annotate +scheme/Schrodinger.m @ 1301:8978521b0f06 default

Fix incorrect package name.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 08 Jul 2020 19:11:04 +0200
parents 0c504a21432d
children
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65
33f0654a2413 Fixed mistakes in Schrodinger scheme. BC are now working.
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1 classdef Schrodinger < scheme.Scheme
0
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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 x % Grid
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6 order % Order accuracy for the approximation
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7
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8 D % non-stabalized scheme operator
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9 H % Discrete norm
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10 M % Derivative norm
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11 alpha
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12
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13 D2
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14 Hi
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15 e_l
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16 e_r
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17 d1_l
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18 d1_r
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19 gamm
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20 end
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21
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22 methods
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23 % Solving SE in the form u_t = i*u_xx -i*V;
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24 function obj = Schrodinger(m,xlim,order,V)
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25 default_arg('V',0);
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26
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27 [x, h] = util.get_grid(xlim{:},m);
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28
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29 ops = sbp.Ordinary(m,h,order);
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30
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31 obj.D2 = sparse(ops.derivatives.D2);
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32 obj.H = sparse(ops.norms.H);
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33 obj.Hi = sparse(ops.norms.HI);
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34 obj.M = sparse(ops.norms.M);
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35 obj.e_l = sparse(ops.boundary.e_1);
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36 obj.e_r = sparse(ops.boundary.e_m);
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37 obj.d1_l = sparse(ops.boundary.S_1);
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38 obj.d1_r = sparse(ops.boundary.S_m);
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39
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40
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41 if isa(V,'function_handle')
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42 V_vec = V(x);
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43 else
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44 V_vec = x*0 + V;
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45 end
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46
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47 V_mat = spdiags(V_vec,0,m,m);
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49 obj.D = 1i * obj.D2 - 1i * V_mat;
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50
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51 obj.m = m;
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52 obj.h = h;
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53 obj.order = order;
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54
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55 obj.x = x;
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56 end
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57
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58
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59 % Closure functions return the opertors applied to the own doamin to close the boundary
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60 % 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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61 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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62 % type is a string specifying the type of boundary condition if there are several.
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63 % data is a function returning the data that should be applied at the boundary.
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64 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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65 % neighbour_boundary is a string specifying which boundary to interface to.
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66 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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67 default_arg('type','dirichlet');
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68 default_arg('data',0);
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69
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70 [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary);
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71 s = obj.getBoundarySign(boundary);
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72
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73 switch type
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74 % Dirichlet boundary condition
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75 case {'D','d','dirichlet'}
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76 tau = s * 1i*d;
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77 closure = obj.Hi*tau*e';
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78
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79 switch class(data)
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80 case 'double'
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81 penalty = -obj.Hi*tau*data;
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82 case 'function_handle'
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83 penalty = @(t)-obj.Hi*tau*data(t);
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84 otherwise
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85 error('Wierd data argument!')
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86 end
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87
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88 % Unknown, boundary condition
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89 otherwise
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90 error('No such boundary condition: type = %s',type);
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91 end
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92 end
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93
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94 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type)
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95 % u denotes the solution in the own domain
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96 % v denotes the solution in the neighbour domain
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97 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary);
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98 s_u = obj.getBoundarySign(boundary);
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99
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100 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary);
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101 s_v = neighbour_scheme.getBoundarySign(neighbour_boundary);
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102
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103 a = -s_u* 1/2 * 1i ;
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104 b = a';
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105
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106 tau = b*d_u;
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107 sig = -a*e_u;
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108
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109 closure = obj.Hi * (tau*e_u' + sig*d_u');
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110 penalty = obj.Hi * (-tau*e_v' - sig*d_v');
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111 end
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112
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113 % Returns the boundary operator op for the boundary specified by the string boundary.
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114 % op -- string or a cell array of strings
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115 % boundary -- string
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116 function varargout = getBoundaryOperator(obj, op, boundary)
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117 assertIsMember(boundary, {'l', 'r'})
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118
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119 if ~iscell(op)
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120 op = {op};
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121 end
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122
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123 for i = 1:numel(op)
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124 switch op{i}
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125 case 'e'
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126 switch boundary
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127 case 'l'
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128 e = obj.e_l;
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129 case 'r'
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130 e = obj.e_r;
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131 end
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132 varargout{i} = e;
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133
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134 case 'd'
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135 switch boundary
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136 case 'l'
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137 d = obj.d1_l;
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138 case 'r'
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139 d = obj.d1_r;
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140 end
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141 varargout{i} = d;
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142 end
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143 end
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144 end
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145
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146 % Returns square boundary quadrature matrix, of dimension
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147 % corresponding to the number of boundary points
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148 %
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149 % boundary -- string
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150 % Note: for 1d diffOps, the boundary quadrature is the scalar 1.
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151 function H_b = getBoundaryQuadrature(obj, boundary)
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152 assertIsMember(boundary, {'l', 'r'})
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153
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154 H_b = 1;
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155 end
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156
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157 % Returns the boundary sign. The right boundary is considered the positive boundary
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158 % boundary -- string
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159 function s = getBoundarySign(obj, boundary)
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160 assertIsMember(boundary, {'l', 'r'})
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161
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162 switch boundary
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163 case {'r'}
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164 s = 1;
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165 case {'l'}
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166 s = -1;
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167 end
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168 end
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169
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170 function N = size(obj)
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171 N = obj.m;
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172 end
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173
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174 end
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175 end