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annotate +scheme/Schrodinger2dCurve.m~ @ 491:26125cfefe11 feature/quantumTriangles

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Schrodinger 2d runs without exploding with fixed coordinates
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 10 Feb 2017 14:29:53 +0100
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1 classdef Schrodinger2dCurve < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5
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6 grid
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7 xm, ym
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8
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9 order % Order accuracy for the approximation
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10
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11 D % non-stabalized scheme operator
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12 M % Derivative norm
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13 H % Discrete norm
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14 Hi
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15 H_u, H_v % Norms in the x and y directions
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16 Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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17 Hi_u, Hi_v
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18 Hiu, Hiv
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19 D1_v, D1_u
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20 D2_v, D2_u
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21 Du, Dv
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22
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23
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24 e_w, e_e, e_s, e_n
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25 du_w, dv_w
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26 du_e, dv_e
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27 du_s, dv_s
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28 du_n, dv_n
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29 g_1, g_2
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30 c
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31 a11, a12, a22
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32 m_tot, m_u, m_v
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33 p,p_tau
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34 Ji
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35 end
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36
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37 methods
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38 function obj = Schrodinger2dCurve(g ,order, opSet,p,p_tau)
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39 default_arg('opSet',@sbp.D2Variable);
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40 default_arg('c', 1);
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41
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42 obj.p=p;
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43 obj.p_tau=p_tau;
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44 obj.c=1;
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45
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46 m = g.size();
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47 obj.m_u = m(1);
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48 obj.m_v = m(2);
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49 obj.m_tot = g.N();
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50
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51 h = g.scaling();
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52 h_u = h(1);
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53 h_v = h(2);
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54
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55 % Operators
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56 ops_u = opSet(obj.m_u, {0, 1}, order);
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57 ops_v = opSet(obj.m_v, {0, 1}, order);
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58
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59 I_u = speye(obj.m_u);
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60 I_v = speye(obj.m_v);
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61
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62 obj.D1_u = ops_u.D1;
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63 obj.D2_u = ops_u.D2;
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64
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65 H_u = ops_u.H;
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66 Hi_u = ops_u.HI;
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67 e_l_u = ops_u.e_l;
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68 e_r_u = ops_u.e_r;
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69 d1_l_u = ops_u.d1_l;
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70 d1_r_u = ops_u.d1_r;
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71
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72 obj.D1_v = ops_v.D1;
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73 obj.D2_v = ops_v.D2;
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74 H_v = ops_v.H;
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75 Hi_v = ops_v.HI;
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76 e_l_v = ops_v.e_l;
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77 e_r_v = ops_v.e_r;
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78 d1_l_v = ops_v.d1_l;
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79 d1_r_v = ops_v.d1_r;
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80
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81 obj.Du = kr(obj.D1_u,I_v);
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82 obj.Dv = kr(I_u,obj.D1_v);
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83
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84 obj.H = kr(H_u,H_v);
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85 obj.Hi = kr(Hi_u,Hi_v);
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86 obj.Hu = kr(H_u,I_v);
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87 obj.Hv = kr(I_u,H_v);
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88 obj.Hiu = kr(Hi_u,I_v);
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89 obj.Hiv = kr(I_u,Hi_v);
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90
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91 obj.e_w = kr(e_l_u,I_v);
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92 obj.e_e = kr(e_r_u,I_v);
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93 obj.e_s = kr(I_u,e_l_v);
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94 obj.e_n = kr(I_u,e_r_v);
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95 obj.du_w = kr(d1_l_u,I_v);
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96 obj.dv_w = (obj.e_w'*obj.Dv)';
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97 obj.du_e = kr(d1_r_u,I_v);
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98 obj.dv_e = (obj.e_e'*obj.Dv)';
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99 obj.du_s = (obj.e_s'*obj.Du)';
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100 obj.dv_s = kr(I_u,d1_l_v);
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101 obj.du_n = (obj.e_n'*obj.Du)';
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102 obj.dv_n = kr(I_u,d1_r_v);
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103
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104 % obj.x_u = x_u;
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105 % obj.x_v = x_v;
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106 % obj.y_u = y_u;
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107 % obj.y_v = y_v;
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108
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109 obj.m = m;
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110 obj.h = [h_u h_v];
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111 obj.order = order;
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112 obj.grid = g;
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113
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114
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115 end
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116
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117
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118 function [D ]= d_fun(obj,t)
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119 % Metric derivatives
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120 ti = parametrization.Ti.points(obj.p.p1(t),obj.p.p2(t),obj.p.p3(t),obj.p.p4(t));
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121 ti_tau = parametrization.Ti.points(obj.p_tau.p1(t),obj.p_tau.p2(t),obj.p_tau.p3(t),obj.p_tau.p4(t));
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122
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123 lcoords=points(obj.grid);
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124 [obj.xm,obj.ym]= ti.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2));
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125 [x_tau,y_tau]= ti_tau.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2));
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126 x = reshape(obj.xm,obj.m_tot,1);
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127 y = reshape(obj.ym,obj.m_tot,1);
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128
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129 x_tau = reshape(x_tau,obj.m_tot,1);
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130 y_tau = reshape(y_tau,obj.m_tot,1);
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131
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
132 x_u = obj.Du*x;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
133 x_v = obj.Dv*x;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
134 y_u = obj.Du*y;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
135 y_v = obj.Dv*y;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
136
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
137 J = x_u.*y_v - x_v.*y_u;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
138 a11 = 1./J.* (x_v.^2 + y_v.^2);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
139 a12 = -1./J .* (x_u.*x_v + y_u.*y_v);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
140 a22 = 1./J .* (x_u.^2 + y_u.^2);
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diff changeset
141
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
142 obj.a11=a11;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
143 obj.a12=a12;
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Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
144 obj.a22=a22;
