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annotate +scheme/Schrodinger2dCurve.m @ 497:4905446f165e feature/quantumTriangles

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Added 2D interface to shrodinger
author Ylva Rydin <ylva.rydin@telia.com>
date Sat, 25 Feb 2017 12:44:01 +0100
parents 6b8297f66c91
children 324c927d8b1d
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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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6b95a894cbd7 fixed a bug in the metric coefficients but something is wrong at the boundaries
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22 x,y
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23 b1, b2
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24 b1_u,b2_v
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25 DU, DV, DUU, DUV, DVU, DVV
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26
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27 e_w, e_e, e_s, e_n
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28 du_w, dv_w
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29 du_e, dv_e
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30 du_s, dv_s
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31 du_n, dv_n
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32 g_1, g_2
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33 c
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34 ind
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35 t_up
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36
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37 a11, a12, a22
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38 m_tot, m_u, m_v
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39 p
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40 Ji
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41 end
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42
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43 methods
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44 function obj = Schrodinger2dCurve(g ,order, opSet,p)
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45 default_arg('opSet',@sbp.D2Variable);
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46 default_arg('c', 1);
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47
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48 obj.p=p;
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49 obj.c=1;
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50
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51 m = g.size();
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52 obj.m_u = m(1);
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53 obj.m_v = m(2);
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54 obj.m_tot = g.N();
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55 obj.grid=g;
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56
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57 h = g.scaling();
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58 h_u = h(1);
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59 h_v = h(2);
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60
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61 % Operators
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62 ops_u = opSet(obj.m_u, {0, 1}, order);
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63 ops_v = opSet(obj.m_v, {0, 1}, order);
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64
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65 I_u = speye(obj.m_u);
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66 I_v = speye(obj.m_v);
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67
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68 obj.D1_u = ops_u.D1;
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69 obj.D2_u = ops_u.D2;
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70
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71 H_u = ops_u.H;
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72 Hi_u = ops_u.HI;
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73 e_l_u = ops_u.e_l;
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74 e_r_u = ops_u.e_r;
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75 d1_l_u = ops_u.d1_l;
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76 d1_r_u = ops_u.d1_r;
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77
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78 obj.D1_v = ops_v.D1;
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79 obj.D2_v = ops_v.D2;
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80 H_v = ops_v.H;
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81 Hi_v = ops_v.HI;
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82 e_l_v = ops_v.e_l;
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83 e_r_v = ops_v.e_r;
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84 d1_l_v = ops_v.d1_l;
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85 d1_r_v = ops_v.d1_r;
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86
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87 obj.Du = kr(obj.D1_u,I_v);
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88 obj.Dv = kr(I_u,obj.D1_v);
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89
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90 obj.H = kr(H_u,H_v);
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91 obj.Hi = kr(Hi_u,Hi_v);
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92 obj.Hu = kr(H_u,I_v);
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93 obj.Hv = kr(I_u,H_v);
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94 obj.Hiu = kr(Hi_u,I_v);
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95 obj.Hiv = kr(I_u,Hi_v);
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96
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97 obj.e_w = kr(e_l_u,I_v);
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98 obj.e_e = kr(e_r_u,I_v);
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99 obj.e_s = kr(I_u,e_l_v);
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100 obj.e_n = kr(I_u,e_r_v);
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101 obj.du_w = kr(d1_l_u,I_v);
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102 obj.dv_w = (obj.e_w'*obj.Dv)';
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103 obj.du_e = kr(d1_r_u,I_v);
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104 obj.dv_e = (obj.e_e'*obj.Dv)';
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105 obj.du_s = (obj.e_s'*obj.Du)';
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106 obj.dv_s = kr(I_u,d1_l_v);
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107 obj.du_n = (obj.e_n'*obj.Du)';
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108 obj.dv_n = kr(I_u,d1_r_v);
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109
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110 obj.DUU = sparse(obj.m_tot);
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111 obj.DVV = sparse(obj.m_tot);
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112 obj.ind = grid.funcToMatrix(obj.grid, 1:obj.m_tot);
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113
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114 obj.m = m;
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115 obj.h = [h_u h_v];
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116 obj.order = order;
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117 obj.D = @(t)obj.d_fun(t);
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118 obj.variable_update(0);
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119 end
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120
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121 function [D] = d_fun(obj,t)
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122 % obj.update_vairables(t); In driscretization?
