Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 389:42c89b5eedc0 feature/beams
Add borrowing constants for D2 operators in D4Variable
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 10 Jan 2017 17:31:28 +0100 |
| parents | 32df00102268 |
| children | 359861563866 |
| 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 x_u |
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31 x_v |
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32 y_u |
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33 y_v |
| 0 | 34 end |
| 35 | |
| 36 methods | |
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37 function obj = Wave2dCurve(g ,order, c, opSet) |
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38 default_arg('opSet',@sbp.D2Variable); |
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39 default_arg('c', 1); |
| 0 | 40 |
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41 assert(isa(g, 'grid.Curvilinear')) |
| 0 | 42 |
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43 m = g.size(); |
| 0 | 44 m_u = m(1); |
| 45 m_v = m(2); | |
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46 m_tot = g.N(); |
| 0 | 47 |
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48 h = g.scaling(); |
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49 h_u = h(1); |
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50 h_v = h(2); |
| 0 | 51 |
| 52 % Operators | |
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53 ops_u = opSet(m_u, {0, 1}, order); |
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54 ops_v = opSet(m_v, {0, 1}, order); |
| 0 | 55 |
| 56 I_u = speye(m_u); | |
| 57 I_v = speye(m_v); | |
| 58 | |
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59 D1_u = ops_u.D1; |
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60 D2_u = ops_u.D2; |
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61 H_u = ops_u.H; |
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62 Hi_u = ops_u.HI; |
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63 e_l_u = ops_u.e_l; |
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64 e_r_u = ops_u.e_r; |
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65 d1_l_u = ops_u.d1_l; |
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66 d1_r_u = ops_u.d1_r; |
| 0 | 67 |
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68 D1_v = ops_v.D1; |
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69 D2_v = ops_v.D2; |
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70 H_v = ops_v.H; |
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71 Hi_v = ops_v.HI; |
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72 e_l_v = ops_v.e_l; |
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73 e_r_v = ops_v.e_r; |
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74 d1_l_v = ops_v.d1_l; |
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75 d1_r_v = ops_v.d1_r; |
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76 |
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77 Du = kr(D1_u,I_v); |
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78 Dv = kr(I_u,D1_v); |
| 0 | 79 |
| 80 % Metric derivatives | |
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81 coords = g.points(); |
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82 x = coords(:,1); |
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83 y = coords(:,2); |
| 0 | 84 |
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85 x_u = Du*x; |
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86 x_v = Dv*x; |
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87 y_u = Du*y; |
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88 y_v = Dv*y; |
| 0 | 89 |
| 90 J = x_u.*y_v - x_v.*y_u; | |
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91 a11 = 1./J .* (x_v.^2 + y_v.^2); |
| 0 | 92 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); |
| 93 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 94 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 95 | |
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96 % Assemble full operators |
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97 L_12 = spdiags(a12, 0, m_tot, m_tot); |
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98 Duv = Du*L_12*Dv; |
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99 Dvu = Dv*L_12*Du; |
| 0 | 100 |
| 101 Duu = sparse(m_tot); | |
| 102 Dvv = sparse(m_tot); | |
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103 ind = grid.funcToMatrix(g, 1:m_tot); |
| 0 | 104 |
| 105 for i = 1:m_v | |
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106 D = D2_u(a11(ind(:,i))); |
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107 p = ind(:,i); |
| 0 | 108 Duu(p,p) = D; |
| 109 end | |
| 110 | |
| 111 for i = 1:m_u | |
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112 D = D2_v(a22(ind(i,:))); |
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113 p = ind(i,:); |
| 0 | 114 Dvv(p,p) = D; |
| 115 end | |
| 116 | |
| 117 obj.H = kr(H_u,H_v); | |
| 118 obj.Hi = kr(Hi_u,Hi_v); | |
| 119 obj.Hu = kr(H_u,I_v); | |
| 120 obj.Hv = kr(I_u,H_v); | |
| 121 obj.Hiu = kr(Hi_u,I_v); | |
| 122 obj.Hiv = kr(I_u,Hi_v); | |
| 123 | |
| 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 | |
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137 obj.x_u = x_u; |
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138 obj.x_v = x_v; |
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139 obj.y_u = y_u; |
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140 obj.y_v = y_v; |
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141 |
| 0 | 142 obj.m = m; |
| 143 obj.h = [h_u h_v]; | |
| 144 obj.order = order; | |
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145 obj.grid = g; |
| 0 | 146 |
| 147 obj.c = c; | |
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148 obj.J = spdiags(J, 0, m_tot, m_tot); |
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149 obj.Ji = spdiags(1./J, 0, m_tot, m_tot); |
| 0 | 150 obj.a11 = a11; |
| 151 obj.a12 = a12; | |
| 152 obj.a22 = a22; | |
| 153 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
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154 obj.lambda = lambda; |
| 0 | 155 |
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156 obj.gamm_u = h_u*ops_u.borrowing.M.d1; |
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157 obj.gamm_v = h_v*ops_v.borrowing.M.d1; |
| 0 | 158 end |
| 159 | |
| 160 | |
| 161 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 162 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 163 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 164 % type is a string specifying the type of boundary condition if there are several. | |
| 165 % data is a function returning the data that should be applied at the boundary. | |
| 166 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 167 % neighbour_boundary is a string specifying which boundary to interface to. | |
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168 function [closure, penalty] = boundary_condition(obj, boundary, type, parameter) |
| 0 | 169 default_arg('type','neumann'); |
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170 default_arg('parameter', []); |
| 0 | 171 |
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172 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv , ~, ~, ~, scale_factor] = obj.get_boundary_ops(boundary); |
| 0 | 173 switch type |
| 174 % Dirichlet boundary condition | |
| 175 case {'D','d','dirichlet'} | |
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176 % v denotes the solution in the neighbour domain |
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177 tuning = 1.2; |
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178 % tuning = 20.2; |
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179 [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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180 |
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181 a_n = spdiag(coeff_n); |
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182 a_t = spdiag(coeff_t); |
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183 |
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184 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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185 |
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186 u = obj; |
| 0 | 187 |
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188 b1 = gamm*u.lambda./u.a11.^2; |
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189 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 190 |
