Mercurial > repos > public > sbplib

annotate +sbp/+implementations/d2_blocknorm_4.m @ 1037:2d7ba44340d0 feature/burgers1d

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents f7ac3cd6eeaa
children
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
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
11 H=speye(m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 H(1:4,1:4)=H_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
13 H(m-3:m,m-3:m)=rot90( H_U(1:4,1:4) ,2 );
261
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
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
17 e=ones(m,1);
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
18 Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
19 % 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));
261
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_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
22
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
23 Q(1:4,1:4)=Q_U;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
24 Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
25
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
26 D1=H\Q;
261
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 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
29
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
30
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
31
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
32 % 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));
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
33 M=-spdiags([-e 16*e -30*e 16*e -e], -2:2, m, m)/12;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
34
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
35 M(1:4,1:4)=M_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
37 M(m-3:m,m-3:m)=rot90( M_U ,2 );
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
38 M=M/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
39
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40 DS_U=[0.25e2 / 0.12e2 -4 3 -0.4e1 / 0.3e1 0.1e1 / 0.4e1;];
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
41 DS=sparse(m,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42 DS(1,1:5)=DS_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43 DS(m,m-4:m)=fliplr(DS_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
44 DS=DS/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
45
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
46 D2=H\(-M+DS);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
47
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
48 % d3=[-1 3 -3 1];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
49 % t3=sum(abs(d3));
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
50 % DD_3(1:1,1:4)=[d3];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
51 % DD_3(m:m,m-3:m)=[d3];
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53 % This works for wave eq.
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
54 % For studs interface in 1D no AD is needed.
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
55 % ADD=1*h/(t3)*DD_3'*DD_3;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
56
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
57 e_1 = sparse(m,1);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 e_1(1)= 1;
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
59 e_m = sparse(m,1);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
60 e_m(end)= 1;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
61 S_1 = -DS(1,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62 S_m = DS(end,:)';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63
267
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
Martin Almquist <martin.almquist@it.uu.se>
parents: 266
diff changeset
64 Q = H*D1-(-(e_1*e_1') + (e_m*e_m'));
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
65 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
66 end