Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 26:ed6a704b028d
Made some changes to error functions and comparison functions before finalizing convergence script.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Fri, 25 Sep 2015 14:54:26 +0200 |
| parents | 5f6b0b6a012b |
| children | 97a638f91fb8 |
| rev | line source |
|---|---|
| 0 | 1 classdef Wave2dCurve < scheme.Scheme |
| 2 properties | |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 h % Grid spacing | |
| 5 u,v % Grid | |
| 6 x,y % Values of x and y for each grid point | |
| 7 X,Y % Grid point locations as matrices | |
| 8 order % Order accuracy for the approximation | |
| 9 | |
| 10 D % non-stabalized scheme operator | |
| 11 M % Derivative norm | |
| 12 c | |
| 13 J, Ji | |
| 14 a11, a12, a22 | |
| 15 | |
| 16 H % Discrete norm | |
| 17 Hi | |
| 18 H_u, H_v % Norms in the x and y directions | |
| 19 Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. | |
| 20 Hi_u, Hi_v | |
| 21 Hiu, Hiv | |
| 22 e_w, e_e, e_s, e_n | |
| 23 du_w, dv_w | |
| 24 du_e, dv_e | |
| 25 du_s, dv_s | |
| 26 du_n, dv_n | |
| 27 gamm_u, gamm_v | |
| 28 end | |
| 29 | |
| 30 methods | |
| 31 function obj = Wave2dCurve(m,ti,order,c,opSet) | |
| 32 default_arg('opSet',@sbp.Variable); | |
| 33 | |
| 34 if length(m) == 1 | |
| 35 m = [m m]; | |
| 36 end | |
| 37 | |
| 38 m_u = m(1); | |
| 39 m_v = m(2); | |
| 40 m_tot = m_u*m_v; | |
| 41 | |
| 42 [u, h_u] = util.get_grid(0, 1, m_u); | |
| 43 [v, h_v] = util.get_grid(0, 1, m_v); | |
| 44 | |
| 45 | |
| 46 % Operators | |
| 47 ops_u = opSet(m_u,h_u,order); | |
| 48 ops_v = opSet(m_v,h_v,order); | |
| 49 | |
| 50 I_u = speye(m_u); | |
| 51 I_v = speye(m_v); | |
| 52 | |
| 53 D1_u = sparse(ops_u.derivatives.D1); | |
| 54 D2_u = ops_u.derivatives.D2; | |
| 55 H_u = sparse(ops_u.norms.H); | |
| 56 Hi_u = sparse(ops_u.norms.HI); | |
| 57 % M_u = sparse(ops_u.norms.M); | |
| 58 e_l_u = sparse(ops_u.boundary.e_1); | |
| 59 e_r_u = sparse(ops_u.boundary.e_m); | |
| 60 d1_l_u = sparse(ops_u.boundary.S_1); | |
| 61 d1_r_u = sparse(ops_u.boundary.S_m); | |
| 62 | |
| 63 D1_v = sparse(ops_v.derivatives.D1); | |
| 64 D2_v = ops_v.derivatives.D2; | |
| 65 H_v = sparse(ops_v.norms.H); | |
| 66 Hi_v = sparse(ops_v.norms.HI); | |
| 67 % M_v = sparse(ops_v.norms.M); | |
| 68 e_l_v = sparse(ops_v.boundary.e_1); | |
| 69 e_r_v = sparse(ops_v.boundary.e_m); | |
| 70 d1_l_v = sparse(ops_v.boundary.S_1); | |
| 71 d1_r_v = sparse(ops_v.boundary.S_m); | |
| 72 | |
| 73 | |
| 74 % Metric derivatives | |
| 75 [X,Y] = ti.map(u,v); | |
| 76 | |
| 77 [x_u,x_v] = gridDerivatives(X,D1_u,D1_v); | |
| 78 [y_u,y_v] = gridDerivatives(Y,D1_u,D1_v); | |
| 79 | |
| 80 | |
| 81 | |
| 82 J = x_u.*y_v - x_v.*y_u; | |
| 83 a11 = 1./J .* (x_v.^2 + y_v.^2); %% GÖR SOM MATRISER | |
| 84 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); | |
| 85 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 86 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 87 | |
| 88 dof_order = reshape(1:m_u*m_v,m_v,m_u); | |
| 89 | |
| 90 Duu = sparse(m_tot); | |
| 91 Dvv = sparse(m_tot); | |
| 92 | |
| 93 for i = 1:m_v | |
| 94 D = D2_u(a11(i,:)); | |
| 95 p = dof_order(i,:); | |
| 96 Duu(p,p) = D; | |
| 97 end | |
| 98 | |
| 99 for i = 1:m_u | |
| 100 D = D2_v(a22(:,i)); | |
| 101 p = dof_order(:,i); | |
| 102 Dvv(p,p) = D; | |
| 103 end | |
| 104 | |
| 105 L_12 = spdiags(a12(:),0,m_tot,m_tot); | |
| 106 Du = kr(D1_u,I_v); | |
| 107 Dv = kr(I_u,D1_v); | |
| 108 | |
| 109 Duv = Du*L_12*Dv; | |
| 110 Dvu = Dv*L_12*Du; | |
| 111 | |
| 112 | |
| 113 | |
| 114 obj.H = kr(H_u,H_v); | |
| 115 obj.Hi = kr(Hi_u,Hi_v); | |
| 116 obj.Hu = kr(H_u,I_v); | |
| 117 obj.Hv = kr(I_u,H_v); | |
| 118 obj.Hiu = kr(Hi_u,I_v); | |
| 119 obj.Hiv = kr(I_u,Hi_v); | |
| 120 | |
| 121 % obj.M = kr(M_u,H_v)+kr(H_u,M_v); | |
