Mercurial > repos > public > sbplib
annotate +scheme/Wave2dCurve.m @ 303:f18142c1530b
Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 13 Oct 2016 09:34:42 +0200 |
| parents | 19d0c9325a3e |
| children | e070ebd94d9d 9d1fc984f40d |
| 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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97a638f91fb8
Added function spdiag(). Fixed a bunch of bugs in the Wave2dCurve scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
5
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changeset
|
28 lambda |
| 0 | 29 end |
| 30 | |
| 31 methods | |
| 32 function obj = Wave2dCurve(m,ti,order,c,opSet) | |
|
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f18142c1530b
Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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33 default_arg('opSet',@sbp.D2Variable); |
|
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Added function spdiag(). Fixed a bunch of bugs in the Wave2dCurve scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
5
diff
changeset
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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 | |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
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changeset
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49 ops_u = opSet(m_u, {0, 1}, order); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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50 ops_v = opSet(m_v, {0, 1}, order); |
| 0 | 51 |
| 52 I_u = speye(m_u); | |
| 53 I_v = speye(m_v); | |
| 54 | |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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55 D1_u = sparse(ops_u.D1); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
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parents:
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56 D2_u = ops_u.D2; |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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57 H_u = sparse(ops_u.H); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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58 Hi_u = sparse(ops_u.HI); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
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changeset
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59 % M_u = sparse(ops_u.M); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
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parents:
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60 e_l_u = sparse(ops_u.e_l); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
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parents:
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61 e_r_u = sparse(ops_u.e_r); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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62 d1_l_u = sparse(ops_u.d1_l); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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63 d1_r_u = sparse(ops_u.d1_r); |
| 0 | 64 |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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65 D1_v = sparse(ops_v.D1); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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66 D2_v = ops_v.D2; |
|
f18142c1530b
Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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67 H_v = sparse(ops_v.H); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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68 Hi_v = sparse(ops_v.HI); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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69 % M_v = sparse(ops_v.M); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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70 e_l_v = sparse(ops_v.e_l); |
|
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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71 e_r_v = sparse(ops_v.e_r); |
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Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
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changeset
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72 d1_l_v = sparse(ops_v.d1_l); |
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f18142c1530b
Fixed Wave2dCurve for new operators. Some cleanup in d2_variable_4.
Jonatan Werpers <jonatan@werpers.com>
parents:
96
diff
changeset
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73 d1_r_v = sparse(ops_v.d1_r); |
| 0 | 74 |
| 75 % Metric derivatives | |
| 76 [X,Y] = ti.map(u,v); | |
| 77 | |
| 78 [x_u,x_v] = gridDerivatives(X,D1_u,D1_v); | |
| 79 [y_u,y_v] = gridDerivatives(Y,D1_u,D1_v); | |
| 80 | |
| 81 | |
| 82 | |
| 83 J = x_u.*y_v - x_v.*y_u; | |
| 84 a11 = 1./J .* (x_v.^2 + y_v.^2); %% GÖR SOM MATRISER | |
| 85 a12 = -1./J .* (x_u.*x_v + y_u.*y_v); | |
| 86 a22 = 1./J .* (x_u.^2 + y_u.^2); | |
| 87 lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2)); | |
| 88 | |
| 89 dof_order = reshape(1:m_u*m_v,m_v,m_u); | |
| 90 | |
| 91 Duu = sparse(m_tot); | |
| 92 Dvv = sparse(m_tot); | |
| 93 | |
| 94 for i = 1:m_v | |
| 95 D = D2_u(a11(i,:)); | |
| 96 p = dof_order(i,:); | |
| 97 Duu(p,p) = D; | |
| 98 end | |
| 99 | |
| 100 for i = 1:m_u | |
| 101 D = D2_v(a22(:,i)); | |
| 102 p = dof_order(:,i); | |
| 103 Dvv(p,p) = D; | |
| 104 end | |
| 105 | |
| 106 L_12 = spdiags(a12(:),0,m_tot,m_tot); | |
| 107 Du = kr(D1_u,I_v); | |
| 108 Dv = kr(I_u,D1_v); | |