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123 D = obj.Ji*(-1/2*(obj.b1*obj.Du-obj.b1_u+obj.Du*obj.b1) - 1/2*(obj.b2*obj.Dv - obj.b2_v +obj.Dv*obj.b2) + 1i*obj.c^2*(obj.DUU + obj.DUV + obj.DVU + obj.DVV));
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124
497
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125 end
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126
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127
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128 function [D ]= variable_update(obj,t)
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129 % Metric derivatives
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130 if(obj.t_up == t)
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131 return
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132 else
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133 ti = parametrization.Ti.points(obj.p{1}(t),obj.p{2}(t),obj.p{3}(t),obj.p{4}(t));
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134 ti_tau = parametrization.Ti.points(obj.p{5}(t),obj.p{6}(t),obj.p{7}(t),obj.p{8}(t));
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diff changeset
135
4905446f165e Added 2D interface to shrodinger
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parents: 493
diff changeset
136 lcoords=points(obj.grid);
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
137 [obj.xm,obj.ym]= ti.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2));
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parents: 493
diff changeset
138 [x_tau,y_tau]= ti_tau.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2));
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parents: 493
diff changeset
139 x = reshape(obj.xm,obj.m_tot,1);
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parents: 493
diff changeset
140 y = reshape(obj.ym,obj.m_tot,1);
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diff changeset
141 obj.x = x;
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parents: 493
diff changeset
142 obj.y = y;
4905446f165e Added 2D interface to shrodinger
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diff changeset
143
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
144 x_tau = reshape(x_tau,obj.m_tot,1);
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parents: 493
diff changeset
145 y_tau = reshape(y_tau,obj.m_tot,1);
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diff changeset
146
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
147 x_u = obj.Du*x;
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
148 x_v = obj.Dv*x;
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
149 y_u = obj.Du*y;
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parents: 493
diff changeset
150 y_v = obj.Dv*y;
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
151
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
152 J = x_u.*y_v - x_v.*y_u;
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
153 a11 = 1./J.* (x_v.^2 + y_v.^2);
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parents: 493
diff changeset
154 a12 = -1./J .* (x_u.*x_v + y_u.*y_v);
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
155 a22 = 1./J .* (x_u.^2 + y_u.^2);
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parents: 493
diff changeset
156
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
157 obj.a11 = a11;
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
158 obj.a12 = a12;
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
159 obj.a22 = a22;
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diff changeset
160
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
161 % Assemble full operators
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diff changeset
162 L_12 = spdiags(a12, 0, obj.m_tot, obj.m_tot);
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parents: 493
diff changeset
163 obj.DUV = obj.Du*L_12*obj.Dv;
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parents: 493
diff changeset
164 obj.DVU = obj.Dv*L_12*obj.Du;
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diff changeset
165
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diff changeset
166
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
167 for i = 1:obj.m_v
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parents: 493
diff changeset
168 D = obj.D2_u(a11(obj.ind(:,i)));
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diff changeset
169 p = obj.ind(:,i);
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diff changeset
170 obj.DUU(p,p) = D;
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diff changeset
171 end
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diff changeset
172
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diff changeset
173 for i = 1:obj.m_u
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parents: 493
diff changeset
174 D = obj.D2_v(a22(obj.ind(i,:)));
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diff changeset
175 p = obj.ind(i,:);
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diff changeset
176 obj.DVV(p,p) = D;
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diff changeset
177 end
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diff changeset
178
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diff changeset
179 Ji = spdiags(1./J, 0, obj.m_tot, obj.m_tot);
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diff changeset
180 obj.Ji = Ji;
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diff changeset
181 obj.g_1 = x_v.*y_tau-x_tau.*y_v;
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diff changeset
182 obj.g_2 = x_tau.*y_u - y_tau.*x_u;
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diff changeset
183
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parents: 493
diff changeset
184 obj.b1 = spdiags(obj.g_1, 0, obj.m_tot, obj.m_tot);
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diff changeset
185 obj.b2 = spdiags(obj.g_2, 0, obj.m_tot, obj.m_tot);
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diff changeset
186
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Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
187 obj.b1_u = spdiags(obj.Du*obj.g_1, 0, obj.m_tot, obj.m_tot);
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diff changeset
188 obj.b2_v = spdiags(obj.Dv*obj.g_2, 0, obj.m_tot, obj.m_tot);
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parents: 493
diff changeset
189 obj.t_up=t;
490
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190 end
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parents:
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191 end
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diff changeset
192
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parents:
diff changeset
193 % Closure functions return the opertors applied to the own doamin to close the boundary
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diff changeset
194 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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diff changeset
195 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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196 % type is a string specifying the type of boundary condition if there are several.
