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annotate +scheme/Schrodinger1dCurve.m @ 498:324c927d8b1d feature/quantumTriangles

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chnaged sbp interfacein 1d among many things
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 03 Mar 2017 16:19:41 +0100
parents 437fad4a47e1
children b7280c6c6b9a
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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 t_up
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21 x
429
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22
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23 V_mat
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24 D1
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25 D2
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26 Hi
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27 e_l
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28 e_r
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29 d1_l
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30 d1_r
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31 gamm
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32 end
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33
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34 methods
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35 % Solving SE in the form u_t = i*u_xx +i*V on deforming 1D domain;
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36 function obj = Schrodinger1dCurve(g,order,boundaries,V,constJi)
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37 default_arg('V',0);
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38 default_arg('constJi',false)
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39 xilim={0 1};
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40 m = N(g);
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41 if constJi
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42 ops = sbp.D2Standard(m,xilim,order);
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43 else
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44 ops = sbp.D4Variable(m,xilim,order);
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45 end
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46
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47 obj.x_l = boundaries{1};
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48 obj.x_r = boundaries{2};
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49 obj.ddt_x_l = boundaries{3};
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50 obj.ddt_x_r = boundaries{4};
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51
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52 obj.xi=ops.x;
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53 obj.h=ops.h;
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54 obj.D2 = ops.D2;
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55 obj.D1 = ops.D1;
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56 obj.H = ops.H;
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57 obj.Hi = ops.HI;
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58 obj.M = ops.M;
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59 obj.e_l = ops.e_l;
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60 obj.e_r = ops.e_r;
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61 obj.d1_l = ops.d1_l;
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62 obj.d1_r = ops.d1_r;
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63 obj.grid = g;
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64
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65 if isa(V,'function_handle')
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66 V_vec = V(obj.x);
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67 else
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68 V_vec = obj.xi*0 + V;
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69 end
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70
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71 obj.V_mat = spdiags(V_vec,0,m,m);
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72 obj.D = @(t) obj.d_fun(t);
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73 obj.m = m;
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74 obj.order = order;
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75 end
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76
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77
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78 % Closure functions return the opertors appliedo to the own doamin to close the boundary
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79 % 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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80 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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81 % type is a string specifying the type of boundary condition if there are several.
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82 % data is a function returning the data that should be applied at the boundary.
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83 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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84 % neighbour_boundary is a string specifying which boundary to interface to.
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85
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86 function [D] = d_fun(obj,t)
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87 % obj.update_vairables(t); In driscretization?
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88 D= obj.Ji*(-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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89
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90 end
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91
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92
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93 function [] = variable_update(obj,t)
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94 if (t == obj.t_up)
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95 return
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96 else
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97 x_r = obj.x_r(t);
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98 x_l = obj.x_l(t);
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99 ddt_x_r = obj. ddt_x_r(t);
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100 ddt_x_l = obj.ddt_x_l(t);
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101 obj.x = obj.xi*(x_r -x_l) + x_l;
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102 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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103
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104 obj.Ji = sparse(diag(1./(x_r - x_l + 0*obj.x)));
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105 obj.a_xi = sparse(diag(-1*(ddt_x_r - ddt_x_l + 0*obj.x)));
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106 obj.t_up = t;
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107 end
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108 end
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109
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110 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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111 default_arg('type','dirichlet');
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112 default_arg('data',0);
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113
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114 [e,d,s,p] = obj.get_boundary_ops(boundary);
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115
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116 switch type
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117 % Dirichlet boundary condition
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118 case {'D','d','dirichlet'}
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119 tau1 = @(t) s * 1i*obj.Ji(p,p)^2*d;
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120 tau2 = @(t) obj.Ji*(-1*s*obj.a(p,p) - abs(obj.a(p,p)))/4*e;
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121 closure = @(t) obj.Hi*tau1(t)*e' + obj.Hi*tau2(obj.a)*e';
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122
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123 switch class(data)
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124 case 'double'
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125 penalty = @(t) -obj.Ji*(obj.Hi*tau1*data+obj.Hi*tau2(obj.a)*data);
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126 % case 'function_handle'
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127 % penalty = @(t)-obj.Hi*tau*data(t);
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128 otherwise
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129 error('Wierd data argument!')
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130 end
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131
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132 % Unknown, boundary condition
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133 otherwise
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134 error('No such boundary condition: type = %s',type);
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135 end
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136 end
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137
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138 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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139 % u denotes the solution in the own domain
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140 % v denotes the solution in the neighbour domain
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141 [e_u,d_u,s_u,p_u] = obj.get_boundary_ops(boundary);
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142 [e_v,d_v,s_v,p_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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143
498
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144 a1 = s_u* 1/2 * 1i ;
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145 b1 = -s_u* 1/2 * 1i;
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146 gamma = @(a) -obj.Ji*s_u*a(p_u,p_u)/2*e_u;
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147
498
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148 tau = @(t) a1*obj.Ji(p_u,p_u)^2*d_u;
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149 sig = b1*e_u;
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150
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151 closure = @(t) obj.Hi * (tau(t)*e_u' + sig*obj.Ji(p_u,p_u)^2*d_u' + gamma(obj.a)*e_u');
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152 penalty = @(t) obj.Hi * (-tau(t)*e_v' - sig*obj.Ji(p_u,p_u)^2*d_v' - gamma(obj.a)*e_v');
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153 end
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154
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155 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
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156 % The right boundary is considered the positive boundary
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157 function [e,d,s,p] = get_boundary_ops(obj,boundary)
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158 switch boundary
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159 case 'l'
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160 e = obj.e_l;
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161 d = obj.d1_l;
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162 s = -1;
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163 p=1;
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164 case 'r'
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165 e = obj.e_r;
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166 d = obj.d1_r;
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167 s = 1;
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168 p=obj.m;
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169 otherwise
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170 error('No such boundary: boundary = %s',boundary);
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171 end
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172 end
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173
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174 function N = size(obj)
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175 N = obj.m;
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176 end
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177
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178 end
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179
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180 methods(Static)
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181 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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182 % and bound_v of scheme schm_v.
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183 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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184 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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185 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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186 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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187 end
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188 end
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189 end