| 109 | |
| 110 Duv = Du*L_12*Dv; | |
| 111 Dvu = Dv*L_12*Du; | |
| 112 | |
| 113 | |
| 114 | |
| 115 obj.H = kr(H_u,H_v); | |
| 116 obj.Hi = kr(Hi_u,Hi_v); | |
| 117 obj.Hu = kr(H_u,I_v); | |
| 118 obj.Hv = kr(I_u,H_v); | |
| 119 obj.Hiu = kr(Hi_u,I_v); | |
| 120 obj.Hiv = kr(I_u,Hi_v); | |
| 121 | |
| 122 % obj.M = kr(M_u,H_v)+kr(H_u,M_v); | |
| 123 obj.e_w = kr(e_l_u,I_v); | |
| 124 obj.e_e = kr(e_r_u,I_v); | |
| 125 obj.e_s = kr(I_u,e_l_v); | |
| 126 obj.e_n = kr(I_u,e_r_v); | |
| 127 obj.du_w = kr(d1_l_u,I_v); | |
| 128 obj.dv_w = (obj.e_w'*Dv)'; | |
| 129 obj.du_e = kr(d1_r_u,I_v); | |
| 130 obj.dv_e = (obj.e_e'*Dv)'; | |
| 131 obj.du_s = (obj.e_s'*Du)'; | |
| 132 obj.dv_s = kr(I_u,d1_l_v); | |
| 133 obj.du_n = (obj.e_n'*Du)'; | |
| 134 obj.dv_n = kr(I_u,d1_r_v); | |
| 135 | |
| 136 obj.m = m; | |
| 137 obj.h = [h_u h_v]; | |
| 138 obj.order = order; | |
| 139 | |
| 140 | |
| 141 obj.c = c; | |
| 142 obj.J = spdiags(J(:),0,m_tot,m_tot); | |
| 143 obj.Ji = spdiags(1./J(:),0,m_tot,m_tot); | |
| 144 obj.a11 = a11; | |
| 145 obj.a12 = a12; | |
| 146 obj.a22 = a22; | |
| 147 obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); | |
| 148 obj.u = u; | |
| 149 obj.v = v; | |
| 150 obj.X = X; | |
| 151 obj.Y = Y; | |
| 152 obj.x = X(:); | |
| 153 obj.y = Y(:); | |
|
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97a638f91fb8
Added function spdiag(). Fixed a bunch of bugs in the Wave2dCurve scheme.
Jonatan Werpers <jonatan@werpers.com>
parents:
5
diff
changeset
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154 obj.lambda = lambda; |
| 0 | 155 |
| 156 obj.gamm_u = h_u*ops_u.borrowing.M.S; | |
| 157 obj.gamm_v = h_v*ops_v.borrowing.M.S; | |
| 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. | |
| 168 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 169 default_arg('type','neumann'); | |
| 170 default_arg('data',0); | |
| 171 | |
| 172 [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 173 | |
| 174 switch type | |
| 175 % Dirichlet boundary condition | |
| 176 case {'D','d','dirichlet'} | |
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177 % v denotes the solution in the neighbour domain |
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178 tuning = 1.2; |
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179 % tuning = 20.2; |
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180 [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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181 |
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182 a_n = spdiag(coeff_n); |
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183 a_t = spdiag(coeff_t); |
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184 |
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185 F = (s * a_n * d_n' + s * a_t*d_t')'; |
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186 |
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187 u = obj; |
| 0 | 188 |
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189 b1 = gamm*u.lambda./u.a11.^2; |
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190 b2 = gamm*u.lambda./u.a22.^2; |
| 0 | 191 |
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192 tau = -1./b1 - 1./b2; |
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193 tau = tuning * spdiag(tau(:)); |
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194 sig1 = 1/2; |
| 0 | 195 |
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196 penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; |
| 0 | 197 |
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198 closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; |
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199 pp = -obj.Ji*obj.c^2 * penalty_parameter_1; |
| 0 | 200 switch class(data) |
| 201 case 'double' | |
| 202 penalty = pp*data; | |
| 203 case 'function_handle' | |
| 204 penalty = @(t)pp*data(t); | |
| 205 otherwise | |
| 206 error('Weird data argument!') | |
| 207 end | |
| 208 | |
| 209 | |
| 210 % Neumann boundary condition | |
| 211 case {'N','n','neumann'} | |
| 212 c = obj.c; | |
| 213 | |
| 214 | |
| 215 a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); | |
| 216 a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); | |
| 217 d = (a_n * d_n' + a_t*d_t')'; | |
| 218 | |
| 219 tau1 = -s; | |
| 220 tau2 = 0; | |
| 221 tau = c.^2 * obj.Ji*(tau1*e + tau2*d); | |
| 222 | |
| 223 closure = halfnorm_inv*tau*d'; | |
| 224 | |
| 225 pp = halfnorm_inv*tau; | |
| 226 switch class(data) | |
| 227 case 'double' | |
| 228 penalty = pp*data; | |
| 229 case 'function_handle' | |
| 230 penalty = @(t)pp*data(t); | |
| 231 otherwise | |
| 232 error('Weird data argument!') | |
| 233 end | |
| 234 | |
| 235 % Unknown, boundary condition | |
| 236 otherwise | |
| 237 error('No such boundary condition: type = %s',type); | |
| 238 end | |
| 239 end | |
| 240 | |
| 241 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 242 % u denotes the solution in the own domain | |
| 243 % v denotes the solution in the neighbour domain | |
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244 tuning = 1.2; |
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parents:
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245 % tuning = 20.2; |
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246 [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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247 [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 | 248 |
