Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 201:38f203f00f3a feature/grids
Exeendend tests of multiblock.DiffOp.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 14 Jun 2016 15:07:34 +0200 |
| parents | 19d0c9325a3e |
| children | f18142c1530b |
| 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 | |
|
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parents:
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28 lambda |
| 0 | 29 end |
| 30 | |
| 31 methods | |
| 32 function obj = Wave2dCurve(m,ti,order,c,opSet) | |
| 33 default_arg('opSet',@sbp.Variable); | |
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34 default_arg('c', 1); |
| 0 | 35 |
| 36 if length(m) == 1 | |
| 37 m = [m m]; | |
| 38 end | |
| 39 | |
| 40 m_u = m(1); | |
| 41 m_v = m(2); | |
| 42 m_tot = m_u*m_v; | |
| 43 | |
| 44 [u, h_u] = util.get_grid(0, 1, m_u); | |
| 45 [v, h_v] = util.get_grid(0, 1, m_v); | |
| 46 | |
| 47 | |
| 48 % Operators | |
| 49 ops_u = opSet(m_u,h_u,order); | |
| 50 ops_v = opSet(m_v,h_v,order); | |
| 51 | |
| 52 I_u = speye(m_u); | |
| 53 I_v = speye(m_v); | |
| 54 | |
| 55 D1_u = sparse(ops_u.derivatives.D1); | |
| 56 D2_u = ops_u.derivatives.D2; | |
| 57 H_u = sparse(ops_u.norms.H); | |
| 58 Hi_u = sparse(ops_u.norms.HI); | |
| 59 % M_u = sparse(ops_u.norms.M); | |
| 60 e_l_u = sparse(ops_u.boundary.e_1); | |
| 61 e_r_u = sparse(ops_u.boundary.e_m); | |
| 62 d1_l_u = sparse(ops_u.boundary.S_1); | |
| 63 d1_r_u = sparse(ops_u.boundary.S_m); | |
| 64 | |
| 65 D1_v = sparse(ops_v.derivatives.D1); | |
| 66 D2_v = ops_v.derivatives.D2; | |
| 67 H_v = sparse(ops_v.norms.H); | |
| 68 Hi_v = sparse(ops_v.norms.HI); | |
| 69 % M_v = sparse(ops_v.norms.M); | |
| 70 e_l_v = sparse(ops_v.boundary.e_1); | |
| 71 e_r_v = sparse(ops_v.boundary.e_m); | |
| 72 d1_l_v = sparse(ops_v.boundary.S_1); | |
| 73 d1_r_v = sparse(ops_v.boundary.S_m); | |
| 74 | |
| 75 | |
| 76 % Metric derivatives | |
| 77 [X,Y] = ti.map(u,v); | |
| 78 | |
| 79 [x_u,x_v] = gridDerivatives(X,D1_u,D1_v); | |
| 80 [y_u,y_v] = gridDerivatives(Y,D1_u,D1_v); | |
| 81 | |
| 82 | |
| 83 | |
| 84 J = x_u.*y_v - x_v.*y_u; | |
| 85 a11 = 1./J .* (x_v.^2 + y_v.^2); %% GÖR SOM MATRISER | |
| 86 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); | |
| 87 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 88 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 89 | |
| 90 dof_order = reshape(1:m_u*m_v,m_v,m_u); | |
| 91 | |
| 92 Duu = sparse(m_tot); | |
| 93 Dvv = sparse(m_tot); | |
| 94 | |
| 95 for i = 1:m_v | |
| 96 D = D2_u(a11(i,:)); | |
| 97 p = dof_order(i,:); | |
| 98 Duu(p,p) = D; | |
| 99 end | |
| 100 | |
| 101 for i = 1:m_u | |
| 102 D = D2_v(a22(:,i)); | |
| 103 p = dof_order(:,i); | |
| 104 Dvv(p,p) = D; | |
| 105 end | |
| 106 | |
| 107 L_12 = spdiags(a12(:),0,m_tot,m_tot); | |
| 108 Du = kr(D1_u,I_v); | |
| 109 Dv = kr(I_u,D1_v); | |
| 110 | |
| 111 Duv = Du*L_12*Dv; | |
| 112 Dvu = Dv*L_12*Du; | |
| 113 | |
| 114 | |
| 115 | |
| 116 obj.H = kr(H_u,H_v); | |
| 117 obj.Hi = kr(Hi_u,Hi_v); | |
| 118 obj.Hu = kr(H_u,I_v); | |
| 119 obj.Hv = kr(I_u,H_v); | |
| 120 obj.Hiu = kr(Hi_u,I_v); | |
| 121 obj.Hiv = kr(I_u,Hi_v); | |
| 122 | |
| 123 % obj.M = kr(M_u,H_v)+kr(H_u,M_v); | |
| 124 obj.e_w = kr(e_l_u,I_v); | |
| 125 obj.e_e = kr(e_r_u,I_v); | |
| 126 obj.e_s = kr(I_u,e_l_v); | |
| 127 obj.e_n = kr(I_u,e_r_v); | |
| 128 obj.du_w = kr(d1_l_u,I_v); | |
| 129 obj.dv_w = (obj.e_w'*Dv)'; | |
| 130 obj.du_e = kr(d1_r_u,I_v); | |
| 131 obj.dv_e = (obj.e_e'*Dv)'; | |
| 132 obj.du_s = (obj.e_s'*Du)'; | |
| 133 obj.dv_s = kr(I_u,d1_l_v); | |
| 134 obj.du_n = (obj.e_n'*Du)'; | |
| 135 obj.dv_n = kr(I_u,d1_r_v); | |
| 136 | |
| 137 obj.m = m; | |
| 138 obj.h = [h_u h_v]; | |
| 139 obj.order = order; | |
| 140 | |
| 141 | |
| 142 obj.c = c; | |
| 143 obj.J = spdiags(J(:),0,m_tot,m_tot); | |
| 144 obj.Ji = spdiags(1./J(:),0,m_tot,m_tot); | |
| 145 obj.a11 = a11; | |
| 146 obj.a12 = a12; | |
| 147 obj.a22 = a22; | |
| 148 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
| 149 obj.u = u; | |
| 150 obj.v = v; | |
| 151 obj.X = X; | |
| 152 obj.Y = Y; | |
| 153 obj.x = X(:); | |
| 154 obj.y = Y(:); | |
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parents:
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155 obj.lambda = lambda; |
| 0 | 156 |
| 157 obj.gamm_u = h_u*ops_u.borrowing.M.S; | |
| 158 obj.gamm_v = h_v*ops_v.borrowing.M.S; | |
| 159 end | |
| 160 | |
| 161 | |
| 162 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 163 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 164 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 165 % type is a string specifying the type of boundary condition if there are several. | |
| 166 % data is a function returning the data that should be applied at the boundary. | |
