Mercurial > repos > public > sbplib

annotate +sbp/+implementations/d2_blocknorm_8.m @ 1198:2924b3a9b921 feature/d2_compatible

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
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_8(m,h)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
2 % Eighth order
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
3
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 BP = 8;
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 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
6 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
7 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
8
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
9 e_1=sparse(m,1);e_1(1)=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
10 e_m=sparse(m,1);e_m(m)=1;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
11
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
12 H_U=[ 0.704266523e9 / 0.4180377600e10 0.4579586639e10 / 0.16257024000e11 -0.3623870581e10 / 0.9754214400e10 0.12753127559e11 / 0.29262643200e11 -0.3687413731e10 / 0.9754214400e10 0.2169892891e10 / 0.9754214400e10 -0.13224544841e11 / 0.146313216000e12 0.4142047e7 / 0.199065600e9;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
13 0.4579586639e10 / 0.16257024000e11 0.36543258551e11 / 0.20901888000e11 -0.8235820121e10 / 0.6967296000e10 0.1800520829e10 / 0.1393459200e10 -0.3725834681e10 / 0.4180377600e10 0.2588501879e10 / 0.6967296000e10 -0.10477621e8 / 0.995328000e9 -0.6589395529e10 / 0.146313216000e12;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
14 -0.3623870581e10 / 0.9754214400e10 -0.8235820121e10 / 0.6967296000e10 0.765685439e9 / 0.258048000e9 -0.3254203513e10 / 0.1393459200e10 0.2477267447e10 / 0.1393459200e10 -0.456533e6 / 0.491520e6 0.873043831e9 / 0.6967296000e10 0.4279558279e10 / 0.48771072000e11;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
15 0.12753127559e11 / 0.29262643200e11 0.1800520829e10 / 0.1393459200e10 -0.3254203513e10 / 0.1393459200e10 0.16428690611e11 / 0.4180377600e10 -0.460605929e9 / 0.199065600e9 0.1897042423e10 / 0.1393459200e10 -0.1151273401e10 / 0.4180377600e10 -0.65906413e8 / 0.650280960e9;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
16 -0.3687413731e10 / 0.9754214400e10 -0.3725834681e10 / 0.4180377600e10 0.2477267447e10 / 0.1393459200e10 -0.460605929e9 / 0.199065600e9 0.11663916211e11 / 0.4180377600e10 -0.307273957e9 / 0.278691840e9 0.117995903e9 / 0.464486400e9 0.95035807e8 / 0.1170505728e10;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
17 0.2169892891e10 / 0.9754214400e10 0.2588501879e10 / 0.6967296000e10 -0.456533e6 / 0.491520e6 0.1897042423e10 / 0.1393459200e10 -0.307273957e9 / 0.278691840e9 0.17436823e8 / 0.10321920e8 -0.1274455129e10 / 0.6967296000e10 -0.338917493e9 / 0.9754214400e10;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
18 -0.13224544841e11 / 0.146313216000e12 -0.10477621e8 / 0.995328000e9 0.873043831e9 / 0.6967296000e10 -0.1151273401e10 / 0.4180377600e10 0.117995903e9 / 0.464486400e9 -0.1274455129e10 / 0.6967296000e10 0.22041718711e11 / 0.20901888000e11 0.468461293e9 / 0.48771072000e11;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
19 0.4142047e7 / 0.199065600e9 -0.6589395529e10 / 0.146313216000e12 0.4279558279e10 / 0.48771072000e11 -0.65906413e8 / 0.650280960e9 0.95035807e8 / 0.1170505728e10 -0.338917493e9 / 0.9754214400e10 0.468461293e9 / 0.48771072000e11 0.20832744839e11 / 0.20901888000e11;
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
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
22
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
23 H=speye(m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
24 H(1:8,1:8)=H_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