| 122 obj.e_w = kr(e_l_u,I_v); | |
| 123 obj.e_e = kr(e_r_u,I_v); | |
| 124 obj.e_s = kr(I_u,e_l_v); | |
| 125 obj.e_n = kr(I_u,e_r_v); | |
| 126 obj.du_w = kr(d1_l_u,I_v); | |
| 127 obj.dv_w = (obj.e_w'*Dv)'; | |
| 128 obj.du_e = kr(d1_r_u,I_v); | |
| 129 obj.dv_e = (obj.e_e'*Dv)'; | |
| 130 obj.du_s = (obj.e_s'*Du)'; | |
| 131 obj.dv_s = kr(I_u,d1_l_v); | |
| 132 obj.du_n = (obj.e_n'*Du)'; | |
| 133 obj.dv_n = kr(I_u,d1_r_v); | |
| 134 | |
| 135 obj.m = m; | |
| 136 obj.h = [h_u h_v]; | |
| 137 obj.order = order; | |
| 138 | |
| 139 | |
| 140 obj.c = c; | |
| 141 obj.J = spdiags(J(:),0,m_tot,m_tot); | |
| 142 obj.Ji = spdiags(1./J(:),0,m_tot,m_tot); | |
| 143 obj.a11 = a11; | |
| 144 obj.a12 = a12; | |
| 145 obj.a22 = a22; | |
| 146 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
| 147 obj.u = u; | |
| 148 obj.v = v; | |
| 149 obj.X = X; | |
| 150 obj.Y = Y; | |
| 151 obj.x = X(:); | |
| 152 obj.y = Y(:); | |
| 153 | |
| 154 obj.gamm_u = h_u*ops_u.borrowing.M.S; | |
| 155 obj.gamm_v = h_v*ops_v.borrowing.M.S; | |
| 156 end | |
| 157 | |
| 158 | |
| 159 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 160 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 161 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 162 % type is a string specifying the type of boundary condition if there are several. | |
| 163 % data is a function returning the data that should be applied at the boundary. | |
| 164 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 165 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 166 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 167 default_arg('type','neumann'); | |
| 168 default_arg('data',0); | |
| 169 | |
| 170 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 171 | |
| 172 switch type | |
| 173 % Dirichlet boundary condition | |
| 174 case {'D','d','dirichlet'} | |
| 175 error('not implemented') | |
| 176 alpha = obj.alpha; | |
| 177 | |
| 178 % tau1 < -alpha^2/gamma | |
| 179 tuning = 1.1; | |
| 180 tau1 = -tuning*alpha/gamm; | |
| 181 tau2 = s*alpha; | |
| 182 | |
| 183 p = tau1*e + tau2*d; | |
| 184 | |
| 185 closure = halfnorm_inv*p*e'; | |
| 186 | |
| 187 pp = halfnorm_inv*p; | |
| 188 switch class(data) | |
| 189 case 'double' | |
| 190 penalty = pp*data; | |
| 191 case 'function_handle' | |
| 192 penalty = @(t)pp*data(t); | |
| 193 otherwise | |
| 194 error('Weird data argument!') | |
| 195 end | |
| 196 | |
| 197 | |
| 198 % Neumann boundary condition | |
| 199 case {'N','n','neumann'} | |
| 200 c = obj.c; | |
| 201 | |
| 202 | |
| 203 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 204 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 205 d = (a_n * d_n' + a_t*d_t')'; | |
| 206 | |
| 207 tau1 = -s; | |
| 208 tau2 = 0; | |
| 209 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 210 | |
| 211 closure = halfnorm_inv*tau*d'; | |
| 212 | |
| 213 pp = halfnorm_inv*tau; | |
| 214 switch class(data) | |
| 215 case 'double' | |
| 216 penalty = pp*data; | |
| 217 case 'function_handle' | |
| 218 penalty = @(t)pp*data(t); | |
| 219 otherwise | |
| 220 error('Weird data argument!') | |
| 221 end | |
| 222 | |
| 223 % Unknown, boundary condition | |
| 224 otherwise | |
| 225 error('No such boundary condition: type = %s',type); | |
| 226 end | |
| 227 end | |
| 228 | |
| 229 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 230 % u denotes the solution in the own domain | |
| 231 % v denotes the solution in the neighbour domain | |
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232 tuning = 1.2; |
| 0 | 233 [e_u, d_n_u, d_t_u, coeff_n_u, coeff_t_u, s_u, gamm_u, halfnorm_inv_u_n, halfnorm_inv_u_t, halfnorm_u_t] = obj.get_boundary_ops(boundary); |
| 234 [e_v, d_n_v, d_t_v, coeff_n_v, coeff_t_v, s_v, gamm_v, halfnorm_inv_v_n, halfnorm_inv_v_t, halfnorm_v_t] = neighbour_scheme.get_boundary_ops(boundary); | |
