical derivatives
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	20 M % Gradient inner product
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	21
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	22 % Metric coefficients
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	23 J, Ji
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	24 a11, a12, a22
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	25 x_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	26 x_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	27 y_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	28 y_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	29
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	30 % Inner product and operators for logical coordinates
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	31 H_u, H_v % Norms in the x and y directions
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	32 Hi_u, Hi_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	33 Hu,Hv % Kroneckerd norms. 1'Hxv corresponds to integration in the x dir.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	34 Hiu, Hiv
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	35 du_w, dv_w
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	36 du_e, dv_e
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	37 du_s, dv_s
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	38 du_n, dv_n
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	39 gamm_u, gamm_v
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	40 h11_u, h11_v
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	41 lambda
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	42
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	43 % Number of boundary points in minumum check
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	44 bp
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	45
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	46 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	47
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	48 methods
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	49 % Implements adiv(bgrad(u)) as a SBP scheme
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	50 % TODO: Implement proper H, it should be the real physical quadrature, the logic quadrature may be but in a separate variable (H_logic?)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	51
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	52 function obj = LaplaceCurvilinearVirtaMin(g ,order, a, b, opSet)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	53 default_arg('opSet',@sbp.D2Variable);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	54 default_arg('a', 1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	55 default_arg('b', 1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	56
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	57 if b ~=1
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	58 error('Not implemented yet')
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	59 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	60
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	61 % Number of boundary points in minimum check
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	62 switch order
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	63 case 2
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	64 obj.bp = 2;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	65 case 4
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	66 obj.bp = 4;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	67 case 6
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	68 obj.bp = 7;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	69 end
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	70
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	71 % assert(isa(g, 'grid.Curvilinear'))
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	72 if isa(a, 'function_handle')
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	73 a = grid.evalOn(g, a);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	74 a = spdiag(a);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	75 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	76
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	77 m = g.size();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	78 m_u = m(1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	79 m_v = m(2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	80 m_tot = g.N();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	81
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	82 h = g.scaling();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	83 h_u = h(1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	84 h_v = h(2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	85
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	86
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	87 % 1D operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	88 ops_u = opSet(m_u, {0, 1}, order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	89 ops_v = opSet(m_v, {0, 1}, order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	90
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	91 I_u = speye(m_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	92 I_v = speye(m_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	93
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	94 D1_u = ops_u.D1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	95 D2_u = ops_u.D2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	96 H_u = ops_u.H;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	97 Hi_u = ops_u.HI;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	98 e_l_u = ops_u.e_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	99 e_r_u = ops_u.e_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	100 d1_l_u = ops_u.d1_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	101 d1_r_u = ops_u.d1_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	102
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	103 D1_v = ops_v.D1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	104 D2_v = ops_v.D2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	105 H_v = ops_v.H;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	106 Hi_v = ops_v.HI;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	107 e_l_v = ops_v.e_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	108 e_r_v = ops_v.e_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	109 d1_l_v = ops_v.d1_l;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	110 d1_r_v = ops_v.d1_r;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	111
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	112
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	113 % Logical operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	114 Du = kr(D1_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	115 Dv = kr(I_u,D1_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	116 obj.Hu = kr(H_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	117 obj.Hv = kr(I_u,H_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	118 obj.Hiu = kr(Hi_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	119 obj.Hiv = kr(I_u,Hi_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	120
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	121 e_w = kr(e_l_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	122 e_e = kr(e_r_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	123 e_s = kr(I_u,e_l_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	124 e_n = kr(I_u,e_r_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	125 obj.du_w = kr(d1_l_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	126 obj.dv_w = (e_w'*Dv)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	127 obj.du_e = kr(d1_r_u,I_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	128 obj.dv_e = (e_e'*Dv)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	129 obj.du_s = (e_s'*Du)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	130 obj.dv_s = kr(I_u,d1_l_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	131 obj.du_n = (e_n'*Du)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	132 obj.dv_n = kr(I_u,d1_r_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	133
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	134
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	135 % Metric coefficients
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	136 coords = g.points();
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	137 x = coords(:,1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	138 y = coords(:,2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	139
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	140 x_u = Du*x;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	141 x_v = Dv*x;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	142 y_u = Du*y;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	143 y_v = Dv*y;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	144
