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annotate +scheme/Schrodinger2dCurve.m @ 491:26125cfefe11 feature/quantumTriangles
Schrodinger 2d runs without exploding with fixed coordinates
| author | Ylva Rydin <ylva.rydin@telia.com> |
|---|---|
| date | Fri, 10 Feb 2017 14:29:53 +0100 |
| parents | +grid/Schrodinger2dCurve.m@b13d44271ead |
| children | 6b95a894cbd7 |
| rev | line source |
|---|---|
| 490 | 1 classdef Schrodinger2dCurve < scheme.Scheme |
| 2 properties | |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 h % Grid spacing | |
| 5 | |
| 6 grid | |
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7 xm, ym |
| 490 | 8 |
| 9 order % Order accuracy for the approximation | |
| 10 | |
| 11 D % non-stabalized scheme operator | |
| 12 M % Derivative norm | |
| 13 H % Discrete norm | |
| 14 Hi | |
| 15 H_u, H_v % Norms in the x and y directions | |
| 16 Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. | |
| 17 Hi_u, Hi_v | |
| 18 Hiu, Hiv | |
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19 D1_v, D1_u |
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20 D2_v, D2_u |
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21 Du, Dv |
| 490 | 22 |
| 23 | |
| 24 e_w, e_e, e_s, e_n | |
| 25 du_w, dv_w | |
| 26 du_e, dv_e | |
| 27 du_s, dv_s | |
| 28 du_n, dv_n | |
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29 g_1, g_2 |
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30 c |
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31 a11, a12, a22 |
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32 m_tot, m_u, m_v |
| 490 | 33 p,p_tau |
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34 Ji |
| 490 | 35 end |
| 36 | |
| 37 methods | |
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38 function obj = Schrodinger2dCurve(g ,order, opSet,p,p_tau) |
| 490 | 39 default_arg('opSet',@sbp.D2Variable); |
| 40 default_arg('c', 1); | |
| 41 | |
| 42 obj.p=p; | |
| 43 obj.p_tau=p_tau; | |
| 44 obj.c=1; | |
| 45 | |
| 46 m = g.size(); | |
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47 obj.m_u = m(1); |
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48 obj.m_v = m(2); |
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49 obj.m_tot = g.N(); |
| 490 | 50 |
| 51 h = g.scaling(); | |
| 52 h_u = h(1); | |
| 53 h_v = h(2); | |
| 54 | |
| 55 % Operators | |
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56 ops_u = opSet(obj.m_u, {0, 1}, order); |
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57 ops_v = opSet(obj.m_v, {0, 1}, order); |
| 490 | 58 |
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59 I_u = speye(obj.m_u); |
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60 I_v = speye(obj.m_v); |
| 490 | 61 |
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62 obj.D1_u = ops_u.D1; |
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63 obj.D2_u = ops_u.D2; |
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64 |
| 490 | 65 H_u = ops_u.H; |
| 66 Hi_u = ops_u.HI; | |
| 67 e_l_u = ops_u.e_l; | |
| 68 e_r_u = ops_u.e_r; | |
| 69 d1_l_u = ops_u.d1_l; | |
| 70 d1_r_u = ops_u.d1_r; | |
| 71 | |
| 72 obj.D1_v = ops_v.D1; | |
| 73 obj.D2_v = ops_v.D2; | |
| 74 H_v = ops_v.H; | |
| 75 Hi_v = ops_v.HI; | |
| 76 e_l_v = ops_v.e_l; | |
| 77 e_r_v = ops_v.e_r; | |
| 78 d1_l_v = ops_v.d1_l; | |
| 79 d1_r_v = ops_v.d1_r; | |
| 80 | |
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81 obj.Du = kr(obj.D1_u,I_v); |
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82 obj.Dv = kr(I_u,obj.D1_v); |
| 490 | 83 |
| 84 obj.H = kr(H_u,H_v); | |
| 85 obj.Hi = kr(Hi_u,Hi_v); | |
| 86 obj.Hu = kr(H_u,I_v); | |
| 87 obj.Hv = kr(I_u,H_v); | |
| 88 obj.Hiu = kr(Hi_u,I_v); | |
| 89 obj.Hiv = kr(I_u,Hi_v); | |
| 90 | |
| 91 obj.e_w = kr(e_l_u,I_v); | |
| 92 obj.e_e = kr(e_r_u,I_v); | |
| 93 obj.e_s = kr(I_u,e_l_v); | |
| 94 obj.e_n = kr(I_u,e_r_v); | |
| 95 obj.du_w = kr(d1_l_u,I_v); | |
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96 obj.dv_w = (obj.e_w'*obj.Dv)'; |
| 490 | 97 obj.du_e = kr(d1_r_u,I_v); |
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98 obj.dv_e = (obj.e_e'*obj.Dv)'; |