25 H(m-7:m,m-7:m)=rot90( H_U(1:8,1:8) ,2 );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
26 H=H*h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
27 HI=inv(H);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
28
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
29 % Q=-(1/280*diag(ones(m-4,1),4)-4/105*diag(ones(m-3,1),3)+1/5*diag(ones(m-2,1),2)-4/5*diag(ones(m-1,1),1)+4/5*diag(ones(m-1,1),-1)-1/5*diag(ones(m-2,1),-2)+4/105*diag(ones(m-3,1),-3)-1/280*diag(ones(m-4,1),-4));
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
30 diags = -4:4;
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
31 stencil = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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 Q = stripeMatrix(stencil, diags, m);
261
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 Q_U = [-0.1e1 / 0.2e1 0.16262381e8 / 0.15876000e8 -0.3770744693e10 / 0.3048192000e10 0.290431859e9 / 0.203212800e9 -0.363704879e9 / 0.304819200e9 0.206906927e9 / 0.304819200e9 -0.248883679e9 / 0.1016064000e10 0.2665637e7 / 0.62208000e8; -0.16262381e8 / 0.15876000e8 0 0.138589901e9 / 0.62208000e8 -0.31764881e8 / 0.12441600e8 0.461249e6 / 0.193536e6 -0.347232997e9 / 0.217728000e9 0.1788157e7 / 0.2488320e7 -0.5926349e7 / 0.37632000e8; 0.3770744693e10 / 0.3048192000e10 -0.138589901e9 / 0.62208000e8 0 0.11741773e8 / 0.5443200e7 -0.39109817e8 / 0.17418240e8 0.10216441e8 / 0.5376000e7 -0.245131109e9 / 0.217728000e9 0.92809903e8 / 0.304819200e9; -0.290431859e9 / 0.203212800e9 0.31764881e8 / 0.12441600e8 -0.11741773e8 / 0.5443200e7 0 0.4634999e7 / 0.2488320e7 -0.144219869e9 / 0.87091200e8 0.17445643e8 / 0.14515200e8 -0.38142949e8 / 0.101606400e9; 0.363704879e9 / 0.304819200e9 -0.461249e6 / 0.193536e6 0.39109817e8 / 0.17418240e8 -0.4634999e7 / 0.2488320e7 0 0.7992221e7 / 0.5443200e7 -0.817951e6 / 0.829440e6 0.4455517e7 / 0.13547520e8; -0.206906927e9 / 0.304819200e9 0.347232997e9 / 0.217728000e9 -0.10216441e8 / 0.5376000e7 0.144219869e9 / 0.87091200e8 -0.7992221e7 / 0.5443200e7 0 0.68487373e8 / 0.62208000e8 -0.1032638773e10 / 0.3048192000e10; 0.248883679e9 / 0.1016064000e10 -0.1788157e7 / 0.2488320e7 0.245131109e9 / 0.217728000e9 -0.17445643e8 / 0.14515200e8 0.817951e6 / 0.829440e6 -0.68487373e8 / 0.62208000e8 0 0.39529771e8 / 0.47628000e8; -0.2665637e7 / 0.62208000e8 0.5926349e7 / 0.37632000e8 -0.92809903e8 / 0.304819200e9 0.38142949e8 / 0.101606400e9 -0.4455517e7 / 0.13547520e8 0.1032638773e10 / 0.3048192000e10 -0.39529771e8 / 0.47628000e8 0;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
35
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
36 Q(1:8,1:8)=Q_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
37 Q(m-7:m,m-7:m)=rot90( -Q_U(1:8,1:8) ,2 );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
38
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
39 D1=H\Q;
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
40
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
41
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
42 M_U =[0.27667249117e11 / 0.18289152000e11 -0.17100791927e11 / 0.6096384000e10 0.6123596021e10 / 0.2032128000e10 -0.12420079921e11 / 0.3657830400e10 0.3352522937e10 / 0.1219276800e10 -0.3030351383e10 / 0.2032128000e10 0.8955233071e10 / 0.18289152000e11 -0.448917533e9 / 0.6096384000e10; -0.2443029521e10 / 0.870912000e9 0.3279926909e10 / 0.373248000e9 -0.150833107e9 / 0.11612160e8 0.2418903029e10 / 0.174182400e9 -0.1195687489e10 / 0.104509440e9 0.1864443097e10 / 0.290304000e9 -0.275412413e9 / 0.124416000e9 0.26267539e8 / 0.74649600e8; 0.875033123e9 / 0.290304000e9 -0.754432799e9 / 0.58060800e8 0.262316881e9 / 0.10752000e8 -0.1615952663e10 / 0.58060800e8 0.1304948581e10 / 0.58060800e8 -0.59605951e8 / 0.4608000e7 0.270029509e9 / 0.58060800e8 -0.225377137e9 / 0.290304000e9; -0.71086111e8 / 