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	145 J = x_u.y_v - x_v.y_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	146 a11 = 1./J .* (x_v.^2 + y_v.^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	147 a12 = -1./J .* (x_u.x_v + y_u.y_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	148 a22 = 1./J .* (x_u.^2 + y_u.^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	149 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	150
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	151 obj.x_u = x_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	152 obj.x_v = x_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	153 obj.y_u = y_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	154 obj.y_v = y_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	155
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	156
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	157 % Assemble full operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	158 L_12 = spdiag(a12);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	159 Duv = DuL_12Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	160 Dvu = DvL_12Du;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	161
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	162 Duu = sparse(m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	163 Dvv = sparse(m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	164 ind = grid.funcToMatrix(g, 1:m_tot);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	165
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	166 for i = 1:m_v
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	167 D = D2_u(a11(ind(:,i)));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	168 p = ind(:,i);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	169 Duu(p,p) = D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	170 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	171
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	172 for i = 1:m_u
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	173 D = D2_v(a22(ind(i,:)));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	174 p = ind(i,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	175 Dvv(p,p) = D;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	176 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	177
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	178
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	179 % Physical operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	180 obj.J = spdiag(J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	181 obj.Ji = spdiag(1./J);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	182
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	183 obj.D = obj.Jia(Duu + Duv + Dvu + Dvv);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	184 obj.H = obj.J*kr(H_u,H_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	185 obj.Hi = obj.Ji*kr(Hi_u,Hi_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	186
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	187 obj.e_w = e_w;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	188 obj.e_e = e_e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	189 obj.e_s = e_s;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	190 obj.e_n = e_n;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	191
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	192 %% normal derivatives
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	193 I_w = ind(1,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	194 I_e = ind(end,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	195 I_s = ind(:,1);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	196 I_n = ind(:,end);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	197
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	198 a11_w = spdiag(a11(I_w));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	199 a12_w = spdiag(a12(I_w));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	200 a11_e = spdiag(a11(I_e));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	201 a12_e = spdiag(a12(I_e));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	202 a22_s = spdiag(a22(I_s));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	203 a12_s = spdiag(a12(I_s));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	204 a22_n = spdiag(a22(I_n));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	205 a12_n = spdiag(a12(I_n));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	206
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	207 s_w = sqrt((e_w'x_v).^2 + (e_w'y_v).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	208 s_e = sqrt((e_e'x_v).^2 + (e_e'y_v).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	209 s_s = sqrt((e_s'x_u).^2 + (e_s'y_u).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	210 s_n = sqrt((e_n'x_u).^2 + (e_n'y_u).^2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	211
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	212 obj.d_w = -1(spdiag(1./s_w)(a11_wobj.du_w' + a12_wobj.dv_w'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	213 obj.d_e = (spdiag(1./s_e)(a11_eobj.du_e' + a12_e*obj.dv_e'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	214 obj.d_s = -1(spdiag(1./s_s)(a22_sobj.dv_s' + a12_sobj.du_s'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	215 obj.d_n = (spdiag(1./s_n)(a22_nobj.dv_n' + a12_n*obj.du_n'))';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	216
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	217 obj.Dx = spdiag( y_v./J)Du + spdiag(-y_u./J)Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	218 obj.Dy = spdiag(-x_v./J)Du + spdiag( x_u./J)Dv;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	219
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	220 %% Boundary inner products
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	221 obj.H_w = H_v*spdiag(s_w);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	222 obj.H_e = H_v*spdiag(s_e);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	223 obj.H_s = H_u*spdiag(s_s);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	224 obj.H_n = H_u*spdiag(s_n);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	225
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	226 % Misc.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	227 obj.m = m;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	228 obj.h = [h_u h_v];
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	229 obj.order = order;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	230 obj.grid = g;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	231
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	232 obj.a = a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	233 obj.b = b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	234 obj.a11 = a11;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	235 obj.a12 = a12;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	236 obj.a22 = a22;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	237 obj.lambda = lambda;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	238
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	239 obj.gamm_u = h_u*ops_u.borrowing.M.d1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	240 obj.gamm_v = h_v*ops_v.borrowing.M.d1;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	241
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	242 obj.h11_u = h_u*ops_u.borrowing.H11;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	243 obj.h11_v = h_v*ops_v.borrowing.H11;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	244 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	245
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	246
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	247 % Closure functions return the opertors applied to the own doamin to close the boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	248 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	249 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	250 % type is a string specifying the type of boundary condition if there are several.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	251 % data is a function returning the data that should be applied at the boundary.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	252 % neighbour_scheme is an instance of Scheme that should be interfaced to.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	253 % neighbour_boundary is a string specifying which boundary to interface to.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	254 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	255 default_arg('type','neumann');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	256 default_arg('parameter', []);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	257
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	258 [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	259 H_b = obj.getBoundaryQuadrature(boundary);
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	260 [gamm, h11] = obj.getBoundaryBorrowing(boundary);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	261