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99 obj.du_s = (obj.e_s'*obj.Du)'; |
| 490 | 100 obj.dv_s = kr(I_u,d1_l_v); |
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101 obj.du_n = (obj.e_n'*obj.Du)'; |
| 490 | 102 obj.dv_n = kr(I_u,d1_r_v); |
| 103 | |
| 104 % obj.x_u = x_u; | |
| 105 % obj.x_v = x_v; | |
| 106 % obj.y_u = y_u; | |
| 107 % obj.y_v = y_v; | |
| 108 | |
| 109 obj.m = m; | |
| 110 obj.h = [h_u h_v]; | |
| 111 obj.order = order; | |
| 112 obj.grid = g; | |
| 113 | |
| 114 | |
| 115 end | |
| 116 | |
| 117 | |
| 118 function [D ]= d_fun(obj,t) | |
| 119 % Metric derivatives | |
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120 ti = parametrization.Ti.points(obj.p.p1(t),obj.p.p2(t),obj.p.p3(t),obj.p.p4(t)); |
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121 ti_tau = parametrization.Ti.points(obj.p_tau.p1(t),obj.p_tau.p2(t),obj.p_tau.p3(t),obj.p_tau.p4(t)); |
| 490 | 122 |
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123 lcoords=points(obj.grid); |
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124 [obj.xm,obj.ym]= ti.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2)); |
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125 [x_tau,y_tau]= ti_tau.map(lcoords(1:obj.m_v:end,1),lcoords(1:obj.m_u,2)); |
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126 x = reshape(obj.xm,obj.m_tot,1); |
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127 y = reshape(obj.ym,obj.m_tot,1); |
| 490 | 128 |
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129 x_tau = reshape(x_tau,obj.m_tot,1); |
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130 y_tau = reshape(y_tau,obj.m_tot,1); |
| 490 | 131 |
| 132 x_u = obj.Du*x; | |
| 133 x_v = obj.Dv*x; | |
| 134 y_u = obj.Du*y; | |
| 135 y_v = obj.Dv*y; | |
| 136 | |
| 137 J = x_u.*y_v - x_v.*y_u; | |
| 138 a11 = 1./J.* (x_v.^2 + y_v.^2); | |
| 139 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); | |
| 140 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
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141 |
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142 obj.a11=a11; |
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143 obj.a12=a12; |
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144 obj.a22=a22; |
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145 |
| 490 | 146 % Assemble full operators |
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147 L_12 = spdiags(a12, 0, obj.m_tot, obj.m_tot); |
| 490 | 148 Duv = obj.Du*L_12*obj.Dv; |
| 149 Dvu = obj.Dv*L_12*obj.Du; | |
| 150 | |
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151 Duu = sparse(obj.m_tot); |
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152 Dvv = sparse(obj.m_tot); |
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153 ind = grid.funcToMatrix(obj.grid, 1:obj.m_tot); |
| 490 | 154 |
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155 |
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156 for i = 1:obj.m_v |
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157 D = obj.D2_u(a11(ind(:,i))); |
| 490 | 158 p = ind(:,i); |
| 159 Duu(p,p) = D; | |
| 160 end | |
| 161 | |
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162 for i = 1:obj.m_u |
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163 D = obj.D2_v(a22(ind(i,:))); |
| 490 | 164 p = ind(i,:); |
| 165 Dvv(p,p) = D; | |
| 166 end | |
| 167 | |
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168 Ji = spdiags(1./J, 0, obj.m_tot, obj.m_tot); |
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169 obj.Ji=Ji; |
| 490 | 170 obj.g_1 = x_tau.*y_v-y_tau.*x_v; |
| 171 obj.g_2 = -x_tau.*y_u + y_tau.*x_u; | |
| 172 | |
| 173 %Add the flux splitting | |
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174 D = Ji*(obj.g_1.*obj.Du + obj.g_2.*obj.Dv + 1i*obj.c^2*(Duu + Duv + Dvu + Dvv)); %% g_1' och g_2'? |
| 490 | 175 |
| 176 % obj.gamm_u = h_u*ops_u.borrowing.M.d1; | |
| 177 % obj.gamm_v = h_v*ops_v.borrowing.M.d1; | |
| 178 | |
| 179 end | |
| 180 | |
| 181 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 182 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 183 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 184 % type is a string specifying the type of boundary condition if there are several. | |
