sbplib: +scheme/LaplaceCurvilinearMin.m annotate

annotate +scheme/LaplaceCurvilinearMin.m @ 1138:afd06a84b69c feature/laplace_curvilinear_test

Bugfixes in VirtaMin.interfaceStandard()

author	Martin Almquist <malmquist@stanford.edu>
date	Mon, 10 Jun 2019 14:39:14 +0200
parents	eee71789f13b
children	6bc93c091682

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 LaplaceCurvilinearMin < 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 dim % Number of spatial dimensions
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 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	8
eee71789f13b Add LaplaceCurvilinear schemes 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 order % Order of 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	10
eee71789f13b Add LaplaceCurvilinear schemes 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 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	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
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	15 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	16 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	17 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	18 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	19 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	20 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	21 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	22
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	24 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	25 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	26 K
eee71789f13b Add LaplaceCurvilinear schemes 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 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	28 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	29 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	30 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	31 s_w, s_e, s_s, s_n % Boundary integral scale factors
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	34 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	35 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	36 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	37 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	38 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	39 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	40 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	41 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	42
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	43 % Borrowing constants
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	44 theta_M_u, theta_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	45 theta_R_u, theta_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	46 theta_H_u, theta_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	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 % Temporary, only used for nonconforming interfaces but should be removed.
eee71789f13b Add LaplaceCurvilinear schemes 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 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	50 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	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 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	53 % 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	54 % 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	55
eee71789f13b Add LaplaceCurvilinear schemes 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 function obj = LaplaceCurvilinearMin(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	57 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	58 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	59 default_arg('b', @(x,y) 0*x + 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	60
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	61 % 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	62 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	63 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	64 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	65 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	66
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	67 if isa(b, '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	68 b = grid.evalOn(g, 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	69 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	70
eee71789f13b Add LaplaceCurvilinear schemes 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 % If b is scalar
eee71789f13b Add LaplaceCurvilinear schemes 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 length(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	73 % b = b*speye(g.N(), 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	74 b = b*ones(g.N(), 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	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 b = spdiag(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	77
eee71789f13b Add LaplaceCurvilinear schemes 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 dim = 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	79 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	80 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	81 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	82 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	83
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	85 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	86 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	87
eee71789f13b Add LaplaceCurvilinear schemes 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 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	89 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	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 K = cell(dim, dim);
eee71789f13b Add LaplaceCurvilinear schemes 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 K{1,1} = spdiag(y_v./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	153 K{1,2} = spdiag(-y_u./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	154 K{2,1} = spdiag(-x_v./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	155 K{2,2} = spdiag(x_u./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	156 obj.K = K;
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 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	159 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	160 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	161 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	162
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	164 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	165 Duv = DubL_12*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	166 Dvu = DvbL_12*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	167
eee71789f13b Add LaplaceCurvilinear schemes 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 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	169 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	170 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	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_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	173 b_a11 = b*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	174 D = D2_u(b_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	175 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	176 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	177 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	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 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	180 b_a22 = b*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	181 D = D2_v(b_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	182 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	183 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	184 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	185
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	188 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	189 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	190
eee71789f13b Add LaplaceCurvilinear schemes 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 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	192 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	193 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	194
eee71789f13b Add LaplaceCurvilinear schemes 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 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	196 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	197 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	198 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	199
eee71789f13b Add LaplaceCurvilinear schemes 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 %% 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	201 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	202 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	203 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	204 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	205
eee71789f13b Add LaplaceCurvilinear schemes 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 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	207 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	208 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	209 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	210 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	211 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	212 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	213 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	214
eee71789f13b Add LaplaceCurvilinear schemes 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 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	216 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	217 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	218 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	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 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	221 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	222 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	223 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	224
eee71789f13b Add LaplaceCurvilinear schemes 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 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	226 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	227
eee71789f13b Add LaplaceCurvilinear schemes 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 %% 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	229 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	230 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	231 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	232 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	233
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	235 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	236 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	237 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	238 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	239 obj.dim = dim;