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	262 lambda = obj.lambda;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	263 mx = obj.m(1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	264 my = obj.m(2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	265 bp = obj.bp;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	266
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	267 lambda_mat = reshape(lambda, my, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	268 switch boundary
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	269 case 'w'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	270 lambda_min = min(lambda_mat(:,1:bp), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	271 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	272 case 'e'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	273 lambda_min = min(lambda_mat(:,end-bp+1:end), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	274 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	275 case 's'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	276 lambda_min = min(lambda_mat(1:bp,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	277 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	278 case 'n'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	279 lambda_min = min(lambda_mat(end-bp+1:end,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	280 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	281 end
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	282 lambda_min = lambda_mat(:);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	283
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	284 switch type
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	285 % Dirichlet boundary condition
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	286 case {'D','d','dirichlet'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	287 tuning = 1.0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	288
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	289 switch boundary
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	290 case {'w', 'e'}
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	291 b1 = gamm*lambda_min./obj.a11.^2;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	292 b2 = h11 *lambda./obj.a22.^2;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	293 case {'s', 'n'}
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	294 b1 = h11 *lambda./obj.a11.^2;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	295 b2 = gamm*lambda_min./obj.a22.^2;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	296 end
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	297
1141 91058813b6e7 Multiply by 2 in VirtaMin so that scheme is actually provably stable. Martin Almquist <malmquist@stanford.edu> parents: 1138 diff changeset	298 tau1 = 2tuning spdiag(-1./b1 - 1./b2);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	299 tau2 = 1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	300
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	301 tau = (tau1e + tau2d)*H_b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	302
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	303 closure = obj.aobj.Hitau*e';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	304 penalty = -obj.aobj.Hitau;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	305
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	306
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	307 % Neumann boundary condition
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	308 case {'N','n','neumann'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	309 tau1 = -1;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	310 tau2 = 0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	311 tau = (tau1e + tau2d)*H_b;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	312
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	313 closure = obj.aobj.Hitau*d';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	314 penalty = -obj.aobj.Hitau;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	315
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	316
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	317 % Unknown, boundary condition
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	318 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	319 error('No such boundary condition: type = %s',type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	320 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	321 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	322
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	323 % type Struct that specifies the interface coupling.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	324 % Fields:
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	325 % -- tuning: penalty strength, defaults to 1.2
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	326 % -- interpolation: type of interpolation, default 'none'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	327 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	328
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	329 defaultType.tuning = 1.0;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	330 defaultType.interpolation = 'none';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	331 default_struct('type', defaultType);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	332
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	333 switch type.interpolation
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	334 case {'none', ''}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	335 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	336 case {'op','OP'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	337 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	338 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	339 error('Unknown type of interpolation: %s ', type.interpolation);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	340 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	341 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	342
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	343 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	344 tuning = type.tuning;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	345
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	346 % u denotes the solution in the own domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	347 % v denotes the solution in the neighbour domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	348 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	349 H_b_u = obj.getBoundaryQuadrature(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	350 I_u = obj.getBoundaryIndices(boundary);
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	351 [gamm_u, h11_u] = obj.getBoundaryBorrowing(boundary);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	352
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	353 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	354 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	355 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	356 [gamm_v, h11_v] = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	357
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	358 u = obj;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	359 v = neighbour_scheme;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	360
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	361 % Minimum check for u
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	362 lambda_u = obj.lambda;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	363 mx = obj.m(1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	364 my = obj.m(2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	365 bp = obj.bp;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	366
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	367 lambda_mat = reshape(lambda_u, my, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	368 switch boundary
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	369 case 'w'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	370 lambda_min = min(lambda_mat(:,1:bp), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	371 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	372 case 'e'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	373 lambda_min = min(lambda_mat(:,end-bp+1:end), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	374 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	375 case 's'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	376 lambda_min = min(lambda_mat(1:bp,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	377 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	378 case 'n'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	379 lambda_min = min(lambda_mat(end-bp+1:end,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	380 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	381 end
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	382 lambda_min_u = lambda_mat(:);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	383
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	384 % Minimum check for v