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249 a_n_u = spdiag(coeff_n_u); |
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parents:
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250 a_t_u = spdiag(coeff_t_u); |
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parents:
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251 a_n_v = spdiag(coeff_n_v); |
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parents:
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252 a_t_v = spdiag(coeff_t_v); |
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parents:
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253 |
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254 F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; |
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parents:
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255 F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; |
| 0 | 256 |
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257 u = obj; |
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258 v = neighbour_scheme; |
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259 |
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260 b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; |
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Jonatan Werpers <jonatan@werpers.com>
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261 b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; |
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262 b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; |
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263 b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; |
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264 |
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265 tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); |
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266 tau = tuning * spdiag(tau(:)); |
| 0 | 267 sig1 = 1/2; |
| 83 | 268 sig2 = -1/2; |
| 0 | 269 |
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270 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 | 271 penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; |
| 272 | |
| 273 | |
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274 closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); |
| 83 | 275 penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); |
| 0 | 276 end |
| 277 | |
| 278 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 279 % The right boundary is considered the positive boundary | |
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280 % |
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281 % I -- the indecies of the boundary points in the grid matrix |
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282 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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283 |
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284 gridMatrix = zeros(obj.m(2),obj.m(1)); |
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285 gridMatrix(:) = 1:numel(gridMatrix); |
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286 |
| 0 | 287 switch boundary |
| 288 case 'w' | |
| 289 e = obj.e_w; | |
| 290 d_n = obj.du_w; | |
| 291 d_t = obj.dv_w; | |
| 292 s = -1; | |
| 293 | |
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294 I = gridMatrix(:,1); |
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295 coeff_n = obj.a11(I); |
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296 coeff_t = obj.a12(I); |
| 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 = gridMatrix(:,end); |
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304 coeff_n = obj.a11(I); |
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305 coeff_t = obj.a12(I); |
| 0 | 306 case 's' |
| 307 e = obj.e_s; | |
| 308 d_n = obj.dv_s; | |
| 309 d_t = obj.du_s; | |
| 310 s = -1; | |
| 311 | |
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312 I = gridMatrix(1,:)'; |
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313 coeff_n = obj.a22(I); |
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314 coeff_t = obj.a12(I); |
| 0 | 315 case 'n' |
| 316 e = obj.e_n; | |
| 317 d_n = obj.dv_n; | |
| 318 d_t = obj.du_n; | |
| 319 s = 1; | |
| 320 | |
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321 I = gridMatrix(end,:)'; |
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322 coeff_n = obj.a22(I); |
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323 coeff_t = obj.a12(I); |
| 0 | 324 otherwise |
| 325 error('No such boundary: boundary = %s',boundary); | |
| 326 end | |
| 327 | |
| 328 switch boundary | |
| 329 case {'w','e'} | |
| 330 halfnorm_inv_n = obj.Hiu; | |
| 331 halfnorm_inv_t = obj.Hiv; | |
| 332 halfnorm_t = obj.Hv; | |
| 333 gamm = obj.gamm_u; | |
| 334 case {'s','n'} | |
| 335 halfnorm_inv_n = obj.Hiv; | |
| 336 halfnorm_inv_t = obj.Hiu; | |
| 337 halfnorm_t = obj.Hu; | |
| 338 gamm = obj.gamm_v; | |
| 339 end | |
| 340 end | |
| 341 | |
| 342 function N = size(obj) | |
| 343 N = prod(obj.m); | |
| 344 end | |
| 345 | |
| 346 end | |
| 347 | |
| 348 methods(Static) | |
| 349 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 350 % and bound_v of scheme schm_v. | |
| 351 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 352 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 353 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 354 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 355 end | |
| 356 end | |
| 357 end |