comparison +sbp/+implementations/d4_variable_4.m @ 314:88584b0cfba1 feature/beams

Corrections and clean up order 4
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 23 Sep 2016 22:55:30 +0200
parents 9230c056a574
children 297d2cbfbe15
comparison
equal deleted inserted replaced
313:52b4cdf27633 314:88584b0cfba1
11 BP = 6; 11 BP = 6;
12 if(m<2*BP) 12 if(m<2*BP)
13 error(['Operator requires at least ' num2str(2*BP) ' grid points']); 13 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
14 end 14 end
15 15
16 H = speye(m,m); 16 % Norm
17 H(1:4,1:4) = diag([17/48 59/48 43/48 49/48]); 17 Hv = ones(m,1);
18 H(m-3:m,m-3:m) = rot90(diag([17/48 59/48 43/48 49/48]),2); 18 Hv(1:4) = [17/48 59/48 43/48 49/48];
19 H = H*h; 19 Hv(m-3:m) = rot90(Hv(1:4),2);
20 HI = inv(H); 20 Hv = h*Hv;
21 HI = sparse(HI); 21 H = spdiag(Hv, 0);
22 HI = spdiag(1./Hv, 0);
22 23
23 24
24 % Q=(-1/12*diag(ones(m-2,1),2)+8/12*diag(ones(m-1,1),1)-8/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2)); 25 % Boundary operators
25 e = ones(m,1); 26 e_l = sparse(m,1);
26 % Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12; 27 e_l(1) = 1;
27 % Q_U = [0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2; -0.59e2/0.96e2 0 0.59e2/0.96e2 0; 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2; 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;]; 28 e_r = rot90(e_l, 2);
28 % Q(1:4,1:4)=Q_U;
29 % Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
30 29
31 e_1 = sparse(m,1); 30 d1_l = sparse(m,1);
32 e_1(1) = 1; 31 d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
33 e_m = sparse(m,1); 32 d1_r = -rot90(d1_l);
34 e_m(m) = 1;
35 33
36 % D1=HI*(Q-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ; 34 d2_l = sparse(m,1);
35 d2_l(1:4) = 1/h^2*[2 -5 4 -1];
36 d2_r = rot90(d2_l, 2);
37 37
38 M_U = [ 38 d3_l = sparse(m,1);
39 0.9e1/0.8e1 -0.59e2/0.48e2 0.1e1/0.12e2 0.1e1/0.48e2; 39 d3_l(1:4) = 1/h^3*[-1 3 -3 1];
40 -0.59e2/0.48e2 0.59e2/0.24e2 -0.59e2/0.48e2 0; 40 d3_r = -rot90(d3_l, 2);
41 0.1e1/0.12e2 -0.59e2/0.48e2 0.55e2/0.24e2 -0.59e2/0.48e2;
42 0.1e1/0.48e2 0 -0.59e2/0.48e2 0.59e2/0.24e2;
43 ];
44 % M=-(-1/12*diag(ones(m-2,1),2)+16/12*diag(ones(m-1,1),1)+16/12*diag(ones(m-1,1),-1)-1/12*diag(ones(m-2,1),-2)-30/12*diag(ones(m,1),0));
45 M = -spdiags([-e 16*e -30*e 16*e -e], -2:2, m, m)/12;
46
47 M(1:4,1:4) = M_U;
48
49 M(m-3:m,m-3:m) = rot90( M_U ,2 );
50 M=M/h;
51
52 S_U=[-0.11e2/0.6e1 3 -0.3e1/0.2e1 0.1e1/0.3e1;]/h;
53 S_1=sparse(1,m);
54 S_1(1:4)=S_U;
55 S_m=sparse(1,m);
56 S_m(m-3:m)=fliplr(-S_U);
57 S_1 = S_1';
58 S_m = S_m';