| 167 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 168 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 169 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 170 default_arg('type','neumann'); | |
| 171 default_arg('data',0); | |
| 172 | |
| 173 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 174 | |
| 175 switch type | |
| 176 % Dirichlet boundary condition | |
| 177 case {'D','d','dirichlet'} | |
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178 % v denotes the solution in the neighbour domain |
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179 tuning = 1.2; |
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180 % tuning = 20.2; |
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181 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t] = obj.get_boundary_ops(boundary); |
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182 |
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183 a_n = spdiag(coeff_n); |
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184 a_t = spdiag(coeff_t); |
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185 |
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186 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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187 |
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188 u = obj; |
| 0 | 189 |
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190 b1 = gamm*u.lambda./u.a11.^2; |
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191 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 192 |
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193 tau = -1./b1 - 1./b2; |
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194 tau = tuning * spdiag(tau(:)); |
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195 sig1 = 1/2; |
| 0 | 196 |
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197 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 198 |
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199 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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200 pp = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 201 switch class(data) |
| 202 case 'double' | |
| 203 penalty = pp*data; | |
| 204 case 'function_handle' | |
| 205 penalty = @(t)pp*data(t); | |
| 206 otherwise | |
| 207 error('Weird data argument!') | |
| 208 end | |
| 209 | |
| 210 | |
| 211 % Neumann boundary condition | |
| 212 case {'N','n','neumann'} | |
| 213 c = obj.c; | |
| 214 | |
| 215 | |
| 216 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 217 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 218 d = (a_n * d_n' + a_t*d_t')'; | |
| 219 | |
| 220 tau1 = -s; | |
| 221 tau2 = 0; | |
| 222 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 223 | |
| 224 closure = halfnorm_inv*tau*d'; | |
| 225 | |
| 226 pp = halfnorm_inv*tau; | |
| 227 switch class(data) | |
| 228 case 'double' | |
| 229 penalty = pp*data; | |
| 230 case 'function_handle' | |
| 231 penalty = @(t)pp*data(t); | |
| 232 otherwise | |
| 233 error('Weird data argument!') | |
| 234 end | |
| 235 | |
| 236 % Unknown, boundary condition | |
| 237 otherwise | |
| 238 error('No such boundary condition: type = %s',type); | |
| 239 end | |
| 240 end | |
| 241 | |
| 242 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 243 % u denotes the solution in the own domain | |
| 244 % v denotes the solution in the neighbour domain | |
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245 tuning = 1.2; |
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246 % tuning = 20.2; |
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247 [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, I_u] = obj.get_boundary_ops(boundary); |
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248 [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, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); |
| 0 | 249 |
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250 a_n_u = spdiag(coeff_n_u); |
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251 a_t_u = spdiag(coeff_t_u); |
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252 a_n_v = spdiag(coeff_n_v); |
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253 a_t_v = spdiag(coeff_t_v); |
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254 |
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255 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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256 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 257 |
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258 u = obj; |
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259 v = neighbour_scheme; |
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260 |
