Mercurial > repos > public > sbplib
annotate +scheme/Beam2d.m @ 125:d52e5cdb6eff
Fixed some class name, file name errors.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Wed, 27 Jan 2016 17:37:23 +0100 |
| parents | 48b6fb693025 |
| children | cb2b12246b7e |
| rev | line source |
|---|---|
|
125
d52e5cdb6eff
Fixed some class name, file name errors.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
1 classdef Beam2d < noname.Scheme |
| 0 | 2 properties |
| 3 m % Number of points in each direction, possibly a vector | |
| 4 N % Number of points total | |
| 5 h % Grid spacing | |
| 6 u,v % Grid | |
| 7 x,y % Values of x and y for each grid point | |
| 8 order % Order accuracy for the approximation | |
| 9 | |
| 10 D % non-stabalized scheme operator | |
| 11 M % Derivative norm | |
| 12 alpha | |
| 13 | |
| 14 H % Discrete norm | |
| 15 Hi | |
| 16 H_x, H_y % Norms in the x and y directions | |
| 17 Hx,Hy % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. | |
| 18 Hi_x, Hi_y | |
| 19 Hix, Hiy | |
| 20 e_w, e_e, e_s, e_n | |
| 21 d1_w, d1_e, d1_s, d1_n | |
| 22 d2_w, d2_e, d2_s, d2_n | |
| 23 d3_w, d3_e, d3_s, d3_n | |
| 24 gamm_x, gamm_y | |
| 25 delt_x, delt_y | |
| 26 end | |
| 27 | |
| 28 methods | |
|
125
d52e5cdb6eff
Fixed some class name, file name errors.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
29 function obj = Beam2d(m,lim,order,alpha,opsGen) |
| 0 | 30 default_arg('opsGen',@sbp.Higher); |
| 31 default_arg('a',1); | |
| 32 | |
| 33 if length(m) == 1 | |
| 34 m = [m m]; | |
| 35 end | |
| 36 | |
| 37 m_x = m(1); | |
| 38 m_y = m(2); | |
| 39 | |
| 40 xlim = lim{1}; | |
| 41 ylim = lim{2}; | |
| 42 | |
| 43 [x, h_x] = util.get_grid(xlim{:},m_x); | |
| 44 [y, h_y] = util.get_grid(ylim{:},m_y); | |
| 45 | |
| 46 ops_x = opsGen(m_x,h_x,order); | |
| 47 ops_y = opsGen(m_y,h_y,order); | |
| 48 | |
| 49 I_x = speye(m_x); | |
| 50 I_y = speye(m_y); | |
| 51 | |
| 52 | |
| 53 | |
| 54 | |
| 55 D4_x = sparse(ops_x.derivatives.D4); | |
| 56 H_x = sparse(ops_x.norms.H); | |
| 57 Hi_x = sparse(ops_x.norms.HI); | |
| 58 e_l_x = sparse(ops_x.boundary.e_1); | |
| 59 e_r_x = sparse(ops_x.boundary.e_m); | |
| 60 d1_l_x = sparse(ops_x.boundary.S_1); | |
| 61 d1_r_x = sparse(ops_x.boundary.S_m); | |
| 62 d2_l_x = sparse(ops_x.boundary.S2_1); | |
| 63 d2_r_x = sparse(ops_x.boundary.S2_m); | |
| 64 d3_l_x = sparse(ops_x.boundary.S3_1); | |
| 65 d3_r_x = sparse(ops_x.boundary.S3_m); | |
| 66 | |
| 67 D4_y = sparse(ops_y.derivatives.D4); | |
| 68 H_y = sparse(ops_y.norms.H); | |
| 69 Hi_y = sparse(ops_y.norms.HI); | |
| 70 e_l_y = sparse(ops_y.boundary.e_1); | |
| 71 e_r_y = sparse(ops_y.boundary.e_m); | |
| 72 d1_l_y = sparse(ops_y.boundary.S_1); | |
| 73 d1_r_y = sparse(ops_y.boundary.S_m); | |
| 74 d2_l_y = sparse(ops_y.boundary.S2_1); | |
| 75 d2_r_y = sparse(ops_y.boundary.S2_m); | |
| 76 d3_l_y = sparse(ops_y.boundary.S3_1); | |