59 41
60 42
43 % First derivative SBP operator,
44 stencil = [1/12 -2/3 0 2/3 -1/12];
45 diags = [-1 0 1];
46
47 Q_U = [
48 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
49 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
50 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
51 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
52 ];
53
54 Q = stripeMatrix(stencil, diags, m);
55 Q(1:4,1:4)=Q_U;
56 Q(m-3:m,m-3:m) = -rot90(Q_U, 2);
57
58 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
59
60
61 % Second derivative
61 M=sparse(m,m); 62 M=sparse(m,m);
62 e_1 = sparse(e_1);
63 e_m = sparse(e_m);
64 S_1 = sparse(S_1);
65 S_m = sparse(S_m);
66 63
67 scheme_width = 5; 64 scheme_width = 5;
68 scheme_radius = (scheme_width-1)/2; 65 scheme_radius = (scheme_width-1)/2;
69 r = (1+scheme_radius):(m-scheme_radius); 66 r = (1+scheme_radius):(m-scheme_radius);
70 67
107 % M(M_diag_ind) = [Mm2 Mm1 M0 Mp1 Mp2]; % This is slightly faster 104 % M(M_diag_ind) = [Mm2 Mm1 M0 Mp1 Mp2]; % This is slightly faster
108 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
109 % Kan man skriva det som en multiplikation av en 3-dim matris? 106 % Kan man skriva det som en multiplikation av en 3-dim matris?
110 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 107 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
111 108
112
113
114
115 M(1:6,1:6) = [ 109 M(1:6,1:6) = [
116 0.12e2/0.17e2 * c(1) + 0.59e2/0.192e3 * c(2) + 0.27010400129e11/0.345067064608e12 * c(3) + 0.69462376031e11/0.2070402387648e13 * c(4) -0.59e2/0.68e2 * c(1) - 0.6025413881e10/0.21126554976e11 * c(3) - 0.537416663e9/0.7042184992e10 * c(4) 0.2e1/0.17e2 * c(1) - 0.59e2/0.192e3 * c(2) + 0.213318005e9/0.16049630912e11 * c(4) + 0.2083938599e10/0.8024815456e10 * c(3) 0.3e1/0.68e2 * c(1) - 0.1244724001e10/0.21126554976e11 * c(3) + 0.752806667e9/0.21126554976e11 * c(4) 0.49579087e8/0.10149031312e11 * c(3) - 0.49579087e8/0.10149031312e11 * c(4) -c(4)/0.784e3 + c(3)/0.784e3; 110 0.12e2/0.17e2 * c(1) + 0.59e2/0.192e3 * c(2) + 0.27010400129e11/0.345067064608e12 * c(3) + 0.69462376031e11/0.2070402387648e13 * c(4) -0.59e2/0.68e2 * c(1) - 0.6025413881e10/0.21126554976e11 * c(3) - 0.537416663e9/0.7042184992e10 * c(4) 0.2e1/0.17e2 * c(1) - 0.59e2/0.192e3 * c(2) + 0.213318005e9/0.16049630912e11 * c(4) + 0.2083938599e10/0.8024815456e10 * c(3) 0.3e1/0.68e2 * c(1) - 0.1244724001e10/0.21126554976e11 * c(3) + 0.752806667e9/0.21126554976e11 * c(4) 0.49579087e8/0.10149031312e11 * c(3) - 0.49579087e8/0.10149031312e11 * c(4) -c(4)/0.784e3 + c(3)/0.784e3;