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261 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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262 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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263 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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264 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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265 |
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266 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
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267 tau = tuning * spdiag(tau(:)); |
| 0 | 268 sig1 = 1/2; |
| 83 | 269 sig2 = -1/2; |
| 0 | 270 |
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271 penalty_parameter_1 = halfnorm_inv_u_n*(e_u*tau + sig1*halfnorm_inv_u_t*F_u*e_u'*halfnorm_u_t*e_u); |
| 0 | 272 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 273 | |
| 274 | |
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275 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 276 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 277 end |
| 278 | |
| 279 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 280 % The right boundary is considered the positive boundary | |
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281 % |
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282 % I -- the indecies of the boundary points in the grid matrix |
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283 function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I] = get_boundary_ops(obj,boundary) |
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284 |
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285 gridMatrix = zeros(obj.m(2),obj.m(1)); |
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286 gridMatrix(:) = 1:numel(gridMatrix); |
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287 |
| 0 | 288 switch boundary |
| 289 case 'w' | |
| 290 e = obj.e_w; | |
| 291 d_n = obj.du_w; | |
| 292 d_t = obj.dv_w; | |
| 293 s = -1; | |
| 294 | |
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295 I = gridMatrix(:,1); |
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296 coeff_n = obj.a11(I); |
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297 coeff_t = obj.a12(I); |
| 0 | 298 case 'e' |
| 299 e = obj.e_e; | |
| 300 d_n = obj.du_e; | |
| 301 d_t = obj.dv_e; | |
| 302 s = 1; | |
| 303 | |
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Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
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304 I = gridMatrix(:,end); |
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305 coeff_n = obj.a11(I); |
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53fe4b64f65e
Minor cleaning of Wave2dCurve.
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parents:
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306 coeff_t = obj.a12(I); |
| 0 | 307 case 's' |
| 308 e = obj.e_s; | |
| 309 d_n = obj.dv_s; | |
| 310 d_t = obj.du_s; | |
| 311 s = -1; | |
| 312 | |
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Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
Jonatan Werpers <jonatan@werpers.com>
parents:
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313 I = gridMatrix(1,:)'; |
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314 coeff_n = obj.a22(I); |
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parents:
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315 coeff_t = obj.a12(I); |
| 0 | 316 case 'n' |
| 317 e = obj.e_n; | |
| 318 d_n = obj.dv_n; | |
| 319 d_t = obj.du_n; | |
| 320 s = 1; | |
| 321 | |
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Wave2DCurve: Fixed error in tau. Also made random guess at fixing theory from paper.
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322 I = gridMatrix(end,:)'; |
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323 coeff_n = obj.a22(I); |
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parents:
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324 coeff_t = obj.a12(I); |
| 0 | 325 otherwise |
| 326 error('No such boundary: boundary = %s',boundary); | |
| 327 end | |
| 328 | |
| 329 switch boundary | |
| 330 case {'w','e'} | |
| 331 halfnorm_inv_n = obj.Hiu; | |
| 332 halfnorm_inv_t = obj.Hiv; | |
| 333 halfnorm_t = obj.Hv; | |
| 334 gamm = obj.gamm_u; | |
| 335 case {'s','n'} | |
| 336 halfnorm_inv_n = obj.Hiv; | |
| 337 halfnorm_inv_t = obj.Hiu; | |
| 338 halfnorm_t = obj.Hu; | |
| 339 gamm = obj.gamm_v; | |
| 340 end | |
| 341 end | |
| 342 | |
| 343 function N = size(obj) | |
| 344 N = prod(obj.m); | |
| 345 end | |
| 346 | |
| 347 end | |
| 348 | |
| 349 methods(Static) | |
| 350 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 351 % and bound_v of scheme schm_v. | |
| 352 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 353 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 354 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 355 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 356 end | |
| 357 end | |
| 358 end |