Mercurial > repos > public > sbplib
annotate +scheme/Wave2d.m @ 282:18c023aaf3f7 v0.1
Merge.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 12 Sep 2016 11:14:00 +0200 |
| parents | a8ed986fcf57 |
| children | 459eeb99130f |
| rev | line source |
|---|---|
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a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
1 classdef Wave2d < scheme.Scheme |
| 0 | 2 properties |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 h % Grid spacing | |
| 5 x,y % Grid | |
| 6 X,Y % Values of x and y for each grid point | |
| 7 order % Order accuracy for the approximation | |
| 8 | |
| 9 D % non-stabalized scheme operator | |
| 10 M % Derivative norm | |
| 11 alpha | |
| 12 | |
| 13 H % Discrete norm | |
| 14 Hi | |
| 15 H_x, H_y % Norms in the x and y directions | |
| 16 Hx,Hy % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. | |
| 17 Hi_x, Hi_y | |
| 18 Hix, Hiy | |
| 19 e_w, e_e, e_s, e_n | |
| 20 d1_w, d1_e, d1_s, d1_n | |
| 21 gamm_x, gamm_y | |
| 22 end | |
| 23 | |
| 24 methods | |
|
55
a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
25 function obj = Wave2d(m,lim,order,alpha) |
|
a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
26 default_arg('alpha',1); |
|
a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
27 |
|
a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
28 xlim = lim{1}; |
|
a8ed986fcf57
Minor renaming and clean up in 2d wave schemes.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
29 ylim = lim{2}; |
| 0 | 30 |
| 31 if length(m) == 1 | |
| 32 m = [m m]; | |
| 33 end | |
| 34 | |
| 35 m_x = m(1); | |
| 36 m_y = m(2); | |
| 37 | |
| 38 [x, h_x] = util.get_grid(xlim{:},m_x); | |
| 39 [y, h_y] = util.get_grid(ylim{:},m_y); | |
| 40 | |
| 41 ops_x = sbp.Ordinary(m_x,h_x,order); | |
| 42 ops_y = sbp.Ordinary(m_y,h_y,order); | |
| 43 | |
| 44 I_x = speye(m_x); | |
| 45 I_y = speye(m_y); | |
| 46 | |
| 47 D2_x = sparse(ops_x.derivatives.D2); | |
| 48 H_x = sparse(ops_x.norms.H); | |
| 49 Hi_x = sparse(ops_x.norms.HI); | |
| 50 M_x = sparse(ops_x.norms.M); | |
| 51 e_l_x = sparse(ops_x.boundary.e_1); | |
| 52 e_r_x = sparse(ops_x.boundary.e_m); | |
| 53 d1_l_x = sparse(ops_x.boundary.S_1); | |
| 54 d1_r_x = sparse(ops_x.boundary.S_m); | |
| 55 | |
| 56 D2_y = sparse(ops_y.derivatives.D2); | |
| 57 H_y = sparse(ops_y.norms.H); | |
| 58 Hi_y = sparse(ops_y.norms.HI); | |
| 59 M_y = sparse(ops_y.norms.M); | |
| 60 e_l_y = sparse(ops_y.boundary.e_1); | |
| 61 e_r_y = sparse(ops_y.boundary.e_m); | |
| 62 d1_l_y = sparse(ops_y.boundary.S_1); | |
| 63 d1_r_y = sparse(ops_y.boundary.S_m); | |
| 64 | |
| 65 D2 = kr(D2_x, I_y) + kr(I_x, D2_y); | |
| 66 obj.H = kr(H_x,H_y); | |
| 67 obj.Hx = kr(H_x,I_y); | |
| 68 obj.Hy = kr(I_x,H_y); | |
| 69 obj.Hix = kr(Hi_x,I_y); | |
| 70 obj.Hiy = kr(I_x,Hi_y); | |
| 71 obj.Hi = kr(Hi_x,Hi_y); | |
| 72 obj.M = kr(M_x,H_y)+kr(H_x,M_y); | |
| 73 obj.e_w = kr(e_l_x,I_y); | |
| 74 obj.e_e = kr(e_r_x,I_y); | |
| 75 obj.e_s = kr(I_x,e_l_y); | |
| 76 obj.e_n = kr(I_x,e_r_y); | |
| 77 obj.d1_w = kr(d1_l_x,I_y); | |
| 78 obj.d1_e = kr(d1_r_x,I_y); | |
| 79 obj.d1_s = kr(I_x,d1_l_y); | |
| 80 obj.d1_n = kr(I_x,d1_r_y); | |
| 81 | |
| 82 obj.m = m; | |
| 83 obj.h = [h_x h_y]; | |
| 84 obj.order = order; | |
| 85 | |
| 86 obj.alpha = alpha; | |
| 87 obj.D = alpha*D2; | |
| 88 obj.x = x; | |
| 89 obj.y = y; | |
| 90 obj.X = kr(x,ones(m_y,1)); | |
| 91 obj.Y = kr(ones(m_x,1),y); | |
| 92 | |
| 93 obj.gamm_x = h_x*ops_x.borrowing.M.S; | |
| 94 obj.gamm_y = h_y*ops_y.borrowing.M.S; | |
| 95 end | |
| 96 | |
| 97 | |
| 98 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 99 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 100 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 101 % type is a string specifying the type of boundary condition if there are several. | |
| 102 % data is a function returning the data that should be applied at the boundary. | |