117 -0.59e2/0.68e2 * c(1) - 0.6025413881e10/0.21126554976e11 * c(3) - 0.537416663e9/0.7042184992e10 * c(4) 0.3481e4/0.3264e4 * c(1) + 0.9258282831623875e16/0.7669235228057664e16 * c(3) + 0.236024329996203e15/0.1278205871342944e16 * c(4) -0.59e2/0.408e3 * c(1) - 0.29294615794607e14/0.29725717938208e14 * c(3) - 0.2944673881023e13/0.29725717938208e14 * c(4) -0.59e2/0.1088e4 * c(1) + 0.260297319232891e15/0.2556411742685888e16 * c(3) - 0.60834186813841e14/0.1278205871342944e16 * c(4) -0.1328188692663e13/0.37594290333616e14 * c(3) + 0.1328188692663e13/0.37594290333616e14 * c(4) -0.8673e4/0.2904112e7 * c(3) + 0.8673e4/0.2904112e7 * c(4); 111 -0.59e2/0.68e2 * c(1) - 0.6025413881e10/0.21126554976e11 * c(3) - 0.537416663e9/0.7042184992e10 * c(4) 0.3481e4/0.3264e4 * c(1) + 0.9258282831623875e16/0.7669235228057664e16 * c(3) + 0.236024329996203e15/0.1278205871342944e16 * c(4) -0.59e2/0.408e3 * c(1) - 0.29294615794607e14/0.29725717938208e14 * c(3) - 0.2944673881023e13/0.29725717938208e14 * c(4) -0.59e2/0.1088e4 * c(1) + 0.260297319232891e15/0.2556411742685888e16 * c(3) - 0.60834186813841e14/0.1278205871342944e16 * c(4) -0.1328188692663e13/0.37594290333616e14 * c(3) + 0.1328188692663e13/0.37594290333616e14 * c(4) -0.8673e4/0.2904112e7 * c(3) + 0.8673e4/0.2904112e7 * c(4);
118 0.2e1/0.17e2 * c(1) - 0.59e2/0.192e3 * c(2) + 0.213318005e9/0.16049630912e11 * c(4) + 0.2083938599e10/0.8024815456e10 * c(3) -0.59e2/0.408e3 * c(1) - 0.29294615794607e14/0.29725717938208e14 * c(3) - 0.2944673881023e13/0.29725717938208e14 * c(4) c(1)/0.51e2 + 0.59e2/0.192e3 * c(2) + 0.13777050223300597e17/0.26218083221499456e17 * c(4) + 0.564461e6/0.13384296e8 * c(5) + 0.378288882302546512209e21/0.270764341349677687456e21 * c(3) c(1)/0.136e3 - 0.125059e6/0.743572e6 * c(5) - 0.4836340090442187227e19/0.5525802884687299744e19 * c(3) - 0.17220493277981e14/0.89177153814624e14 * c(4) -0.10532412077335e14/0.42840005263888e14 * c(4) + 0.1613976761032884305e19/0.7963657098519931984e19 * c(3) + 0.564461e6/0.4461432e7 * c(5) -0.960119e6/0.1280713392e10 * c(4) - 0.3391e4/0.6692148e7 * c(5) + 0.33235054191e11/0.26452850508784e14 * c(3); 112 0.2e1/0.17e2 * c(1) - 0.59e2/0.192e3 * c(2) + 0.213318005e9/0.16049630912e11 * c(4) + 0.2083938599e10/0.8024815456e10 * c(3) -0.59e2/0.408e3 * c(1) - 0.29294615794607e14/0.29725717938208e14 * c(3) - 0.2944673881023e13/0.29725717938208e14 * c(4) c(1)/0.51e2 + 0.59e2/0.192e3 * c(2) + 0.13777050223300597e17/0.26218083221499456e17 * c(4) + 0.564461e6/0.13384296e8 * c(5) + 0.378288882302546512209e21/0.270764341349677687456e21 * c(3) c(1)/0.136e3 - 0.125059e6/0.743572e6 * c(5) - 0.4836340090442187227e19/0.5525802884687299744e19 * c(3) - 0.17220493277981e14/0.89177153814624e14 * c(4) -0.10532412077335e14/0.42840005263888e14 * c(4) + 0.1613976761032884305e19/0.7963657098519931984e19 * c(3) + 0.564461e6/0.4461432e7 * c(5) -0.960119e6/0.1280713392e10 * c(4) - 0.3391e4/0.6692148e7 * c(5) + 0.33235054191e11/0.26452850508784e14 * c(3);