| 77 d3_r_y = sparse(ops_y.boundary.S3_m); | |
| 78 | |
| 79 | |
| 80 D4 = kr(D4_x, I_y) + kr(I_x, D4_y); | |
| 81 | |
| 82 % Norms | |
| 83 obj.H = kr(H_x,H_y); | |
| 84 obj.Hx = kr(H_x,I_x); | |
| 85 obj.Hy = kr(I_x,H_y); | |
| 86 obj.Hix = kr(Hi_x,I_y); | |
| 87 obj.Hiy = kr(I_x,Hi_y); | |
| 88 obj.Hi = kr(Hi_x,Hi_y); | |
| 89 | |
| 90 % Boundary operators | |
| 91 obj.e_w = kr(e_l_x,I_y); | |
| 92 obj.e_e = kr(e_r_x,I_y); | |
| 93 obj.e_s = kr(I_x,e_l_y); | |
| 94 obj.e_n = kr(I_x,e_r_y); | |
| 95 obj.d1_w = kr(d1_l_x,I_y); | |
| 96 obj.d1_e = kr(d1_r_x,I_y); | |
| 97 obj.d1_s = kr(I_x,d1_l_y); | |
| 98 obj.d1_n = kr(I_x,d1_r_y); | |
| 99 obj.d2_w = kr(d2_l_x,I_y); | |
| 100 obj.d2_e = kr(d2_r_x,I_y); | |
| 101 obj.d2_s = kr(I_x,d2_l_y); | |
| 102 obj.d2_n = kr(I_x,d2_r_y); | |
| 103 obj.d3_w = kr(d3_l_x,I_y); | |
| 104 obj.d3_e = kr(d3_r_x,I_y); | |
| 105 obj.d3_s = kr(I_x,d3_l_y); | |
| 106 obj.d3_n = kr(I_x,d3_r_y); | |
| 107 | |
| 108 obj.m = m; | |
| 109 obj.h = [h_x h_y]; | |
| 110 obj.order = order; | |
| 111 | |
| 112 obj.alpha = alpha; | |
| 113 obj.D = alpha*D4; | |
| 114 obj.u = x; | |
| 115 obj.v = y; | |
| 116 obj.x = kr(x,ones(m_y,1)); | |
| 117 obj.y = kr(ones(m_x,1),y); | |
| 118 | |
| 119 obj.gamm_x = h_x*ops_x.borrowing.N.S2/2; | |
| 120 obj.delt_x = h_x^3*ops_x.borrowing.N.S3/2; | |
| 121 | |
| 122 obj.gamm_y = h_y*ops_y.borrowing.N.S2/2; | |
| 123 obj.delt_y = h_y^3*ops_y.borrowing.N.S3/2; | |
| 124 end | |
| 125 | |
| 126 | |
| 127 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 128 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 129 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 130 % type is a string specifying the type of boundary condition if there are several. | |
| 131 % data is a function returning the data that should be applied at the boundary. | |
| 132 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 133 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 134 function [closure, penalty_e,penalty_d] = boundary_condition(obj,boundary,type,data) | |
| 135 default_arg('type','dn'); | |
| 136 default_arg('data',0); | |
| 137 | |
| 138 [e,d1,d2,d3,s,gamm,delt,halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 139 | |
| 140 switch type | |
| 141 % Dirichlet-neumann boundary condition | |
| 142 case {'dn'} | |
| 143 alpha = obj.alpha; | |
| 144 | |
| 145 % tau1 < -alpha^2/gamma | |
| 146 tuning = 1.1; | |
| 147 | |
| 148 tau1 = tuning * alpha/delt; | |
| 149 tau4 = s*alpha; | |
| 150 | |
| 151 sig2 = tuning * alpha/gamm; | |
| 152 sig3 = -s*alpha; | |
| 153 | |
| 154 tau = tau1*e+tau4*d3; | |
| 155 sig = sig2*d1+sig3*d2; | |
| 156 | |
| 157 closure = halfnorm_inv*(tau*e' + sig*d1'); | |
| 158 | |
| 159 pp_e = halfnorm_inv*tau; | |
| 160 pp_d = halfnorm_inv*sig; | |
| 161 switch class(data) | |
| 162 case 'double' | |
| 163 penalty_e = pp_e*data; | |
| 164 penalty_d = pp_d*data; | |
| 165 case 'function_handle' | |
