Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 339:3135e13ae509 feature/beams
Implemented free BC. Not tested yet.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 24 Oct 2016 17:01:34 +0200 |
| parents | e070ebd94d9d |
| children | 85c2fe06d551 |
| 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 |
| 0 | 29 end |
| 30 | |
| 31 methods | |
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32 function obj = Wave2dCurve(g ,order, c, opSet) |
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33 default_arg('opSet',@sbp.D2Variable); |
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34 default_arg('c', 1); |
| 0 | 35 |
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36 assert(isa(g, 'grid.Curvilinear')) |
| 0 | 37 |
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38 m = g.size(); |
| 0 | 39 m_u = m(1); |
| 40 m_v = m(2); | |
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41 m_tot = g.N(); |
| 0 | 42 |
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43 h = g.scaling(); |
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44 h_u = h(1); |
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45 h_v = h(2); |
| 0 | 46 |
| 47 % Operators | |
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48 ops_u = opSet(m_u, {0, 1}, order); |
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49 ops_v = opSet(m_v, {0, 1}, order); |
| 0 | 50 |
| 51 I_u = speye(m_u); | |
| 52 I_v = speye(m_v); | |
| 53 | |
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54 D1_u = ops_u.D1; |
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55 D2_u = ops_u.D2; |
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56 H_u = ops_u.H; |
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57 Hi_u = ops_u.HI; |
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58 e_l_u = ops_u.e_l; |
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59 e_r_u = ops_u.e_r; |
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60 d1_l_u = ops_u.d1_l; |
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61 d1_r_u = ops_u.d1_r; |
| 0 | 62 |
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63 D1_v = ops_v.D1; |
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64 D2_v = ops_v.D2; |
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65 H_v = ops_v.H; |
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66 Hi_v = ops_v.HI; |
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67 e_l_v = ops_v.e_l; |
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68 e_r_v = ops_v.e_r; |
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69 d1_l_v = ops_v.d1_l; |
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70 d1_r_v = ops_v.d1_r; |
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71 |
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72 Du = kr(D1_u,I_v); |
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73 Dv = kr(I_u,D1_v); |
| 0 | 74 |
| 75 % Metric derivatives | |
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76 coords = g.points(); |
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77 x = coords(:,1); |
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78 y = coords(:,2); |
| 0 | 79 |
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80 x_u = Du*x; |
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81 x_v = Dv*x; |
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82 y_u = Du*y; |
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83 y_v = Dv*y; |
| 0 | 84 |
| 85 J = x_u.*y_v - x_v.*y_u; | |
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86 a11 = 1./J .* (x_v.^2 + y_v.^2); |
| 0 | 87 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); |
| 88 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 89 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 90 | |
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91 % Assemble full operators |
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92 L_12 = spdiags(a12, 0, m_tot, m_tot); |
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93 Duv = Du*L_12*Dv; |
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94 Dvu = Dv*L_12*Du; |
| 0 | 95 |
| 96 Duu = sparse(m_tot); | |
| 97 Dvv = sparse(m_tot); | |
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98 ind = grid.funcToMatrix(g, 1:m_tot); |
| 0 | 99 |
| 100 for i = 1:m_v | |
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101 D = D2_u(a11(ind(:,i))); |
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102 p = ind(:,i); |
| 0 | 103 Duu(p,p) = D; |
| 104 end | |
| 105 | |
| 106 for i = 1:m_u | |
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107 D = D2_v(a22(ind(i,:))); |
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108 p = ind(i,:); |
| 0 | 109 Dvv(p,p) = D; |
| 110 end | |
| 111 | |
| 112 obj.H = kr(H_u,H_v); | |
| 113 obj.Hi = kr(Hi_u,Hi_v); | |
| 114 obj.Hu = kr(H_u,I_v); | |
| 115 obj.Hv = kr(I_u,H_v); | |
| 116 obj.Hiu = kr(Hi_u,I_v); | |
| 117 obj.Hiv = kr(I_u,Hi_v); | |
| 118 | |
| 119 obj.e_w = kr(e_l_u,I_v); | |
| 120 obj.e_e = kr(e_r_u,I_v); | |
| 121 obj.e_s = kr(I_u,e_l_v); | |
| 122 obj.e_n = kr(I_u,e_r_v); | |
| 123 obj.du_w = kr(d1_l_u,I_v); | |
| 124 obj.dv_w = (obj.e_w'*Dv)'; | |
| 125 obj.du_e = kr(d1_r_u,I_v); | |
| 126 obj.dv_e = (obj.e_e'*Dv)'; | |
| 127 obj.du_s = (obj.e_s'*Du)'; | |
| 128 obj.dv_s = kr(I_u,d1_l_v); | |
| 129 obj.du_n = (obj.e_n'*Du)'; | |
| 130 obj.dv_n = kr(I_u,d1_r_v); | |
| 131 | |
| 132 obj.m = m; | |
| 133 obj.h = [h_u h_v]; | |
| 134 obj.order = order; | |
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135 obj.grid = g; |
| 0 | 136 |
| 137 obj.c = c; | |
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138 obj.J = spdiags(J, 0, m_tot, m_tot); |
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139 obj.Ji = spdiags(1./J, 0, m_tot, m_tot); |
| 0 | 140 obj.a11 = a11; |
| 141 obj.a12 = a12; | |
| 142 obj.a22 = a22; | |
| 143 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
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144 obj.lambda = lambda; |
| 0 | 145 |
| 146 obj.gamm_u = h_u*ops_u.borrowing.M.S; | |
| 147 obj.gamm_v = h_v*ops_v.borrowing.M.S; | |
| 148 end | |
| 149 | |
| 150 | |
| 151 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 152 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 153 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 154 % type is a string specifying the type of boundary condition if there are several. | |
| 155 % data is a function returning the data that should be applied at the boundary. | |
| 156 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 157 % neighbour_boundary is a string specifying which boundary to interface to. | |
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158 function [closure, penalty] = boundary_condition(obj,boundary,type) |
| 0 | 159 default_arg('type','neumann'); |
| 160 | |
| 161 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 162 | |
| 163 switch type | |
| 164 % Dirichlet boundary condition | |
| 165 case {'D','d','dirichlet'} | |
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166 % v denotes the solution in the neighbour domain |
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167 tuning = 1.2; |