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	241 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	242 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	243 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	244 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	245 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	246 obj.s_w = 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	247 obj.s_e = 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	248 obj.s_s = 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	249 obj.s_n = 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	250
eee71789f13b Add LaplaceCurvilinear schemes 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 obj.theta_M_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	252 obj.theta_M_v = h_v*ops_v.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	253
eee71789f13b Add LaplaceCurvilinear schemes 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 obj.theta_R_u = h_u*ops_u.borrowing.R.delta_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	255 obj.theta_R_v = h_v*ops_v.borrowing.R.delta_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	256
eee71789f13b Add LaplaceCurvilinear schemes 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 obj.theta_H_u = h_u*ops_u.borrowing.H11;
eee71789f13b Add LaplaceCurvilinear schemes 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 obj.theta_H_v = h_v*ops_v.borrowing.H11;
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	260 % Temporary
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	261 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	262 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	263
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	264
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	265 % 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	266 % 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	267 % 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	268 % 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	269 % 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	270 % 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	271 % 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	272 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	273 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	274 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	275
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	276 e = obj.getBoundaryOperator('e', 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	277 d = obj.getBoundaryOperator('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	278 H_b = 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	279 s_b = obj.getBoundaryScaling(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	280 [th_H, ~, th_R] = 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	281 m = obj.getBoundaryNumber(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	282
eee71789f13b Add LaplaceCurvilinear schemes 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 K = obj.K;
eee71789f13b Add LaplaceCurvilinear schemes 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 J = obj.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	285 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	286 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	287 b_b = e'obj.be;
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	289 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	290 % 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	291 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	292 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	293
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	294 sigma = 0*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	295 for i = 1:obj.dim
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	296 sigma = sigma + e'JK{i,m}K{i,m}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	297 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	298 sigma = sigma/s_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	299 tau = tuning(1/th_R + obj.dim/th_H)sigma;
eee71789f13b Add LaplaceCurvilinear schemes 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 closure = aHidb_bH_b*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	302 -aHietaub_bH_be';
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 = -aHidb_bH_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	305 +aHietaub_b*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	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
eee71789f13b Add LaplaceCurvilinear schemes 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 % Neumann boundary condition. Note that the penalty is for du/dn and not b*du/dn.
eee71789f13b Add LaplaceCurvilinear schemes 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 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	310 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	311 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	312 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	313
eee71789f13b Add LaplaceCurvilinear schemes 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 closure = aHitaub_bd';
eee71789f13b Add LaplaceCurvilinear schemes 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 penalty = -aHitau*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	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
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	319 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	320 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	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 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	323
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	325 % 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	326 % -- 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	327 % -- 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	328 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	329
eee71789f13b Add LaplaceCurvilinear schemes 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 % error('Not implemented')
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 defaultType.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	333 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	334 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	335
eee71789f13b Add LaplaceCurvilinear schemes 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 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	337 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	338 [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	339 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	340 [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	341 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	342 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	343 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	344 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	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 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	347 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	348
eee71789f13b Add LaplaceCurvilinear schemes 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 dim = obj.dim;
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	351 % 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	352 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	353 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	354
eee71789f13b Add LaplaceCurvilinear schemes 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 % Boundary operators, 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	356 e_u = u.getBoundaryOperator('e', 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	357 d_u = u.getBoundaryOperator('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	358 s_b_u = u.getBoundaryScaling(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	359 [th_H_u, ~, th_R_u] = u.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	360 m_u = u.getBoundaryNumber(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	361
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	362 % Coefficients, 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	363 K_u = u.K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	364 J_u = u.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	365 b_b_u = e_u'u.be_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	366
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	367 % Boundary operators, 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	368 e_v = v.getBoundaryOperator('e', 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	369 d_v = v.getBoundaryOperator('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	370 s_b_v = v.getBoundaryScaling(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	371 [th_H_v, ~, th_R_v] = v.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	372 m_v = v.getBoundaryNumber(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	373
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	374 % BUGFIX?!?!?
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	375 if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) \|\| (strcmp(boundary,'e') && strcmp(neighbour_boundary,'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	376 e_v = fliplr(e_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	377 d_v = fliplr(d_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	378 s_b_v = rot90(s_b_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	379 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	380
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	381 % Coefficients, 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	382 K_v = v.K;
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	383 J_v = v.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	384 b_b_v = e_v'v.be_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	385
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	386 %--- Penalty strength tau -------------
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	387 sigma_u = 0*b_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	388 sigma_v = 0*b_b_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	389 for i = 1:obj.dim
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	390 sigma_u = sigma_u + e_u'J_uK_u{i,m_u}K_u{i,m_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	391 sigma_v = sigma_v + e_v'J_vK_v{i,m_v}K_v{i,m_v}e_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	392 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	393 sigma_u = sigma_u/s_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	394 sigma_v = sigma_v/s_b_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	395
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	396 tau_R_u = 1/th_R_u*sigma_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	397 tau_R_v = 1/th_R_v*sigma_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	398
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	399 tau_H_u = dim1/th_H_usigma_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	400 tau_H_v = dim1/th_H_vsigma_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	401
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	402 tau = 1/4tuning(b_b_u(tau_R_u + tau_H_u) + b_b_v(tau_R_v + tau_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	403 %--------------------------------------
