Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 449:0707a7192bc3 feature/grids
Add first derivative operators to Wave2DCurve
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 09 May 2017 14:51:29 +0200 |
| parents | 359861563866 |
| children | 8d455e49364f |
| 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 | |
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5 |
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6 grid |
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7 |
| 0 | 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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28 lambda |
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29 |
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30 Dx, Dy % Physical derivatives |
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31 |
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32 x_u |
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33 x_v |
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34 y_u |
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35 y_v |
| 0 | 36 end |
| 37 | |
| 38 methods | |
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39 function obj = Wave2dCurve(g ,order, c, opSet) |
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40 default_arg('opSet',@sbp.D2Variable); |
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41 default_arg('c', 1); |
| 0 | 42 |
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43 assert(isa(g, 'grid.Curvilinear')) |
| 0 | 44 |
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45 m = g.size(); |
| 0 | 46 m_u = m(1); |
| 47 m_v = m(2); | |
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48 m_tot = g.N(); |
| 0 | 49 |
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50 h = g.scaling(); |
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51 h_u = h(1); |
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52 h_v = h(2); |
| 0 | 53 |
| 54 % Operators | |
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55 ops_u = opSet(m_u, {0, 1}, order); |
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56 ops_v = opSet(m_v, {0, 1}, order); |
| 0 | 57 |
| 58 I_u = speye(m_u); | |
| 59 I_v = speye(m_v); | |
| 60 | |
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61 D1_u = ops_u.D1; |
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62 D2_u = ops_u.D2; |
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63 H_u = ops_u.H; |
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64 Hi_u = ops_u.HI; |
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65 e_l_u = ops_u.e_l; |
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66 e_r_u = ops_u.e_r; |
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67 d1_l_u = ops_u.d1_l; |
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68 d1_r_u = ops_u.d1_r; |
| 0 | 69 |
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70 D1_v = ops_v.D1; |
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71 D2_v = ops_v.D2; |
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72 H_v = ops_v.H; |
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73 Hi_v = ops_v.HI; |
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74 e_l_v = ops_v.e_l; |
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75 e_r_v = ops_v.e_r; |
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76 d1_l_v = ops_v.d1_l; |
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77 d1_r_v = ops_v.d1_r; |
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78 |
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79 Du = kr(D1_u,I_v); |
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80 Dv = kr(I_u,D1_v); |
| 0 | 81 |
| 82 % Metric derivatives | |
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83 coords = g.points(); |
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84 x = coords(:,1); |
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85 y = coords(:,2); |
| 0 | 86 |
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87 x_u = Du*x; |
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88 x_v = Dv*x; |
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89 y_u = Du*y; |
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90 y_v = Dv*y; |
| 0 | 91 |
| 92 J = x_u.*y_v - x_v.*y_u; | |
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93 a11 = 1./J .* (x_v.^2 + y_v.^2); |
| 0 | 94 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); |
| 95 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 96 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 97 | |
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98 % Assemble full operators |
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99 L_12 = spdiags(a12, 0, m_tot, m_tot); |
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100 Duv = Du*L_12*Dv; |
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101 Dvu = Dv*L_12*Du; |
| 0 | 102 |
| 103 Duu = sparse(m_tot); | |
| 104 Dvv = sparse(m_tot); | |
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105 ind = grid.funcToMatrix(g, 1:m_tot); |
| 0 | 106 |
| 107 for i = 1:m_v | |
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108 D = D2_u(a11(ind(:,i))); |
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109 p = ind(:,i); |
| 0 | 110 Duu(p,p) = D; |
| 111 end | |
| 112 | |
| 113 for i = 1:m_u | |
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114 D = D2_v(a22(ind(i,:))); |
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115 p = ind(i,:); |
| 0 | 116 Dvv(p,p) = D; |
| 117 end | |
| 118 | |
| 119 obj.H = kr(H_u,H_v); | |
| 120 obj.Hi = kr(Hi_u,Hi_v); | |
| 121 obj.Hu = kr(H_u,I_v); | |
| 122 obj.Hv = kr(I_u,H_v); | |
| 123 obj.Hiu = kr(Hi_u,I_v); | |
| 124 obj.Hiv = kr(I_u,Hi_v); | |
| 125 | |
| 126 obj.e_w = kr(e_l_u,I_v); | |
| 127 obj.e_e = kr(e_r_u,I_v); | |
| 128 obj.e_s = kr(I_u,e_l_v); | |
| 129 obj.e_n = kr(I_u,e_r_v); | |
| 130 obj.du_w = kr(d1_l_u,I_v); | |
| 131 obj.dv_w = (obj.e_w'*Dv)'; | |
| 132 obj.du_e = kr(d1_r_u,I_v); | |
| 133 obj.dv_e = (obj.e_e'*Dv)'; | |
| 134 obj.du_s = (obj.e_s'*Du)'; | |
| 135 obj.dv_s = kr(I_u,d1_l_v); | |
| 136 obj.du_n = (obj.e_n'*Du)'; | |