119 0.3e1/0.68e2 * c(1) - 0.1244724001e10/0.21126554976e11 * c(3) + 0.752806667e9/0.21126554976e11 * c(4) -0.59e2/0.1088e4 * c(1) + 0.260297319232891e15/0.2556411742685888e16 * c(3) - 0.60834186813841e14/0.1278205871342944e16 * c(4) c(1)/0.136e3 - 0.125059e6/0.743572e6 * c(5) - 0.4836340090442187227e19/0.5525802884687299744e19 * c(3) - 0.17220493277981e14/0.89177153814624e14 * c(4) 0.3e1/0.1088e4 * c(1) + 0.507284006600757858213e21/0.475219048083107777984e21 * c(3) + 0.1869103e7/0.2230716e7 * c(5) + c(6)/0.24e2 + 0.1950062198436997e16/0.3834617614028832e16 * c(4) -0.4959271814984644613e19/0.20965546238960637264e20 * c(3) - c(6)/0.6e1 - 0.15998714909649e14/0.37594290333616e14 * c(4) - 0.375177e6/0.743572e6 * c(5) -0.368395e6/0.2230716e7 * c(5) + 0.752806667e9/0.539854092016e12 * c(3) + 0.1063649e7/0.8712336e7 * c(4) + c(6)/0.8e1; 113 0.3e1/0.68e2 * c(1) - 0.1244724001e10/0.21126554976e11 * c(3) + 0.752806667e9/0.21126554976e11 * c(4) -0.59e2/0.1088e4 * c(1) + 0.260297319232891e15/0.2556411742685888e16 * c(3) - 0.60834186813841e14/0.1278205871342944e16 * c(4) c(1)/0.136e3 - 0.125059e6/0.743572e6 * c(5) - 0.4836340090442187227e19/0.5525802884687299744e19 * c(3) - 0.17220493277981e14/0.89177153814624e14 * c(4) 0.3e1/0.1088e4 * c(1) + 0.507284006600757858213e21/0.475219048083107777984e21 * c(3) + 0.1869103e7/0.2230716e7 * c(5) + c(6)/0.24e2 + 0.1950062198436997e16/0.3834617614028832e16 * c(4) -0.4959271814984644613e19/0.20965546238960637264e20 * c(3) - c(6)/0.6e1 - 0.15998714909649e14/0.37594290333616e14 * c(4) - 0.375177e6/0.743572e6 * c(5) -0.368395e6/0.2230716e7 * c(5) + 0.752806667e9/0.539854092016e12 * c(3) + 0.1063649e7/0.8712336e7 * c(4) + c(6)/0.8e1;
134 M = M/h; 128 M = M/h;
135 D2 = HI*(-M-c(1)*e_1*S_1'+c(m)*e_m*S_m'); 129 D2 = HI*(-M-c(1)*e_1*S_1'+c(m)*e_m*S_m');
136 end 130 end
137 D2 = @D2_fun; 131 D2 = @D2_fun;
138 132
139 S2_U=[2 -5 4 -1;]/h^2;
140 S2_1=sparse(1,m);
141 S2_1(1:4)=S2_U;
142 S2_m=sparse(1,m);
143 S2_m(m-3:m)=fliplr(S2_U);
144 S2_1 = S2_1';
145 S2_m = S2_m';
146 133
147 m3 = -1/6; 134 % Fourth derivative
148 m2 = 2; 135 stencil = [-1/6,2,-13/2, 28/3,-13/2,2,-1/6];
149 m1 = -13/2; 136 diags = -3:3;
150 m0 = 28/3;