| 235 | |
| 236 F_u = s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u'; | |
| 237 F_v = s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v'; | |
| 238 | |
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239 u = obj; |
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240 v = neighbour_scheme; |
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241 |
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242 b1_u = gamm_u*u.lambda./u.a11.^2; |
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243 b2_u = gamm_u*u.lambda./u.a22.^2; |
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244 b1_v = gamm_v*v.lambda./v.a11.^2; |
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245 b2_v = gamm_v*v.lambda./v.a22.^2; |
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246 |
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247 |
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248 tau = -1./(4*b1_u) -1/(4*b1_v) -1/(4*b2_u) -1/(4*b2_v); |
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249 m_tot = obj.m(1)*obj.m(2); |
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250 tau = tuning * spdiags(tau(:),0,m_tot,m_tot); |
| 0 | 251 sig1 = 1/2; |
| 252 sig2 = -1/2; | |
| 253 | |
| 254 penalty_parameter_1 = s_u*halfnorm_inv_u_n*(tau + sig1*halfnorm_inv_u_t*F_u'*halfnorm_u_t)*e_u; | |
| 255 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; | |
| 256 | |
| 257 | |
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parents:
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258 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
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259 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' - penalty_parameter_2*F_v'); |
| 0 | 260 end |
| 261 | |
| 262 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 263 % The right boundary is considered the positive boundary | |
| 264 function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t] = get_boundary_ops(obj,boundary) | |
| 265 switch boundary | |
| 266 case 'w' | |
| 267 e = obj.e_w; | |
| 268 d_n = obj.du_w; | |
| 269 d_t = obj.dv_w; | |
| 270 s = -1; | |
| 271 | |
| 272 coeff_n = obj.a11(:,1); | |
| 273 coeff_t = obj.a12(:,1); | |
| 274 case 'e' | |
| 275 e = obj.e_e; | |
| 276 d_n = obj.du_e; | |
| 277 d_t = obj.dv_e; | |
| 278 s = 1; | |
| 279 | |
| 280 coeff_n = obj.a11(:,end); | |
| 281 coeff_t = obj.a12(:,end); | |
| 282 case 's' | |
| 283 e = obj.e_s; | |
| 284 d_n = obj.dv_s; | |
| 285 d_t = obj.du_s; | |
| 286 s = -1; | |
| 287 | |
| 288 coeff_n = obj.a22(1,:)'; | |
| 289 coeff_t = obj.a12(1,:)'; | |
| 290 case 'n' | |
| 291 e = obj.e_n; | |
| 292 d_n = obj.dv_n; | |
| 293 d_t = obj.du_n; | |
| 294 s = 1; | |
| 295 | |
| 296 coeff_n = obj.a22(end,:)'; | |
| 297 coeff_t = obj.a12(end,:)'; | |
| 298 otherwise | |
| 299 error('No such boundary: boundary = %s',boundary); | |
| 300 end | |
| 301 | |
| 302 switch boundary | |
| 303 case {'w','e'} | |
| 304 halfnorm_inv_n = obj.Hiu; | |
| 305 halfnorm_inv_t = obj.Hiv; | |
| 306 halfnorm_t = obj.Hv; | |
| 307 gamm = obj.gamm_u; | |
| 308 case {'s','n'} | |
| 309 halfnorm_inv_n = obj.Hiv; | |
| 310 halfnorm_inv_t = obj.Hiu; | |
| 311 halfnorm_t = obj.Hu; | |
| 312 gamm = obj.gamm_v; | |
| 313 end | |
| 314 end | |
| 315 | |
| 316 function N = size(obj) | |
| 317 N = prod(obj.m); | |
| 318 end | |
| 319 | |
| 320 end | |
| 321 | |
| 322 methods(Static) | |
| 323 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 324 % and bound_v of scheme schm_v. | |
| 325 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 326 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 327 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 328 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 329 end | |
| 330 end | |
| 331 end |