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diff changeset
197 % data is a function returning the data that should be applied at the boundary.
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diff changeset
198 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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diff changeset
199 % neighbour_boundary is a string specifying which boundary to interface to.
497
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diff changeset
200 function [closure, penalty] = boundary_condition(obj, boundary,~)
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diff changeset
201 [e, d_n, d_t, coeff_t, coeff_n s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g] = obj.get_boundary_ops(boundary);
491
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diff changeset
202
490
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diff changeset
203 a_t = spdiag(coeff_t);
497
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diff changeset
204 a_n = spdiag(coeff_n);
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diff changeset
205 F = (s * a_n *d_n' + s * a_t*d_t')';
491
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diff changeset
206 tau1 = 1;
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diff changeset
207 a = spdiag(g);
490
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diff changeset
208 tau2 = (-1*s*a - abs(a))/4;
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diff changeset
209
497
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diff changeset
210 penalty_parameter_1 = @(t) 1*1i*halfnorm_inv_n*halfnorm_inv_t*F*e'*halfnorm_t*e;
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parents: 493
diff changeset
211 penalty_parameter_2 = @(t) halfnorm_inv_n*e*tau2;
490
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diff changeset
212
497
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diff changeset
213 closure = @(t) obj.Ji*obj.c^2 * penalty_parameter_1(t)*e' + obj.Ji* penalty_parameter_2(t)*e';
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parents: 493
diff changeset
214 penalty = @(t) -obj.Ji*obj.c^2 * penalty_parameter_1(t)*e'+ obj.Ji*penalty_parameter_2(t)*e';
490
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diff changeset
215
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diff changeset
216 end
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
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diff changeset
217
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diff changeset
218 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
497
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diff changeset
219 % u denotes the solution in the own domain
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diff changeset
220 % v denotes the solution in the neighbour domain
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
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diff changeset
221 [e_u, d_n_u, d_t_u, coeff_t_u, coeff_n_u,s_u, halfnorm_inv_u_n, halfnorm_inv_u_t, halfnorm_u_t,gamm_u, I_u] = obj.get_boundary_ops(boundary);
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parents: 493
diff changeset
222 [e_v, d_n_v, d_t_v, coeff_t_v, coeff_n_v s_v, halfnorm_inv_v_n, halfnorm_inv_v_t, halfnorm_v_t,gamm_v, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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diff changeset
223
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
224 a_n_u = spdiag(coeff_n_u);
4905446f165e Added 2D interface to shrodinger
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parents: 493
diff changeset
225 a_t_u = spdiag(coeff_t_u);
4905446f165e Added 2D interface to shrodinger
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diff changeset
226 a_n_v = spdiag(coeff_n_v);
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parents: 493
diff changeset
227 a_t_v = spdiag(coeff_t_v);
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diff changeset
228
4905446f165e Added 2D interface to shrodinger
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diff changeset
229 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')';
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parents: 493
diff changeset
230 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')';
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diff changeset
231
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parents: 493
diff changeset
232 a = spdiag(gamm_u);
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diff changeset
233
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diff changeset
234 u = obj;
4905446f165e Added 2D interface to shrodinger
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parents: 493
diff changeset
235 v = neighbour_scheme;
4905446f165e Added 2D interface to shrodinger
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diff changeset
236
4905446f165e Added 2D interface to shrodinger
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diff changeset
237 tau = -1/2*1i;
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
238 sig = 1/2*1i;
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
239 gamm = (-1*s_u*a)/2;
4905446f165e Added 2D interface to shrodinger
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parents: 493
diff changeset
240
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
241 penalty_parameter_1 =@(t) halfnorm_inv_u_n*(e_u*tau + sig*halfnorm_inv_u_t*F_u*e_u'*halfnorm_u_t*e_u);
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
242 penalty_parameter_2 =@(t) halfnorm_inv_u_n * e_u * (-sig + gamm );
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parents: 493
diff changeset
243
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
244 closure =@(t) obj.Ji*obj.c^2 * ( penalty_parameter_1(t)*e_u' + penalty_parameter_2(t)*F_u');
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parents: 493
diff changeset
245 penalty =@(t) obj.Ji*obj.c^2 * (-penalty_parameter_1(t)*e_v' + penalty_parameter_2(t)*F_v');
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
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parents: 490
diff changeset
246 end
490
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parents:
diff changeset