| 370 | 137 obj.dv_n = kr(I_u,d1_r_v); |
| 376 | 138 |
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139 obj.x_u = x_u; |
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140 obj.x_v = x_v; |
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141 obj.y_u = y_u; |
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142 obj.y_v = y_v; |
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143 |
| 0 | 144 obj.m = m; |
| 145 obj.h = [h_u h_v]; | |
| 146 obj.order = order; | |
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147 obj.grid = g; |
| 0 | 148 |
| 149 obj.c = c; | |
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150 obj.J = spdiags(J, 0, m_tot, m_tot); |
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151 obj.Ji = spdiags(1./J, 0, m_tot, m_tot); |
| 0 | 152 obj.a11 = a11; |
| 153 obj.a12 = a12; | |
| 154 obj.a22 = a22; | |
| 155 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
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156 obj.lambda = lambda; |
| 0 | 157 |
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158 obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv; |
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159 obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv; |
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160 |
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161 obj.gamm_u = h_u*ops_u.borrowing.M.d1; |
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162 obj.gamm_v = h_v*ops_v.borrowing.M.d1; |
| 0 | 163 end |
| 164 | |
| 165 | |
| 166 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 167 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 168 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 169 % type is a string specifying the type of boundary condition if there are several. | |
| 170 % data is a function returning the data that should be applied at the boundary. | |
| 171 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 172 % neighbour_boundary is a string specifying which boundary to interface to. | |
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173 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter) |
| 0 | 174 default_arg('type','neumann'); |
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175 default_arg('parameter', []); |
| 0 | 176 |
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177 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv , ~, ~, ~, scale_factor] = obj.get_boundary_ops(boundary); |
| 0 | 178 switch type |
| 179 % Dirichlet boundary condition | |
| 180 case {'D','d','dirichlet'} | |
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181 % v denotes the solution in the neighbour domain |
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182 tuning = 1.2; |
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183 % tuning = 20.2; |
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184 [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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185 |
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186 a_n = spdiag(coeff_n); |
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187 a_t = spdiag(coeff_t); |
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188 |
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189 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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190 |
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191 u = obj; |
| 0 | 192 |
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193 b1 = gamm*u.lambda./u.a11.^2; |
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194 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 195 |
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196 tau = -1./b1 - 1./b2; |
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197 tau = tuning * spdiag(tau); |
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198 sig1 = 1; |
| 0 | 199 |
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200 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 201 |
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202 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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203 penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 204 |
| 205 | |
| 206 % Neumann boundary condition | |
| 207 case {'N','n','neumann'} | |
| 208 c = obj.c; | |
| 209 | |
| 210 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 211 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 212 d = (a_n * d_n' + a_t*d_t')'; | |
| 213 | |
| 214 tau1 = -s; | |
| 215 tau2 = 0; | |
| 216 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 217 | |
| 218 closure = halfnorm_inv*tau*d'; | |
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219 penalty = -halfnorm_inv*tau; |
| 0 | 220 |
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221 % Characteristic boundary condition |
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222 case {'characteristic', 'char', 'c'} |
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223 default_arg('parameter', 1); |
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224 beta = parameter; |
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225 c = obj.c; |
| 0 | 226 |
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227 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); |
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228 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); |
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229 d = s*(a_n * d_n' + a_t*d_t')'; % outward facing normal derivative |
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230 |
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231 tau = -c.^2 * 1/beta*obj.Ji*e; |
|
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232 |
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233 closure{1} = halfnorm_inv*tau/c*spdiag(scale_factor)*e'; |
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234 closure{2} = halfnorm_inv*tau*beta*d'; |
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235 penalty = -halfnorm_inv*tau; |
| 0 | 236 |
| 237 % Unknown, boundary condition | |