151 % M4=m3*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3))+m2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2))+m1*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1))+m0*diag(ones(m,1),0);
152 stencil = [m3,m2,m1,m0,m1,m2,m3];
153 d = (length(stencil)-1)/2;
154 diags = -d:d;
155 M4 = stripeMatrix(stencil, diags, m); 137 M4 = stripeMatrix(stencil, diags, m);
156
157 %M4=(-1/6*(diag(ones(m-3,1),3)+diag(ones(m-3,1),-3) ) + 2*(diag(ones(m-2,1),2)+diag(ones(m-2,1),-2)) -13/2*(diag(ones(m-1,1),1)+diag(ones(m-1,1),-1)) + 28/3*diag(ones(m,1),0));
158 138
159 M4_U = [ 139 M4_U = [
160 0.5762947e7/0.2316384e7 -0.6374287e7/0.1158192e7 0.573947e6/0.165456e6 -0.124637e6/0.289548e6 0.67979e5/0.2316384e7 -0.60257e5/0.1158192e7; 140 0.5762947e7/0.2316384e7 -0.6374287e7/0.1158192e7 0.573947e6/0.165456e6 -0.124637e6/0.289548e6 0.67979e5/0.2316384e7 -0.60257e5/0.1158192e7;
161 -0.6374287e7/0.1158192e7 0.30392389e8/0.2316384e7 -0.2735053e7/0.289548e6 0.273109e6/0.165456e6 0.83767e5/0.1158192e7 0.245549e6/0.2316384e7; 141 -0.6374287e7/0.1158192e7 0.30392389e8/0.2316384e7 -0.2735053e7/0.289548e6 0.273109e6/0.165456e6 0.83767e5/0.1158192e7 0.245549e6/0.2316384e7;
162 0.573947e6/0.165456e6 -0.2735053e7/0.289548e6 0.5266855e7/0.579096e6 -0.1099715e7/0.289548e6 0.869293e6/0.1158192e7 -0.10195e5/0.144774e6; 142 0.573947e6/0.165456e6 -0.2735053e7/0.289548e6 0.5266855e7/0.579096e6 -0.1099715e7/0.289548e6 0.869293e6/0.1158192e7 -0.10195e5/0.144774e6;
164 0.67979e5/0.2316384e7 0.83767e5/0.1158192e7 0.869293e6/0.1158192e7 -0.324229e6/0.72387e5 0.2626501e7/0.330912e6 -0.7115491e7/0.1158192e7; 144 0.67979e5/0.2316384e7 0.83767e5/0.1158192e7 0.869293e6/0.1158192e7 -0.324229e6/0.72387e5 0.2626501e7/0.330912e6 -0.7115491e7/0.1158192e7;
165 -0.60257e5/0.1158192e7 0.245549e6/0.2316384e7 -0.10195e5/0.144774e6 0.1847891e7/0.1158192e7 -0.7115491e7/0.1158192e7 0.21383077e8/0.2316384e7; 145 -0.60257e5/0.1158192e7 0.245549e6/0.2316384e7 -0.10195e5/0.144774e6 0.1847891e7/0.1158192e7 -0.7115491e7/0.1158192e7 0.21383077e8/0.2316384e7;
166 ]; 146 ];
167 147
168 M4(1:6,1:6) = M4_U; 148 M4(1:6,1:6) = M4_U;
149 M4(m-5:m,m-5:m) = rot90(M4_U, 2);
150 M4 = 1/h^3*M4;
169 151
170 M4(m-5:m,m-5:m) = rot90( M4_U ,2 ); 152 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
171 M4 = M4/h^3;
172
173 S3_U = [-1 3 -3 1;]/h^3;
174 S3_1 = sparse(1,m);
175 S3_1(1:4)=S3_U;
176 S3_m = sparse(1,m);
177 S3_m(m-3:m) = fliplr(-S3_U);
178 S3_1 = S3_1';
179 S3_m = S3_m';
180
181 D4=HI*(M4-e_1*S3_1'+e_m*S3_m' + S_1*S2_1'-S_m*S2_m');
182
183
184
185
186
187 end 153 end