0.20901888e8 0.2425994741e10 / 0.174182400e9 -0.1622486807e10 / 0.58060800e8 0.735382895e9 / 0.20901888e8 -0.1016121419e10 / 0.34836480e8 0.190014817e9 / 0.11612160e8 -0.447155539e9 / 0.74649600e8 0.179406911e9 / 0.174182400e9; 0.480578879e9 / 0.174182400e9 -0.6018333509e10 / 0.522547200e9 0.1319413093e10 / 0.58060800e8 -0.205032463e9 / 0.6967296e7 0.551889007e9 / 0.20901888e8 -0.887809303e9 / 0.58060800e8 0.914606453e9 / 0.174182400e9 -0.67482881e8 / 0.74649600e8; -0.434493809e9 / 0.290304000e9 0.1878773977e10 / 0.290304000e9 -0.423185977e9 / 0.32256000e8 0.964538597e9 / 0.58060800e8 -0.894343447e9 / 0.58060800e8 0.345461491e9 / 0.32256000e8 -0.1288081307e10 / 0.290304000e9 0.199200163e9 / 0.290304000e9; 0.183060319e9 / 0.373248000e9 -0.276656573e9 / 0.124416000e9 0.54579137e8 / 0.11612160e8 -0.3169984837e10 / 0.522547200e9 0.184339633e9 / 0.34836480e8 -0.1289417627e10 / 0.290304000e9 0.1431981949e10 / 0.373248000e9 -0.307164061e9 / 0.174182400e9; -0.449332253e9 / 0.6096384000e10 0.1290053923e10 / 0.3657830400e10 -0.1588745239e10 / 0.2032128000e10 0.1267377593e10 / 0.1219276800e10 -0.3326650673e10 / 0.3657830400e10 0.1396036981e10 / 0.2032128000e10 -0.2150231371e10 / 0.1219276800e10 0.52544801501e11 / 0.18289152000e11;];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
43
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
44 % M=-(-1/560*diag(ones(m-4,1),4)+8/315*diag(ones(m-3,1),3)-1/5*diag(ones(m-2,1),2)+8/5*diag(ones(m-1,1),1)+8/5*diag(ones(m-1,1),-1)-1/5*diag(ones(m-2,1),-2)+8/315*diag(ones(m-3,1),-3)-1/560*diag(ones(m-4,1),-4)-205/72*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
45 diags = -4:4;
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 left_stencil = [-1/560,8/315,-1/5,8/5];
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
47 stencil = [left_stencil,-205/72,fliplr(left_stencil)];
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 M = stripeMatrix(stencil, diags, m);
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
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
50 M(1:8,1:8)=M_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
51
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
52 M(m-7:m,m-7:m)=rot90( M_U ,2 );
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
53 M=M/h;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
54
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
55 % DS_U=[0.363e3 / 0.140e3 -7 0.21e2 / 0.2e1 -0.35e2 / 0.3e1 0.35e2 / 0.4e1 -0.21e2 / 0.5e1 0.7e1 / 0.6e1 -0.1e1 / 0.7e1;];
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
56 % DS=sparse(m,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
57 % DS(1,1:8)=DS_U;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
58 % DS(m,m-7:m)=fliplr(DS_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
59 % DS=DS/h;
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 %D2=HI*(-M+DS);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
62
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
63 S_U=-[0.363e3 / 0.140e3 -7 0.21e2 / 0.2e1 -0.35e2 / 0.3e1 0.35e2 / 0.4e1 -0.21e2 / 0.5e1 0.7e1 / 0.6e1 -0.1e1 / 0.7e1;]/h;
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 S_1=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
65 S_1(1:8)=S_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
66 S_m=sparse(1,m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
67 S_m(m-7:m)=fliplr(-S_U);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
68
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
69
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
70 D2=H\(-M - e_1*S_1+e_m*S_m);
261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
71 S_1 = S_1';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
72 S_m = S_m';
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
73 end