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annotate +scheme/Schrodinger1dCurve.m @ 495:b91d23271481 feature/quantumTriangles

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Added new penalty parameter to the interface in shrodinger curve
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 24 Feb 2017 09:04:02 +0100
parents 6b8297f66c91
children 437fad4a47e1
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef Schrodinger1dCurve < 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 xi % Grid
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6 order % Order accuracy for the approximation
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7 grid
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8
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9 D % non-stabalized scheme operator
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10 H % Discrete norm
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11 M % Derivative norm
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12 alpha
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13
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14 V_mat
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15 D1
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16 D2
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17 Hi
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18 e_l
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19 e_r
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20 d1_l
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21 d1_r
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22 gamm
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23 end
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24
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25 methods
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26 % Solving SE in the form u_t = i*u_xx +i*V on deforming 1D domain;
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27 function obj = Schrodinger1dCurve(g,m,order,V,constJi)
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28 default_arg('V',0);
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29 default_arg('constJi',false)
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30 xilim={0 1};
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31 if constJi
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32 ops = sbp.D2Standard(m,xilim,order);
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33 else
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34 ops = sbp.D4Variable(m,xilim,order);
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35 end
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36
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37 obj.xi=ops.x;
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38 obj.h=ops.h;
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39 obj.D2 = ops.D2;
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40 obj.D1 = ops.D1;
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41 obj.H = ops.H;
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42 obj.Hi = ops.HI;
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43 obj.M = ops.M;
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44 obj.e_l = ops.e_l;
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45 obj.e_r = ops.e_r;
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46 obj.d1_l = ops.d1_l;
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47 obj.d1_r = ops.d1_r;
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48 obj.grid = g;
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49
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50
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51 if isa(V,'function_handle')
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52 V_vec = V(obj.x);
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53 else
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54 V_vec = obj.xi*0 + V;
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55 end
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56
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57 obj.V_mat = spdiags(V_vec,0,m,m);
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58 obj.D = @(a,a_xi,Ji) obj.d_fun(a, a_xi, Ji, constJi);
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59 obj.m = m;
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60 obj.order = order;
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61 end
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62
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63
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64 % Closure functions return the opertors appliedo to the own doamin to close the boundary
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65 % 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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66 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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67 % type is a string specifying the type of boundary condition if there are several.
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68 % data is a function returning the data that should be applied at the boundary.
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69 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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70 % neighbour_boundary is a string specifying which boundary to interface to.
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71
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72 function [D] = d_fun(obj,a, a_xi , Ji , constJi)
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73 if constJi
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74 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*Ji*obj.D2 + 1i*obj.V_mat;
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75 else
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76 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
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77 end
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78 end
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79
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80 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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81 default_arg('type','dirichlet');
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82 default_arg('data',0);
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83
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84 [e,d,s,p] = obj.get_boundary_ops(boundary);
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85
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86 switch type
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87 % Dirichlet boundary condition
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88 case {'D','d','dirichlet'}
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89 tau1 = s * 1i*d;
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90 tau2 = @(a) (-1*s*a(p,p) - abs(a(p,p)))/4*e;
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91 closure = @(a) obj.Hi*tau1*e' + obj.Hi*tau2(a)*e';
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92
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93 switch class(data)
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94 case 'double'
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95 penalty = @(a) -(obj.Hi*tau1*data+obj.Hi*tau2(a)*data);
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96 % case 'function_handle'
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97 % penalty = @(t)-obj.Hi*tau*data(t);
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98 otherwise
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99 error('Wierd data argument!')
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100 end
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101
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102 % Unknown, boundary condition
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103 otherwise
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104 error('No such boundary condition: type = %s',type);
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105 end
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106 end
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107
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108 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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109 % u denotes the solution in the own domain
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110 % v denotes the solution in the neighbour domain
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111 [e_u,d_u,s_u,p_u] = obj.get_boundary_ops(boundary);
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112 [e_v,d_v,s_v,p_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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113
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114 a1 = -s_u* 1/2 * 1i ;
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115 b1 = a1';
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116 gamma = -1*s*a(p_u,p_u)/2;
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117
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118 tau = b1*d_u;
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119 sig = -a1*e_u;
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120
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121 closure = @(a) obj.Hi * (tau*e_u' + sig*d_u' + gamma(a));
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122 penalty = @(a) obj.Hi * (-tau*e_v' - sig*d_v' - gamma(a));
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123 end
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124
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125 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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126 % The right boundary is considered the positive boundary
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127 function [e,d,s,p] = get_boundary_ops(obj,boundary)
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128 switch boundary
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129 case 'l'
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130 e = obj.e_l;
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131 d = obj.d1_l;
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132 s = -1;
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133 p=1;
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134 case 'r'
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135 e = obj.e_r;
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136 d = obj.d1_r;
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137 s = 1;
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138 p=obj.m;
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139 otherwise
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140 error('No such boundary: boundary = %s',boundary);
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141 end
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142 end
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143
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144 function N = size(obj)
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145 N = obj.m;
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146 end
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147
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148 end
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149
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150 methods(Static)
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151 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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152 % and bound_v of scheme schm_v.
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153 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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154 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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155 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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156 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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157 end
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158 end
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159 end