| 103 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 104 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 105 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 106 default_arg('type','neumann'); | |
| 107 default_arg('data',0); | |
| 108 | |
| 109 [e,d,s,gamm,halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 110 | |
| 111 switch type | |
| 112 % Dirichlet boundary condition | |
| 113 case {'D','d','dirichlet'} | |
| 114 alpha = obj.alpha; | |
| 115 | |
| 116 % tau1 < -alpha^2/gamma | |
| 117 tuning = 1.1; | |
| 118 tau1 = -tuning*alpha/gamm; | |
| 119 tau2 = s*alpha; | |
| 120 | |
| 121 p = tau1*e + tau2*d; | |
| 122 | |
| 123 closure = halfnorm_inv*p*e'; | |
| 124 | |
| 125 pp = halfnorm_inv*p; | |
| 126 switch class(data) | |
| 127 case 'double' | |
| 128 penalty = pp*data; | |
| 129 case 'function_handle' | |
| 130 penalty = @(t)pp*data(t); | |
| 131 otherwise | |
| 132 error('Wierd data argument!') | |
| 133 end | |
| 134 | |
| 135 | |
| 136 % Neumann boundary condition | |
| 137 case {'N','n','neumann'} | |
| 138 alpha = obj.alpha; | |
| 139 tau1 = -s*alpha; | |
| 140 tau2 = 0; | |
| 141 tau = tau1*e + tau2*d; | |
| 142 | |
| 143 closure = halfnorm_inv*tau*d'; | |
| 144 | |
| 145 pp = halfnorm_inv*tau; | |
| 146 switch class(data) | |
| 147 case 'double' | |
| 148 penalty = pp*data; | |
| 149 case 'function_handle' | |
| 150 penalty = @(t)pp*data(t); | |
| 151 otherwise | |
| 152 error('Wierd data argument!') | |
| 153 end | |
| 154 | |
| 155 % Unknown, boundary condition | |
| 156 otherwise | |
| 157 error('No such boundary condition: type = %s',type); | |
| 158 end | |
| 159 end | |
| 160 | |
| 161 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 162 % u denotes the solution in the own domain | |
| 163 % v denotes the solution in the neighbour domain | |
| 164 [e_u,d_u,s_u,gamm_u, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 165 [e_v,d_v,s_v,gamm_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); | |
| 166 | |
| 167 tuning = 1.1; | |
| 168 | |
| 169 alpha_u = obj.alpha; | |
| 170 alpha_v = neighbour_scheme.alpha; | |
| 171 | |
| 172 % tau1 < -(alpha_u/gamm_u + alpha_v/gamm_v) | |
| 173 | |
| 174 tau1 = -(alpha_u/gamm_u + alpha_v/gamm_v) * tuning; | |
| 175 tau2 = s_u*1/2*alpha_u; | |
| 176 sig1 = s_u*(-1/2); | |
| 177 sig2 = 0; | |
| 178 | |
| 179 tau = tau1*e_u + tau2*d_u; | |
| 180 sig = sig1*e_u + sig2*d_u; | |
| 181 | |
| 182 closure = halfnorm_inv*( tau*e_u' + sig*alpha_u*d_u'); | |
| 183 penalty = halfnorm_inv*(-tau*e_v' - sig*alpha_v*d_v'); | |
| 184 end | |
| 185 | |
| 186 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 187 % The right boundary is considered the positive boundary | |
| 188 function [e,d,s,gamm, halfnorm_inv] = get_boundary_ops(obj,boundary) | |
| 189 switch boundary | |
| 190 case 'w' | |
| 191 e = obj.e_w; | |
| 192 d = obj.d1_w; | |
| 193 s = -1; | |
| 194 gamm = obj.gamm_x; | |
| 195 halfnorm_inv = obj.Hix; | |
| 196 case 'e' | |
| 197 e = obj.e_e; | |
| 198 d = obj.d1_e; | |
| 199 s = 1; | |
| 200 gamm = obj.gamm_x; | |
| 201 halfnorm_inv = obj.Hix; | |
| 202 case 's' | |
| 203 e = obj.e_s; | |
| 204 d = obj.d1_s; | |
| 205 s = -1; | |
| 206 gamm = obj.gamm_y; | |
| 207 halfnorm_inv = obj.Hiy; | |
| 208 case 'n' | |
| 209 e = obj.e_n; | |
| 210 d = obj.d1_n; | |
| 211 s = 1; | |
| 212 gamm = obj.gamm_y; | |
| 213 halfnorm_inv = obj.Hiy; | |
| 214 otherwise | |
| 215 error('No such boundary: boundary = %s',boundary); | |
| 216 end | |
| 217 end | |
| 218 | |
| 219 function N = size(obj) | |
| 220 N = prod(obj.m); | |
| 221 end | |
| 222 | |
| 223 end | |
| 224 | |
| 225 methods(Static) | |
| 226 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 227 % and bound_v of scheme schm_v. | |
| 228 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 229 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 230 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 231 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 232 end | |
| 233 end | |
| 234 end |