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annotate +scheme/Schrodinger1dCurve.m @ 429:dde5760863de feature/quantumTriangles

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Added a scheme for the time deforming shrodinger equation in 1d
author Ylva Rydin <ylva.rydin@telia.com>
date Mon, 06 Feb 2017 09:54:18 +0100
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children 25053554524b
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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(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
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49
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50 if isa(V,'function_handle')
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51 V_vec = V(obj.x);
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52 else
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53 V_vec = obj.xi*0 + V;
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54 end
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55
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56 obj.V_mat = spdiags(V_vec,0,m,m);
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57
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58 obj.D = @(a,a_xi,Ji) obj.d_fun(a, a_xi, Ji, constJi);
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59
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60 obj.m = m;
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61 obj.order = order;
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62 end
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63
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64
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65 % Closure functions return the opertors appliedo to the own doamin to close the boundary
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66 % 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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67 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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68 % type is a string specifying the type of boundary condition if there are several.
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69 % data is a function returning the data that should be applied at the boundary.
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70 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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71 % neighbour_boundary is a string specifying which boundary to interface to.
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72
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73 function [D] = d_fun(obj,a, a_xi , Ji , constJi)
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74 if constJi
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75 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*Ji*obj.D2 + 1i*obj.V_mat;
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76 % D= -a*obj.D1 + 1i*Ji*obj.D2 + 1i*obj.V_mat;
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77 else
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78 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
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79 % D= - a*obj.D1 + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
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80 % D=-obj.D1*a - a_xi + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
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81 end
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82 end
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83
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84 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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85 default_arg('type','dirichlet');
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86 default_arg('data',0);
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87
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88 [e,d,s,p] = obj.get_boundary_ops(boundary);
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89
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90 switch type
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91 % Dirichlet boundary condition
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92 case {'D','d','dirichlet'}
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93 tau1 = s * 1i*d;
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94 tau2 = @(a) (-1*s*a(p,p) - abs(a(p,p)))/4*e;
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95 closure = @(a) obj.Hi*tau1*e' + obj.Hi*tau2(a)*e';
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96
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97 switch class(data)
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98 case 'double'
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99 penalty = @(a) -(obj.Hi*tau1*data+obj.Hi*tau2(a)*data);
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100 % case 'function_handle'
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101 % penalty = @(t)-obj.Hi*tau*data(t);
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102 otherwise
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103 error('Wierd data argument!')
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104 end
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105
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106 % Unknown, boundary condition
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107 otherwise
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108 error('No such boundary condition: type = %s',type);
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109 end
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110 end
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111
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112 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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113 % u denotes the solution in the own domain
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114 % v denotes the solution in the neighbour domain
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115 % [e_u,d_u,s_u] = obj.get_boundary_ops(boundary);
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116 % [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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117
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118 % a = -s_u* 1/2 * 1i ;
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119 % b = a';
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120
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121 % tau = b*d_u;
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122 % sig = -a*e_u;
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123
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124 % closure = obj.Hi * (tau*e_u' + sig*d_u');
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125 % penalty = obj.Hi * (-tau*e_v' - sig*d_v');
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126 end
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127
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128 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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129 % The right boundary is considered the positive boundary
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130 function [e,d,s,p] = get_boundary_ops(obj,boundary)
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131 switch boundary
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132 case 'l'
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133 e = obj.e_l;
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134 d = obj.d1_l;
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135 s = -1;
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136 p=1;
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137 case 'r'
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138 e = obj.e_r;
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139 d = obj.d1_r;
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140 s = 1;
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141 p=obj.m;
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142 otherwise
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143 error('No such boundary: boundary = %s',boundary);
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144 end
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145 end
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146
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147 function N = size(obj)
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148 N = obj.m;
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149 end
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150
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151 end
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152
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153 methods(Static)
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154 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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155 % and bound_v of scheme schm_v.
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156 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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157 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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158 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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159 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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160 end
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161 end
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162 end