| 185 % data is a function returning the data that should be applied at the boundary. | |
| 186 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 187 % neighbour_boundary is a string specifying which boundary to interface to. | |
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188 function [closure, penalty] = boundary_condition(obj, boundary) |
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189 [e, d_n, d_t, coeff_t, s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g] = obj.get_boundary_ops(boundary); |
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190 |
| 490 | 191 a_t = spdiag(coeff_t); |
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192 F = (s * d_n' + s * a_t*d_t')'; |
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193 tau1 = 1; |
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194 a = spdiag(g); |
| 490 | 195 tau2 = (-1*s*a - abs(a))/4; |
| 196 | |
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197 penalty_parameter_1 = 1*1i*halfnorm_inv_n*halfnorm_inv_t*e*F'*halfnorm_t*e; |
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198 penalty_parameter_2 = halfnorm_inv_n*e*tau2; |
| 490 | 199 |
| 200 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e' +obj.Ji* penalty_parameter_2*e'; | |
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201 % penalty = -obj.Ji*obj.c^2 * penalty_parameter_2; |
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202 penalty=0; |
| 490 | 203 |
| 204 end | |
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205 |
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206 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) |
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207 end |
| 490 | 208 |
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209 function [e, d_n, d_t, coeff_t, s, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g, I] = get_boundary_ops(obj, boundary) |
| 490 | 210 |
| 211 % gridMatrix = zeros(obj.m(2),obj.m(1)); | |
| 212 % gridMatrix(:) = 1:numel(gridMatrix); | |
| 213 | |
| 214 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); | |
| 215 | |
| 216 switch boundary | |
| 217 case 'w' | |
| 218 e = obj.e_w; | |
| 219 d_n = obj.du_w; | |
| 220 d_t = obj.dv_w; | |
| 221 s = -1; | |
| 222 | |
| 223 I = ind(1,:); | |
| 224 coeff_t = obj.a12(I); | |
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225 g=obj.g_1(I); |
| 490 | 226 case 'e' |
| 227 e = obj.e_e; | |
| 228 d_n = obj.du_e; | |
| 229 d_t = obj.dv_e; | |
| 230 s = 1; | |
| 231 | |
| 232 I = ind(end,:); | |
| 233 coeff_t = obj.a12(I); | |
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Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
490
diff
changeset
|
234 g=obj.g_1(I); |
| 490 | 235 case 's' |
| 236 e = obj.e_s; | |
| 237 d_n = obj.dv_s; | |
| 238 d_t = obj.du_s; | |
| 239 s = -1; | |
| 240 | |
| 241 I = ind(:,1)'; | |
| 242 coeff_t = obj.a12(I); | |
|
491
26125cfefe11
Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
490
diff
changeset
|
243 g=obj.g_2(I); |
| 490 | 244 case 'n' |
| 245 e = obj.e_n; | |
| 246 d_n = obj.dv_n; | |
| 247 d_t = obj.du_n; | |
| 248 s = 1; | |
| 249 | |
| 250 I = ind(:,end)'; | |
| 251 coeff_t = obj.a12(I); | |
|
491
26125cfefe11
Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
490
diff
changeset
|
252 g=obj.g_2(I); |
| 490 | 253 otherwise |
| 254 error('No such boundary: boundary = %s',boundary); | |
| 255 end | |
| 256 | |
| 257 switch boundary | |
| 258 case {'w','e'} | |
| 259 halfnorm_inv_n = obj.Hiu; | |
| 260 halfnorm_inv_t = obj.Hiv; | |
| 261 halfnorm_t = obj.Hv; | |
|
491
26125cfefe11
Schrodinger 2d runs without exploding with fixed coordinates
Ylva Rydin <ylva.rydin@telia.com>
parents:
490
diff
changeset
|
262 |
| 490 | 263 case {'s','n'} |
| 264 halfnorm_inv_n = obj.Hiv; | |
| 265 halfnorm_inv_t = obj.Hiu; | |
| 266 halfnorm_t = obj.Hu; | |
| 267 end | |
| 268 end | |
| 269 | |
| 270 function N = size(obj) | |
| 271 N = prod(obj.m); | |
| 272 end | |
| 273 | |
| 274 | |
| 275 end | |
| 276 end |