| 238 otherwise | |
| 239 error('No such boundary condition: type = %s',type); | |
| 240 end | |
| 241 end | |
| 242 | |
| 243 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 244 % u denotes the solution in the own domain | |
| 245 % v denotes the solution in the neighbour domain | |
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246 tuning = 1.2; |
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247 % tuning = 20.2; |
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248 [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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249 [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 | 250 |
|
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251 a_n_u = spdiag(coeff_n_u); |
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252 a_t_u = spdiag(coeff_t_u); |
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253 a_n_v = spdiag(coeff_n_v); |
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254 a_t_v = spdiag(coeff_t_v); |
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255 |
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256 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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257 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 258 |
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259 u = obj; |
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260 v = neighbour_scheme; |
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261 |
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262 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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263 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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264 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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265 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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266 |
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267 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
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268 tau = tuning * spdiag(tau); |
| 0 | 269 sig1 = 1/2; |
| 83 | 270 sig2 = -1/2; |
| 0 | 271 |
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272 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 | 273 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 274 | |
| 275 | |
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276 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 277 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 278 end |
| 279 | |
| 280 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 281 % The right boundary is considered the positive boundary | |
|
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282 % |
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283 % I -- the indecies of the boundary points in the grid matrix |
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284 function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I, scale_factor] = get_boundary_ops(obj, boundary) |
|
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285 |
|
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286 % gridMatrix = zeros(obj.m(2),obj.m(1)); |
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287 % gridMatrix(:) = 1:numel(gridMatrix); |
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288 |
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289 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); |
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290 |
| 0 | 291 switch boundary |
| 292 case 'w' | |
| 293 e = obj.e_w; | |
| 294 d_n = obj.du_w; | |
| 295 d_t = obj.dv_w; | |
| 296 s = -1; | |
| 297 | |
|
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298 I = ind(1,:); |
|
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299 coeff_n = obj.a11(I); |
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300 coeff_t = obj.a12(I); |
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301 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 0 | 302 case 'e' |
| 303 e = obj.e_e; | |
| 304 d_n = obj.du_e; | |
| 305 d_t = obj.dv_e; | |
| 306 s = 1; | |
| 307 | |
|
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308 I = ind(end,:); |
|
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309 coeff_n = obj.a11(I); |
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310 coeff_t = obj.a12(I); |
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311 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 0 | 312 case 's' |
| 313 e = obj.e_s; | |
| 314 d_n = obj.dv_s; | |
| 315 d_t = obj.du_s; | |
| 316 s = -1; | |
| 317 | |
|
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318 I = ind(:,1)'; |
|
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319 coeff_n = obj.a22(I); |
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320 coeff_t = obj.a12(I); |
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321 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 322 case 'n' |
| 323 e = obj.e_n; | |
| 324 d_n = obj.dv_n; | |
| 325 d_t = obj.du_n; | |
| 326 s = 1; | |
| 327 | |
|
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328 I = ind(:,end)'; |
|
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329 coeff_n = obj.a22(I); |
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330 coeff_t = obj.a12(I); |
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331 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 332 otherwise |
| 333 error('No such boundary: boundary = %s',boundary); | |
| 334 end | |
| 335 | |
| 336 switch boundary | |
| 337 case {'w','e'} | |
| 338 halfnorm_inv_n = obj.Hiu; | |
| 339 halfnorm_inv_t = obj.Hiv; | |
| 340 halfnorm_t = obj.Hv; | |
| 341 gamm = obj.gamm_u; | |
| 342 case {'s','n'} | |
| 343 halfnorm_inv_n = obj.Hiv; | |
| 344 halfnorm_inv_t = obj.Hiu; | |
| 345 halfnorm_t = obj.Hu; | |
| 346 gamm = obj.gamm_v; | |
| 347 end | |
| 348 end | |
| 349 | |
| 350 function N = size(obj) | |
| 351 N = prod(obj.m); | |
| 352 end | |
| 353 | |
| 354 | |
| 355 end | |
| 356 end |