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191 tau = -1./b1 - 1./b2; |
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192 tau = tuning * spdiag(tau); |
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193 sig1 = 1; |
| 0 | 194 |
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195 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 196 |
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197 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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198 penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 199 |
| 200 | |
| 201 % Neumann boundary condition | |
| 202 case {'N','n','neumann'} | |
| 203 c = obj.c; | |
| 204 | |
| 205 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 206 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 207 d = (a_n * d_n' + a_t*d_t')'; | |
| 208 | |
| 209 tau1 = -s; | |
| 210 tau2 = 0; | |
| 211 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 212 | |
| 213 closure = halfnorm_inv*tau*d'; | |
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214 penalty = -halfnorm_inv*tau; |
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215 |
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216 % Characteristic boundary condition |
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217 case {'characteristic', 'char', 'c'} |
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218 default_arg('parameter', 1); |
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219 beta = parameter; |
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220 c = obj.c; |
| 0 | 221 |
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222 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); |
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223 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); |
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224 d = s*(a_n * d_n' + a_t*d_t')'; % outward facing normal derivative |
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225 |
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226 tau = -c.^2 * 1/beta*obj.Ji*e; |
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227 |
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228 closure{1} = halfnorm_inv*tau/c*spdiag(scale_factor)*e'; |
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229 closure{2} = halfnorm_inv*tau*beta*d'; |
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230 penalty = -halfnorm_inv*tau; |
| 0 | 231 |
| 232 % Unknown, boundary condition | |
| 233 otherwise | |
| 234 error('No such boundary condition: type = %s',type); | |
| 235 end | |
| 236 end | |
| 237 | |
| 238 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 239 % u denotes the solution in the own domain | |
| 240 % v denotes the solution in the neighbour domain | |
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241 tuning = 1.2; |
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242 % tuning = 20.2; |
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243 [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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244 [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 | 245 |
|
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246 a_n_u = spdiag(coeff_n_u); |
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247 a_t_u = spdiag(coeff_t_u); |
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248 a_n_v = spdiag(coeff_n_v); |
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249 a_t_v = spdiag(coeff_t_v); |
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250 |
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251 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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252 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 253 |
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254 u = obj; |
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255 v = neighbour_scheme; |
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256 |
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257 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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258 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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259 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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260 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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261 |
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262 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
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263 tau = tuning * spdiag(tau); |
| 0 | 264 sig1 = 1/2; |
| 83 | 265 sig2 = -1/2; |
| 0 | 266 |
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267 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 | 268 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 269 | |
| 270 | |
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271 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 272 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 273 end |
| 274 | |
| 275 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 276 % The right boundary is considered the positive boundary | |
|
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277 % |
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278 % I -- the indecies of the boundary points in the grid matrix |
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279 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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280 |
|
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281 % gridMatrix = zeros(obj.m(2),obj.m(1)); |
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282 % gridMatrix(:) = 1:numel(gridMatrix); |
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283 |
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284 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); |
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285 |
| 0 | 286 switch boundary |
| 287 case 'w' | |
| 288 e = obj.e_w; | |
| 289 d_n = obj.du_w; | |
| 290 d_t = obj.dv_w; | |
| 291 s = -1; | |
| 292 | |
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293 I = ind(1,:); |
|
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294 coeff_n = obj.a11(I); |
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295 coeff_t = obj.a12(I); |
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296 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 0 | 297 case 'e' |
| 298 e = obj.e_e; | |
| 299 d_n = obj.du_e; | |
| 300 d_t = obj.dv_e; | |
| 301 s = 1; | |
| 302 | |
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303 I = ind(end,:); |
|
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304 coeff_n = obj.a11(I); |
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305 coeff_t = obj.a12(I); |
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306 scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2); |
| 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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313 I = ind(:,1)'; |
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314 coeff_n = obj.a22(I); |
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315 coeff_t = obj.a12(I); |
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316 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 317 case 'n' |
| 318 e = obj.e_n; | |
| 319 d_n = obj.dv_n; | |
| 320 d_t = obj.du_n; | |
| 321 s = 1; | |
| 322 | |
|
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323 I = ind(:,end)'; |
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324 coeff_n = obj.a22(I); |
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325 coeff_t = obj.a12(I); |
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326 scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2); |
| 0 | 327 otherwise |
| 328 error('No such boundary: boundary = %s',boundary); | |
| 329 end | |
| 330 | |
| 331 switch boundary | |
| 332 case {'w','e'} | |
| 333 halfnorm_inv_n = obj.Hiu; | |
| 334 halfnorm_inv_t = obj.Hiv; | |
| 335 halfnorm_t = obj.Hv; | |
| 336 gamm = obj.gamm_u; | |
| 337 case {'s','n'} | |
| 338 halfnorm_inv_n = obj.Hiv; | |
| 339 halfnorm_inv_t = obj.Hiu; | |
| 340 halfnorm_t = obj.Hu; | |
| 341 gamm = obj.gamm_v; | |
| 342 end | |
| 343 end | |
| 344 | |
| 345 function N = size(obj) | |
| 346 N = prod(obj.m); | |
| 347 end | |
| 348 | |
| 349 | |
| 350 end | |
| 351 end |