| 166 penalty_e = @(t)pp_e*data(t); | |
| 167 penalty_d = @(t)pp_d*data(t); | |
| 168 otherwise | |
| 169 error('Wierd data argument!') | |
| 170 end | |
| 171 | |
| 172 % Unknown, boundary condition | |
| 173 otherwise | |
| 174 error('No such boundary condition: type = %s',type); | |
| 175 end | |
| 176 end | |
| 177 | |
| 178 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 179 % u denotes the solution in the own domain | |
| 180 % v denotes the solution in the neighbour domain | |
| 181 [e_u,d1_u,d2_u,d3_u,s_u,gamm_u,delt_u, halfnorm_inv] = obj.get_boundary_ops(boundary); | |
| 182 [e_v,d1_v,d2_v,d3_v,s_v,gamm_v,delt_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); | |
| 183 | |
| 184 tuning = 2; | |
| 185 | |
| 186 alpha_u = obj.alpha; | |
| 187 alpha_v = neighbour_scheme.alpha; | |
| 188 | |
| 189 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning; | |
| 190 % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning; | |
| 191 tau4 = s_u*alpha_u/2; | |
| 192 | |
| 193 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning; | |
| 194 sig3 = -s_u*alpha_u/2; | |
| 195 | |
| 196 phi2 = s_u*1/2; | |
| 197 | |
| 198 psi1 = -s_u*1/2; | |
| 199 | |
| 200 tau = tau1*e_u + tau4*d3_u; | |
| 201 sig = sig2*d1_u + sig3*d2_u ; | |
| 202 phi = phi2*d1_u ; | |
| 203 psi = psi1*e_u ; | |
| 204 | |
| 205 closure = halfnorm_inv*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u'); | |
| 206 penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v'); | |
| 207 end | |
| 208 | |
| 209 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 210 % The right boundary is considered the positive boundary | |
| 211 function [e,d1,d2,d3,s,gamm, delt, halfnorm_inv] = get_boundary_ops(obj,boundary) | |
| 212 switch boundary | |
| 213 case 'w' | |
| 214 e = obj.e_w; | |
| 215 d1 = obj.d1_w; | |
| 216 d2 = obj.d2_w; | |
| 217 d3 = obj.d3_w; | |
| 218 s = -1; | |
| 219 gamm = obj.gamm_x; | |
| 220 delt = obj.delt_x; | |
| 221 halfnorm_inv = obj.Hix; | |
| 222 case 'e' | |
| 223 e = obj.e_e; | |
| 224 d1 = obj.d1_e; | |
| 225 d2 = obj.d2_e; | |
| 226 d3 = obj.d3_e; | |
| 227 s = 1; | |
| 228 gamm = obj.gamm_x; | |
| 229 delt = obj.delt_x; | |
| 230 halfnorm_inv = obj.Hix; | |
| 231 case 's' | |
| 232 e = obj.e_s; | |
| 233 d1 = obj.d1_s; | |
| 234 d2 = obj.d2_s; | |
| 235 d3 = obj.d3_s; | |
| 236 s = -1; | |
| 237 gamm = obj.gamm_y; | |
| 238 delt = obj.delt_y; | |
| 239 halfnorm_inv = obj.Hiy; | |
| 240 case 'n' | |
| 241 e = obj.e_n; | |
| 242 d1 = obj.d1_n; | |
| 243 d2 = obj.d2_n; | |
| 244 d3 = obj.d3_n; | |
| 245 s = 1; | |
| 246 gamm = obj.gamm_y; | |
| 247 delt = obj.delt_y; | |
| 248 halfnorm_inv = obj.Hiy; | |
| 249 otherwise | |
| 250 error('No such boundary: boundary = %s',boundary); | |
| 251 end | |
| 252 end | |
| 253 | |
| 254 function N = size(obj) | |
| 255 N = prod(obj.m); | |
| 256 end | |
| 257 | |
| 258 end | |
| 259 end |