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annotate +scheme/Schrodinger1dCurve.m @ 511:57f3493f851b feature/quantumTriangles

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Added sqrt of Ji in the right places, not sure about the interfaces, will not test it properly now
author Ylva Rydin <ylva.rydin@telia.com>
date Thu, 08 Jun 2017 10:33:36 +0200
parents 508b7493be94
children 32a24485f3e8
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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 x_r
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14 x_l
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15 ddt_x_r
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16 ddt_x_l
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17 a
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18 a_xi
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19 Ji
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20 J
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21 t_up
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22 x
429
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23
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24 V_mat
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25 D1
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26 D2
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27 Hi
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28 e_l
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29 e_r
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30 d1_l
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31 d1_r
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32 gamm
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33 end
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34
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35 methods
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36 % Solving SE in the form u_t = i*u_xx +i*V on deforming 1D domain;
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37 function obj = Schrodinger1dCurve(g,order,boundaries,V,constJi)
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38 default_arg('V',0);
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39 default_arg('constJi',false)
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40 xilim={0 1};
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41 m = N(g);
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42 if constJi
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43 ops = sbp.D2Standard(m,xilim,order);
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44 else
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45 ops = sbp.D4Variable(m,xilim,order);
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46 end
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47
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48 obj.x_l = boundaries{1};
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49 obj.x_r = boundaries{2};
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50 obj.ddt_x_l = boundaries{3};
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51 obj.ddt_x_r = boundaries{4};
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52
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53 obj.xi=ops.x;
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54 obj.h=ops.h;
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55 obj.D2 = ops.D2;
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56 obj.D1 = ops.D1;
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57 obj.H = ops.H;
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58 obj.Hi = ops.HI;
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59 obj.M = ops.M;
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60 obj.e_l = ops.e_l;
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61 obj.e_r = ops.e_r;
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62 obj.d1_l = ops.d1_l;
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63 obj.d1_r = ops.d1_r;
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64 obj.grid = g;
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65
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66 if isa(V,'function_handle')
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67 V_vec = V(obj.x);
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68 else
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69 V_vec = obj.xi*0 + V;
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70 end
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71
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72 obj.V_mat = spdiags(V_vec,0,m,m);
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73 obj.D = @(t) obj.d_fun(t);
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74 obj.m = m;
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75 obj.order = order;
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76 end
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77
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78
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79 % Closure functions return the opertors appliedo to the own doamin to close the boundary
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80 % 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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81 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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82 % type is a string specifying the type of boundary condition if there are several.
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83 % data is a function returning the data that should be applied at the boundary.
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84 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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85 % neighbour_boundary is a string specifying which boundary to interface to.
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86
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87 function [D] = d_fun(obj,t)
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88 obj.variable_update(t); % In driscretization?
511
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89 D = sqrt(obj.Ji)*(-0.5*(obj.D1*obj.a + obj.a*obj.D1) + 1i*obj.D2(diag(obj.Ji)) + 1i*obj.V_mat)*sqrt(obj.Ji);
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90 % D = (-0.5*(obj.D1*obj.a -obj.a_xi+ obj.a*obj.D1) + 1i*obj.D2(diag(obj.Ji)) + 1i*obj.V_mat);
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91 % D= obj.Ji*(-sqrt(obj.a)*obj.D1*sqrt(obj.a) + 0.5*obj.a_xi + 1i*obj.D2(diag(obj.Ji)) + 1i*obj.V_mat);
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92 end
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93
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94
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95 function [] = variable_update(obj,t)
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96 if (t == obj.t_up)
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97 return
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98 else
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99 x_r = obj.x_r(t);
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100 x_l = obj.x_l(t);
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101 ddt_x_r = obj. ddt_x_r(t);
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102 ddt_x_l = obj.ddt_x_l(t);
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103 obj.x = obj.xi*(x_r -x_l) + x_l;
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104 obj.a = sparse(diag((-ddt_x_l*( x_r - x_l) - (obj.x-x_l)*(ddt_x_r-ddt_x_l))/(x_r-x_l)));
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105
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106 obj.Ji = sparse(diag(1./(x_r - x_l + 0*obj.x)));
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107 obj.J = sparse(x_r -x_l);
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108 obj.a_xi = sparse(diag(-1*(ddt_x_r - ddt_x_l + 0*obj.x)));
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109 obj.t_up = t;
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110 end
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111 end
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112
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113 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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114 default_arg('type','dirichlet');
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115 default_arg('data',0);
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116
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117 [e,d,s,p] = obj.get_boundary_ops(boundary);
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118
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119 switch type
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120 % Dirichlet boundary condition
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121 case {'D','d','dirichlet'}
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122 tau1 = @(t) s * 1i*obj.Ji(p,p)*d;
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123 tau2 = @(t) (1*s*obj.a(p,p))/2*e;
511
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124 closure = @(t)obj.Hi*sqrt(obj.Ji)*(tau1(t)*e' + tau2(obj.a)*e')*sqrt(obj.Ji);
429
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125
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126 switch class(data)
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127 case 'double'
511
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128 penalty = @(t) -obj.Hi*sqrt(obj.Ji)*(tau1*data+tau2(obj.a)*data)*sqrt(obj.Ji);
429
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129 % case 'function_handle'
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130 % penalty = @(t)-obj.Hi*tau*data(t);
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131 otherwise
508
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132 error('Weird data argument!')
429
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133 end
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134
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135 % Unknown, boundary condition
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136 otherwise
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137 error('No such boundary condition: type = %s',type);
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138 end
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139 end
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140
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141 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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142 % u denotes the solution in the own domain
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143 % v denotes the solution in the neighbour domain
496
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144 [e_u,d_u,s_u,p_u] = obj.get_boundary_ops(boundary);
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145 [e_v,d_v,s_v,p_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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146
498
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147 a1 = s_u* 1/2 * 1i ;
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148 b1 = -s_u* 1/2 * 1i;
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149 gamma = @(a) s_u*a(p_u,p_u)/2*e_u;
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150
498
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151 tau = @(t) a1*obj.Ji(p_u,p_u)^2*d_u;
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152 sig = b1*e_u;
495
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153
511
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154 closure = @(t) obj.Hi * (tau(t)*e_u' + sig*obj.Ji(p_u,p_u)^2*d_u' + obj.Ji(p_u,p_u)*gamma(obj.a)*e_u');
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155 penalty = @(t) obj.Hi * (-tau(t)*e_v' - sig*obj.Ji(p_u,p_u)^2*d_v' - obj.Ji(p_u,p_u)*gamma(obj.a)*e_v');
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156 end
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157
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158 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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159 % The right boundary is considered the positive boundary
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160 function [e,d,s,p] = get_boundary_ops(obj,boundary)
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161 switch boundary
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162 case 'l'
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163 e = obj.e_l;
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164 d = obj.d1_l;
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165 s = -1;
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166 p=1;
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167 case 'r'
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168 e = obj.e_r;
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169 d = obj.d1_r;
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170 s = 1;
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171 p=obj.m;
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172 otherwise
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173 error('No such boundary: boundary = %s',boundary);
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174 end
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175 end
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176
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177 function N = size(obj)
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178 N = obj.m;
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179 end
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180
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181 end
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182
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183 methods(Static)
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184 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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185 % and bound_v of scheme schm_v.
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186 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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187 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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188 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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189 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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190 end
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191 end
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192 end