247
497
4905446f165e Added 2D interface to shrodinger
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diff changeset
248
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parents: 493
diff changeset
249 function [e, d_n, d_t, coeff_t,coeff_n, s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g, I] = get_boundary_ops(obj, boundary)
490
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parents:
diff changeset
250
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diff changeset
251 % gridMatrix = zeros(obj.m(2),obj.m(1));
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diff changeset
252 % gridMatrix(:) = 1:numel(gridMatrix);
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parents:
diff changeset
253
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parents:
diff changeset
254 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
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diff changeset
255
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parents:
diff changeset
256 switch boundary
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
257 case 'w'
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parents:
diff changeset
258 e = obj.e_w;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
259 d_n = obj.du_w;
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parents:
diff changeset
260 d_t = obj.dv_w;
b13d44271ead Schrodinger2dCurve Added
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
261 s = -1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
262
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parents:
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263 I = ind(1,:);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
264 coeff_t = obj.a12(I);
497
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
265 coeff_n = obj.a11(I);
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents: 490
diff changeset
266 g=obj.g_1(I);
490
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Ylva Rydin <ylva.rydin@telia.com>
parents:
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267 case 'e'
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Ylva Rydin <ylva.rydin@telia.com>
parents:
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268 e = obj.e_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
269 d_n = obj.du_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
270 d_t = obj.dv_e;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
271 s = 1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
272
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
273 I = ind(end,:);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
274 coeff_t = obj.a12(I);
497
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
275 coeff_n = obj.a11(I);
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents: 490
diff changeset
276 g=obj.g_1(I);
490
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
277 case 's'
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
278 e = obj.e_s;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
279 d_n = obj.dv_s;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
280 d_t = obj.du_s;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
281 s = -1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
282
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
283 I = ind(:,1)';
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
284 coeff_t = obj.a12(I);
497
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
285 coeff_n = obj.a11(I);
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents: 490
diff changeset
286 g=obj.g_2(I);
490
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
287 case 'n'
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
288 e = obj.e_n;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
289 d_n = obj.dv_n;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
290 d_t = obj.du_n;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
291 s = 1;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
292
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
293 I = ind(:,end)';
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
294 coeff_t = obj.a12(I);
497
4905446f165e Added 2D interface to shrodinger
Ylva Rydin <ylva.rydin@telia.com>
parents: 493
diff changeset
295 coeff_n = obj.a11(I);
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents: 490
diff changeset
296 g=obj.g_2(I);
490
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
297 otherwise
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
298 error('No such boundary: boundary = %s',boundary);
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parents:
diff changeset
299 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
300
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
301 switch boundary
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
302 case {'w','e'}
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
303 halfnorm_inv_n = obj.Hiu;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
304 halfnorm_inv_t = obj.Hiv;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
305 halfnorm_t = obj.Hv;
491
26125cfefe11 Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents: 490
diff changeset
306
490
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
307 case {'s','n'}
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
308 halfnorm_inv_n = obj.Hiv;
b13d44271ead Schrodinger2dCurve Added
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
309 halfnorm_inv_t = obj.Hiu;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
310 halfnorm_t = obj.Hu;
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
311 end
b13d44271ead Schrodinger2dCurve Added
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
312 end
b13d44271ead Schrodinger2dCurve Added
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
313
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
314 function N = size(obj)
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
315 N = prod(obj.m);
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
316 end
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Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
317 end
b13d44271ead Schrodinger2dCurve Added
Ylva Rydin <ylva.rydin@telia.com>
parents:
diff changeset
318 end