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	404
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	405 % Operators/coefficients that are only required from this side
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	406 Hi = 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	407 H_b = u.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	408 a = u.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	409
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	410 closure = 1/2aHid_ub_b_uH_be_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	411 -1/2aHie_uH_bb_b_ud_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	412 -aHie_utauH_b*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	413
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	414 penalty = -1/2aHid_ub_b_uH_be_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	415 -1/2aHie_uH_bb_b_vd_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	416 +aHie_utauH_b*e_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	417 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	418
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	419 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	420
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	421 % 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	422 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	423 warning('LaplaceCurvilinear: Non-conforming interface uses Virtas penalty strength');
eee71789f13b Add LaplaceCurvilinear schemes 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 warning('LaplaceCurvilinear: Non-conforming interface assumes that b is constant');
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes where the minimum check will be implemented. The Virta scheme will be used for comparison only. Martin Almquist <malmquist@stanford.edu> parents: diff changeset	426 % 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	427 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	428 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	429 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	430
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	433 % 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	434 e_u = obj.getBoundaryOperator('e', 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	435 d_u = obj.getBoundaryOperator('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	436 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	437 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	438 [~, 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	439
eee71789f13b Add LaplaceCurvilinear schemes 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 e_v = neighbour_scheme.getBoundaryOperator('e', 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	441 d_v = neighbour_scheme.getBoundaryOperator('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	442 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	443 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	444 [~, 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	445
eee71789f13b Add LaplaceCurvilinear schemes 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
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	448 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	449 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	450
eee71789f13b Add LaplaceCurvilinear schemes 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 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	452 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	453
eee71789f13b Add LaplaceCurvilinear schemes 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 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	455 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	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 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	458 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	459 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	460 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	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 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	463 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	464
eee71789f13b Add LaplaceCurvilinear schemes 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 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	466 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	467 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	468
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	470 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	471 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	472 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	473
eee71789f13b Add LaplaceCurvilinear schemes 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 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	475 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	476 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	477 -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	478
eee71789f13b Add LaplaceCurvilinear schemes 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 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	480 -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	481 -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	482 -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	483
eee71789f13b Add LaplaceCurvilinear schemes 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 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	485
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	487 % op -- 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	488 % 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	489 function o = 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	490 assertIsMember(op, {'e', '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	491 assertIsMember(boundary, {'w', 'e', '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	492
eee71789f13b Add LaplaceCurvilinear schemes 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 o = 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	494 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	495
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	497 % 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	498 %
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	500 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	501 assertIsMember(boundary, {'w', 'e', '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	502
eee71789f13b Add LaplaceCurvilinear schemes 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 H_b = obj.(['H_', 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	504 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	505
eee71789f13b Add LaplaceCurvilinear schemes 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 % Returns square boundary quadrature scaling 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	507 % 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	508 %
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	510 function s_b = getBoundaryScaling(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	511 assertIsMember(boundary, {'w', 'e', '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	512
eee71789f13b Add LaplaceCurvilinear schemes 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 s_b = obj.(['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	514 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	515
eee71789f13b Add LaplaceCurvilinear schemes 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 % Returns the coordinate number corresponding to 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	517 %
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	519 function m = getBoundaryNumber(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	520 assertIsMember(boundary, {'w', 'e', '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	521
eee71789f13b Add LaplaceCurvilinear schemes 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 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	523 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	524 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	525 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	526 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	527 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	528 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	529
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	531 % 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	532 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	533 assertIsMember(boundary, {'w', 'e', '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	534
eee71789f13b Add LaplaceCurvilinear schemes 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 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	536 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	537 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	538 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	539 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	540 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	541 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	542 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	543 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	544 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	545 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	546 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	547
eee71789f13b Add LaplaceCurvilinear schemes 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 % 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	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 [theta_H, theta_M, theta_R] = getBoundaryBorrowing(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 assertIsMember(boundary, {'w', 'e', '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	552
eee71789f13b Add LaplaceCurvilinear schemes 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 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	554 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	555 theta_H = obj.theta_H_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	556 theta_M = obj.theta_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	557 theta_R = obj.theta_R_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	558 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	559 theta_H = obj.theta_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	560 theta_M = obj.theta_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	561 theta_R = obj.theta_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	562 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	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
eee71789f13b Add LaplaceCurvilinear schemes 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 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	566 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	567 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	568 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	569 end

Mercurial > repos > public > sbplib

annotate +scheme/LaplaceCurvilinearMin.m @ 1138:afd06a84b69c feature/laplace_curvilinear_test