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diff changeset
145
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
146 % Assemble full operators
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
147 L_12 = spdiags(a12, 0, obj.m_tot, obj.m_tot);
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diff changeset
148 Duv = obj.Du*L_12*obj.Dv;
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parents:
diff changeset
149 Dvu = obj.Dv*L_12*obj.Du;
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diff changeset
150
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
151 Duu = sparse(obj.m_tot);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
152 Dvv = sparse(obj.m_tot);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
153 ind = grid.funcToMatrix(obj.grid, 1:obj.m_tot);
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diff changeset
154
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diff changeset
155
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
156 for i = 1:obj.m_v
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
157 D = obj.D2_u(a11(ind(:,i)));
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diff changeset
158 p = ind(:,i);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
159 Duu(p,p) = D;
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parents:
diff changeset
160 end
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parents:
diff changeset
161
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
162 for i = 1:obj.m_u
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Ylva Rydin <ylva.rydin@telia.com>
parents:
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163 D = obj.D2_v(a22(ind(i,:)));
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parents:
diff changeset
164 p = ind(i,:);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
165 Dvv(p,p) = D;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
166 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
167
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
168 Ji = spdiags(1./J, 0, obj.m_tot, obj.m_tot);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
169 obj.Ji=Ji;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
170 obj.g_1 = x_tau.*y_v-y_tau.*x_v;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
171 obj.g_2 = -x_tau.*y_u + y_tau.*x_u;
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parents:
diff changeset
172
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
173 %Add the flux splitting
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
174 D = Ji*(obj.g_1.*obj.Du + obj.g_2.*obj.Dv + 1i*obj.c^2*(Duu + Duv + Dvu + Dvv)); %% g_1' och g_2'?
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
175
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
176 % obj.gamm_u = h_u*ops_u.borrowing.M.d1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
177 % obj.gamm_v = h_v*ops_v.borrowing.M.d1;
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parents:
diff changeset
178
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
179 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
180
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
181 % Closure functions return the opertors applied to the own doamin to close the boundary
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
182 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
183 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
184 % type is a string specifying the type of boundary condition if there are several.
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
185 % data is a function returning the data that should be applied at the boundary.
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
186 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
187 % neighbour_boundary is a string specifying which boundary to interface to.
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
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parents:
diff changeset
188 function [closure, penalty] = boundary_condition(obj, boundary)
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
189 [e, d_n, d_t, coeff_t, s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g] = obj.get_boundary_ops(boundary);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
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parents:
diff changeset
190
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
191 a_t = spdiag(coeff_t);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
192 F = (s * d_n' + s * a_t*d_t')';
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
193 tau1 = 1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
194 a = spdiag(g);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
195 tau2 = (-1*s*a - abs(a))/4;
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parents:
diff changeset
196
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parents:
diff changeset
197 penalty_parameter_1 = 1i*halfnorm_inv_n*halfnorm_inv_t*e*e'*F*halfnorm_t;
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parents:
diff changeset
198 penalty_parameter_2 = halfnorm_inv_n*e*tau2;
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diff changeset
199
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
200 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e' +obj.Ji* penalty_parameter_2*e';
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
201 % penalty = -obj.Ji*obj.c^2 * penalty_parameter_2;
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parents:
diff changeset
202 penalty=0;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
203
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
204 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
205
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
206 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
207 end
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
208
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
209 function [e, d_n, d_t, coeff_t, s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g, I] = get_boundary_ops(obj, boundary)
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parents:
diff changeset
210
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
211 % gridMatrix = zeros(obj.m(2),obj.m(1));
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
212 % gridMatrix(:) = 1:numel(gridMatrix);
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parents:
diff changeset
213
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
214 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
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parents:
diff changeset
215
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
216 switch boundary
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
217 case 'w'
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
218 e = obj.e_w;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
219 d_n = obj.du_w;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
220 d_t = obj.dv_w;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
221 s = -1;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
222
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
223 I = ind(1,:);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
224 coeff_t = obj.a12(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
225 g=obj.g_1(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
226 case 'e'
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
227 e = obj.e_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
228 d_n = obj.du_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
229 d_t = obj.dv_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
230 s = 1;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
231
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
232 I = ind(end,:);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
233 coeff_t = obj.a12(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
234 g=obj.g_1(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
235 case 's'
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
236 e = obj.e_s;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
237 d_n = obj.dv_s;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
238 d_t = obj.du_s;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
239 s = -1;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
240
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
241 I = ind(:,1)';
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
242 coeff_t = obj.a12(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
243 g=obj.g_2(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
244 case 'n'
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
245 e = obj.e_n;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
246 d_n = obj.dv_n;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
247 d_t = obj.du_n;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
248 s = 1;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
249
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
250 I = ind(:,end)';
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
251 coeff_t = obj.a12(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
252 g=obj.g_2(I);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
253 otherwise
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
254 error('No such boundary: boundary = %s',boundary);
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
255 end
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
256
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
257 switch boundary
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
258 case {'w','e'}
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
259 halfnorm_inv_n = obj.Hiu;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
260 halfnorm_inv_t = obj.Hiv;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
261 halfnorm_t = obj.Hv;
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
262
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
263 case {'s','n'}
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
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264 halfnorm_inv_n = obj.Hiv;
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265 halfnorm_inv_t = obj.Hiu;
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266 halfnorm_t = obj.Hu;
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267 end
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268 end
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269
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270 function N = size(obj)
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271 N = prod(obj.m);
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272 end
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273
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274
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275 end
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276 end