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	385 lambda_v = v.lambda;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	386 mx = v.m(1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	387 my = v.m(2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	388 bp = v.bp;
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	389
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	390 lambda_mat = reshape(lambda_v, my, mx);
1138 afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	391 switch neighbour_boundary
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	392 case 'w'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	393 lambda_min = min(lambda_mat(:,1:bp), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	394 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	395 case 'e'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	396 lambda_min = min(lambda_mat(:,end-bp+1:end), [], 2);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	397 lambda_mat = repmat(lambda_min, 1, mx);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	398 case 's'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	399 lambda_min = min(lambda_mat(1:bp,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	400 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	401 case 'n'
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	402 lambda_min = min(lambda_mat(end-bp+1:end,:), [], 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	403 lambda_mat = repmat(lambda_min, my, 1);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	404 end
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	405 lambda_min_v = lambda_mat(:);
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	406
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	407 switch boundary
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	408 case {'w', 'e'}
1138 afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	409 b1_u = gamm_u*lambda_min_u(I_u)./u.a11(I_u).^2;
afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	410 b2_u = h11_u *lambda_u(I_u)./u.a22(I_u).^2;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	411 case {'s', 'n'}
1138 afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	412 b1_u = h11_u *lambda_u(I_u)./u.a11(I_u).^2;
afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	413 b2_u = gamm_u*lambda_min_u(I_u)./u.a22(I_u).^2;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	414 end
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	415
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	416 switch neighbour_boundary
2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	417 case {'w', 'e'}
1138 afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	418 b1_v = gamm_v*lambda_min_v(I_v)./v.a11(I_v).^2;
afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	419 b2_v = h11_v *lambda_v(I_v)./v.a22(I_v).^2;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	420 case {'s', 'n'}
1138 afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	421 b1_v = h11_v *lambda_v(I_v)./v.a11(I_v).^2;
afd06a84b69c Bugfixes in VirtaMin.interfaceStandard() Martin Almquist <malmquist@stanford.edu> parents: 1137 diff changeset	422 b2_v = gamm_v*lambda_min_v(I_v)./v.a22(I_v).^2;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	423 end
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	424
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	425 tau1 = -1./(4b1_u) -1./(4b1_v) -1./(4b2_u) -1./(4b2_v);
1141 91058813b6e7 Multiply by 2 in VirtaMin so that scheme is actually provably stable. Martin Almquist <malmquist@stanford.edu> parents: 1138 diff changeset	426 tau1 = 2tuning spdiag(tau1);
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	427 tau2 = 1/2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	428
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	429 sig1 = -1/2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	430 sig2 = 0;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	431
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	432 tau = (e_utau1 + tau2d_u)*H_b_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	433 sig = (sig1e_u + sig2d_u)*H_b_u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	434
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	435 closure = obj.aobj.Hi( taue_u' + sigd_u');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	436 penalty = obj.aobj.Hi(-taue_v' + sigd_v');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	437 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	438
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	439 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	440
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	441 % TODO: Make this work for curvilinear grids
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	442 warning('LaplaceCurvilinear: Non-conforming grid interpolation only works for Cartesian grids.');
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	443
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	444 % User can request special interpolation operators by specifying type.interpOpSet
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	445 default_field(type, 'interpOpSet', @sbp.InterpOpsOP);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	446 interpOpSet = type.interpOpSet;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	447 tuning = type.tuning;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	448
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	449
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	450 % u denotes the solution in the own domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	451 % v denotes the solution in the neighbour domain
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	452 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	453 H_b_u = obj.getBoundaryQuadrature(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	454 I_u = obj.getBoundaryIndices(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	455 gamm_u = obj.getBoundaryBorrowing(boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	456
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	457 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	458 H_b_v = neighbour_scheme.getBoundaryQuadrature(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	459 I_v = neighbour_scheme.getBoundaryIndices(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	460 gamm_v = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	461
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	462
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	463 % Find the number of grid points along the interface
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	464 m_u = size(e_u, 2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	465 m_v = size(e_v, 2);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	466
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	467 Hi = obj.Hi;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	468 a = obj.a;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	469
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	470 u = obj;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	471 v = neighbour_scheme;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	472
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	473 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	474 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	475 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	476 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	477
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	478 tau_u = -1./(4b1_u) -1./(4b2_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	479 tau_v = -1./(4b1_v) -1./(4b2_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	480
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	481 tau_u = tuning * spdiag(tau_u);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	482 tau_v = tuning * spdiag(tau_v);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	483 beta_u = tau_v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	484
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	485 % Build interpolation operators
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	486 intOps = interpOpSet(m_u, m_v, obj.order, neighbour_scheme.order);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	487 Iu2v = intOps.Iu2v;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	488 Iv2u = intOps.Iv2u;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	489
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	490 closure = aHie_utau_uH_b_u*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	491 aHie_uH_b_uIv2u.badbeta_uIu2v.good*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	492 a1/2Hid_uH_b_u*e_u' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	493 -a1/2Hie_uH_b_u*d_u';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	494
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	495 penalty = -aHie_utau_uH_b_uIv2u.goode_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	496 -aHie_uH_b_uIv2u.badbeta_ue_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	497 -a1/2Hid_uH_b_uIv2u.goode_v' + ...