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168 % tuning = 20.2; |
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169 [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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170 |
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171 a_n = spdiag(coeff_n); |
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172 a_t = spdiag(coeff_t); |
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173 |
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174 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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175 |
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176 u = obj; |
| 0 | 177 |
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178 b1 = gamm*u.lambda./u.a11.^2; |
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179 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 180 |
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181 tau = -1./b1 - 1./b2; |
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182 tau = tuning * spdiag(tau); |
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183 sig1 = 1/2; |
| 0 | 184 |
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185 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 186 |
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187 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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188 penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 189 |
| 190 | |
| 191 % Neumann boundary condition | |
| 192 case {'N','n','neumann'} | |
| 193 c = obj.c; | |
| 194 | |
| 195 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 196 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 197 d = (a_n * d_n' + a_t*d_t')'; | |
| 198 | |
| 199 tau1 = -s; | |
| 200 tau2 = 0; | |
| 201 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 202 | |
| 203 closure = halfnorm_inv*tau*d'; | |
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204 penalty = halfnorm_inv*tau; |
| 0 | 205 |
| 206 | |
| 207 % Unknown, boundary condition | |
| 208 otherwise | |
| 209 error('No such boundary condition: type = %s',type); | |
| 210 end | |
| 211 end | |
| 212 | |
| 213 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 214 % u denotes the solution in the own domain | |
| 215 % v denotes the solution in the neighbour domain | |
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216 tuning = 1.2; |
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217 % tuning = 20.2; |
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218 [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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219 [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 | 220 |
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221 a_n_u = spdiag(coeff_n_u); |
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222 a_t_u = spdiag(coeff_t_u); |
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223 a_n_v = spdiag(coeff_n_v); |
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224 a_t_v = spdiag(coeff_t_v); |
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225 |
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226 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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227 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 228 |
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229 u = obj; |
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230 v = neighbour_scheme; |
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231 |
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232 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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233 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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234 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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235 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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236 |
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237 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
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238 tau = tuning * spdiag(tau); |
| 0 | 239 sig1 = 1/2; |
| 83 | 240 sig2 = -1/2; |
| 0 | 241 |
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242 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 | 243 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 244 | |
| 245 | |
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246 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 247 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 248 end |
| 249 | |
| 250 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 251 % The right boundary is considered the positive boundary | |
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252 % |
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253 % I -- the indecies of the boundary points in the grid matrix |
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254 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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255 |
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256 % gridMatrix = zeros(obj.m(2),obj.m(1)); |
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257 % gridMatrix(:) = 1:numel(gridMatrix); |
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258 |
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259 ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m)); |
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260 |
| 0 | 261 switch boundary |
| 262 case 'w' | |
| 263 e = obj.e_w; | |
| 264 d_n = obj.du_w; | |
| 265 d_t = obj.dv_w; | |
| 266 s = -1; | |
| 267 | |
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268 I = ind(1,:); |
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269 coeff_n = obj.a11(I); |
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270 coeff_t = obj.a12(I); |
| 0 | 271 case 'e' |
| 272 e = obj.e_e; | |
| 273 d_n = obj.du_e; | |
| 274 d_t = obj.dv_e; | |
| 275 s = 1; | |
| 276 | |
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277 I = ind(end,:); |
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278 coeff_n = obj.a11(I); |
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279 coeff_t = obj.a12(I); |
| 0 | 280 case 's' |
| 281 e = obj.e_s; | |
| 282 d_n = obj.dv_s; | |
| 283 d_t = obj.du_s; | |
| 284 s = -1; | |
| 285 | |
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286 I = ind(:,1)'; |
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287 coeff_n = obj.a22(I); |
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288 coeff_t = obj.a12(I); |
| 0 | 289 case 'n' |
| 290 e = obj.e_n; | |
| 291 d_n = obj.dv_n; | |
| 292 d_t = obj.du_n; | |
| 293 s = 1; | |
| 294 | |
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295 I = ind(:,end)'; |
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296 coeff_n = obj.a22(I); |
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297 coeff_t = obj.a12(I); |
| 0 | 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 | |
| 321 end | |
| 322 end |