Mercurial > repos > public > sbplib

annotate +sbp/+implementations/d2_blocknorm_4.m @ 266:bfa130b7abf6 operator_remake

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Added error message for too few grid points to all implementation files.
author Martin Almquist <martin.almquist@it.uu.se>
date Fri, 09 Sep 2016 11:03:13 +0200
parents 6009f2712d13
children f7ac3cd6eeaa
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [H, HI, D1, D2, e_1, e_m, M, Q, S_1, S_m] = d2_blocknorm_4(m,h)
266
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
2
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
3 BP = 4;
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
4 if(m<2*BP)
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
6 end
bfa130b7abf6 Added error message for too few grid points to all implementation files.
Martin Almquist <martin.almquist@it.uu.se>
parents: 261
diff changeset
7
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
8 H_U=[0.751e3 / 0.3456e4 0.661e3 / 0.3456e4 -0.515e3 / 0.3456e4 0.5e1 / 0.128e3; 0.661e3 / 0.3456e4 0.1405e4 / 0.1152e4 -0.3e1 / 0.128e3 0.29e2 / 0.3456e4; -0.515e3 / 0.3456e4 -0.3e1 / 0.128e3 0.989e3 / 0.1152e4 0.149e3 / 0.3456e4; 0.5e1 / 0.128e3 0.29e2 / 0.3456e4 0.149e3 / 0.3456e4 0.3407e4 / 0.3456e4;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
9
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
10
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
11 H=eye(m);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 H(1:4,1:4)=H_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
13 H(m-3:m,m-3:m)=flipud( fliplr(H_U(1:4,1:4) ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
14 H=H*h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
15 HI=inv(H);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
16
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
17 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));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
18
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
19 Q_U = [-0.1e1 / 0.2e1 0.55e2 / 0.72e2 -0.47e2 / 0.144e3 0.1e1 / 0.16e2; -0.55e2 / 0.72e2 0 0.43e2 / 0.48e2 -0.19e2 / 0.144e3; 0.47e2 / 0.144e3 -0.43e2 / 0.48e2 0 0.47e2 / 0.72e2; -0.1e1 / 0.16e2 0.19e2 / 0.144e3 -0.47e2 / 0.72e2 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
20
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
21 Q(1:4,1:4)=Q_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
22 Q(m-3:m,m-3:m)=flipud( fliplr(-Q_U(1:4,1:4) ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
23
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
24 D1=HI*Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
25
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
26 M_U=[0.359e3 / 0.288e3 -0.443e3 / 0.288e3 0.97e2 / 0.288e3 -0.13e2 / 0.288e3; -0.51e2 / 0.32e2 0.325e3 / 0.96e2 -0.191e3 / 0.96e2 0.19e2 / 0.96e2; 0.43e2 / 0.96e2 -0.69e2 / 0.32e2 0.293e3 / 0.96e2 -0.137e3 / 0.96e2; -0.29e2 / 0.288e3 0.89e2 / 0.288e3 -0.427e3 / 0.288e3 0.727e3 / 0.288e3;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
27
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
28
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
29
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
30 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));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
31
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
32 M(1:4,1:4)=M_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
33
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
34 M(m-3:m,m-3:m)=flipud( fliplr( M_U ) );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
35 M=M/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
37 DS_U=[0.25e2 / 0.12e2 -4 3 -0.4e1 / 0.3e1 0.1e1 / 0.4e1;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
38 DS=zeros(m,m);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
39 DS(1,1:5)=DS_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40 DS(m,m-4:m)=fliplr(DS_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
41 DS=DS/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43 D2=HI*(-M+DS);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
44
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
45 d3=[-1 3 -3 1];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
46 t3=sum(abs(d3));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
47 DD_3(1:1,1:4)=[d3];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
48 DD_3(m:m,m-3:m)=[d3];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
49
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
50 % This works for wave eq.
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
51 % For studs interface in 1D no AD is needed.
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52 ADD=1*h/(t3)*DD_3'*DD_3;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
54 e_1 = zeros(m,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
55 e_1(1)= 1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
56 e_m = zeros(m,1);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
57 e_m(end)= 1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 S_1 = -DS(1,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59 S_m = DS(end,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
60
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
61 Q = H*D1-(-e_1*e_1' + e_m*e_m');
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62 M = -(H*D2-(-e_1*S_1' + e_m*S_m'));
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63 end