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	498 -a1/2Hie_uH_b_uIv2u.badd_v';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	499
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	500 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	501
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	502 % Returns the boundary operator op for the boundary specified by the string boundary.
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	503 % op -- string or a cell array of strings
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	504 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	505 function varargout = getBoundaryOperator(obj, op, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	506
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	507 if ~iscell(op)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	508 op = {op};
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	509 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	510
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	511 for i = 1:numel(op)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	512 switch op{i}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	513 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	514 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	515 case 'w'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	516 e = obj.e_w;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	517 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	518 e = obj.e_e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	519 case 's'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	520 e = obj.e_s;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	521 case 'n'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	522 e = obj.e_n;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	523 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	524 error('No such boundary: boundary = %s',boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	525 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	526 varargout{i} = e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	527
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	528 case 'd'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	529 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	530 case 'w'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	531 d = obj.d_w;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	532 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	533 d = obj.d_e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	534 case 's'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	535 d = obj.d_s;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	536 case 'n'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	537 d = obj.d_n;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	538 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	539 error('No such boundary: boundary = %s',boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	540 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	541 varargout{i} = d;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	542 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	543 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	544 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	545
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	546 % Returns square boundary quadrature matrix, of dimension
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	547 % corresponding to the number of boundary points
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	548 %
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	549 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	550 function H_b = getBoundaryQuadrature(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	551
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	552 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	553 case 'w'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	554 H_b = obj.H_w;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	555 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	556 H_b = obj.H_e;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	557 case 's'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	558 H_b = obj.H_s;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	559 case 'n'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	560 H_b = obj.H_n;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	561 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	562 error('No such boundary: boundary = %s',boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	563 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	564 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	565
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	566 % Returns the indices of the boundary points in the grid matrix
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	567 % boundary -- string
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	568 function I = getBoundaryIndices(obj, boundary)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	569 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	570 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	571 case 'w'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	572 I = ind(1,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	573 case 'e'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	574 I = ind(end,:);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	575 case 's'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	576 I = ind(:,1)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	577 case 'n'
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	578 I = ind(:,end)';
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	579 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	580 error('No such boundary: boundary = %s',boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	581 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	582 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	583
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	584 % Returns borrowing constant gamma
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	585 % boundary -- string
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	586 function [gamm, h11] = getBoundaryBorrowing(obj, boundary)
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	587 switch boundary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	588 case {'w','e'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	589 gamm = obj.gamm_u;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	590 h11 = obj.h11_u;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	591 case {'s','n'}
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	592 gamm = obj.gamm_v;
1137 2ff1f366e64a Fix minimum and correct borrowing in VirtaMin scheme. Martin Almquist <malmquist@stanford.edu> parents: 1136 diff changeset	593 h11 = obj.h11_v;
1136 eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	594 otherwise
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	595 error('No such boundary: boundary = %s',boundary);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	596 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	597 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	598
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	599 function N = size(obj)
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	600 N = prod(obj.m);
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	601 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	602 end
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	603 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearVirtaMin.m @ 1210:5e7692ed7c7c feature/laplace_curvilinear_test