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Add 10 and 12 order boundary optimized operators of Mattsson, Almquist, van der Weide #152

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Add 10 and 12 order boundary optimized operators of Mattsson, Almquist, van der Weide #152

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5d7d852
Add norm matrix and boundaries for order 10 accurate mattson
xlxs4 Oct 28, 2022
044305f
Bump minor version
xlxs4 Oct 31, 2022
c8a04cd
Add acc order 10 grid points vector
xlxs4 Nov 1, 2022
07d2004
Remove commented out code
xlxs4 Nov 1, 2022
fe44ec5
Correct boundaries
xlxs4 Nov 2, 2022
3864143
Working difference operator for order 10
xlxs4 Nov 2, 2022
fb5dbf9
Add 10th order coeffs
xlxs4 Nov 3, 2022
87e173d
Add notes on 12th order
xlxs4 Nov 3, 2022
1a64de6
Add xvector and coeffs for 12th order
xlxs4 Nov 3, 2022
9a1068f
Correct dims 12th order coeffs
xlxs4 Nov 3, 2022
6617d10
Add 10th order minimal
xlxs4 Nov 3, 2022
99e394c
Add minimal 12th order notes
xlxs4 Nov 4, 2022
1e0bcc2
Add minimal order 12th coeffs
xlxs4 Nov 4, 2022
40553e9
Add norm matrix weights for accurate 10 and 12 order
xlxs4 Nov 7, 2022
3db8bd2
Add norm matrix weights for minimal 10 and 12 order
xlxs4 Nov 7, 2022
23d343e
Accurate VanDerWeide coeff fix
xlxs4 Dec 9, 2022
6b19bd2
Add VanDerWeide 1st derivative 10th 12th order tests
xlxs4 Dec 9, 2022
6bac4b4
Merge branch 'main' into boundary-optimized-operators
ranocha Dec 12, 2022
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359 changes: 359 additions & 0 deletions dev/MattssonAlmquistVanDerWeide2018Accurate_dev.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -152,3 +152,362 @@ q12 = [0 0 0 0 0 0 0 1//280 -4//105 1//5 -4//5 0]
Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12)

D1 = H \ (Q - 1//2*e*e'); display(D1)



# order 10
h = [
1.0000000000000e-01,
5.8980851260667e-01,
9.5666820955973e-01,
1.1500297411596e+00,
1.1232986993248e+00,
1.0123020150951e+00,
9.9877122702527e-01,
1.0000873322761e+00,
1.0000045540888e+00,
9.9999861455083e-01,
1, 1, 1, 1, 1]
e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
H = Diagonal(h)

q1 = [-5.0000000000000e-01,
6.7548747038002e-01,
-2.6691978151546e-01,
1.4438714982130e-01,
-7.7273673750760e-02,
2.5570078343005e-02,
4.2808774693299e-03,
-8.2902108933389e-03,
3.2031176427908e-03,
-4.4502749689556e-04,
0, 0, 0, 0, 0]'
q2 = [-6.7548747038002e-01,
0,
9.5146052715180e-01,
-4.2442349882626e-01,
2.1538865145190e-01,
-7.1939778160350e-02,
-8.2539187832840e-03,
1.9930661669090e-02,
-7.7433256989613e-03,
1.0681515760869e-03,
0, 0, 0, 0, 0]'
q3 = [2.6691978151546e-01,
-9.5146052715180e-01,
0,
9.6073770842387e-01,
-3.9378595264609e-01,
1.3302097358959e-01,
8.1200458151489e-05,
-2.3849770528789e-02,
9.6600442856829e-03,
-1.3234579460680e-03,
0, 0, 0, 0, 0]'
q4 = [-1.4438714982130e-01,
4.2442349882626e-01,
-9.6073770842387e-01,
0,
9.1551097634196e-01,
-2.8541713079648e-01,
4.1398809121293e-02,
1.7256059167927e-02,
-9.4349194803610e-03,
1.3875650645663e-03,
0, 0, 0, 0, 0]'
q5 = [7.7273673750760e-02,
-2.1538865145190e-01,
3.9378595264609e-01,
-9.1551097634196e-01,
0,
8.3519401865051e-01,
-2.0586492924974e-01,
3.1230261235901e-02,
-2.0969453466651e-04,
-5.0965470499782e-04,
0, 0, 0, 0, 0]'
q6 = [-2.5570078343005e-02,
7.1939778160350e-02,
-1.3302097358959e-01,
2.8541713079648e-01,
-8.3519401865051e-01,
0,
8.1046389580138e-01,
-2.1879194972141e-01,
5.2977237804899e-02,
-9.0146730522360e-03,
7.9365079365079e-04,
0, 0, 0, 0]'
q7 = [-4.2808774693299e-03,
8.2539187832840e-03,
-8.1200458151489e-05,
-4.1398809121293e-02,
2.0586492924974e-01,
-8.1046389580138e-01,
0,
8.2787884456005e-01,
-2.3582460382545e-01,
5.9178678209520e-02,
-9.9206349206349e-03,
7.9365079365079e-04,
0, 0, 0]'
q8 = [8.2902108933389e-03,
-1.9930661669090e-02,
2.3849770528789e-02,
-1.7256059167927e-02,
-3.1230261235901e-02,
2.1879194972141e-01,
-8.2787884456005e-01,
0,
8.3301028859275e-01,
-2.3804321850015e-01,
5.9523809523809e-02,
-9.9206349206349e-03,
7.9365079365079e-04,
0, 0]'
q9 = [-3.2031176427908e-03,
7.7433256989613e-03,
-9.6600442856829e-03,
9.4349194803610e-03,
2.0969453466651e-04,
-5.2977237804899e-02,
2.3582460382545e-01,
-8.3301028859275e-01,
0,
8.3333655748509e-01,
-2.3809523809524e-01,
5.9523809523809e-02,
-9.9206349206349e-03,
7.9365079365079e-04,
0]'
q10 = [4.4502749689556e-04,
-1.0681515760869e-03,
1.3234579460680e-03,
-1.3875650645663e-03,
5.0965470499782e-04,
9.0146730522360e-03,
-5.9178678209520e-02,
2.3804321850015e-01,
-8.3333655748509e-01,
0,
8.3333333333333e-01,
-2.3809523809524e-01,
5.9523809523809e-02,
-9.9206349206349e-03,
7.9365079365079e-04]'
q11 = [0 0 0 0 -1//1260 5//504 -5//84 5//21 -5//6 0 5//6 -5//21 5//84 -5//504 1//1260]
q12 = [0 0 0 0 0 -1//1260 5//504 -5//84 5//21 -5//6 0 5//6 -5//21 5//84 -5//504]
q13 = [0 0 0 0 0 0 -1//1260 5//504 -5//84 5//21 -5//6 0 5//6 -5//21 5//84]
q14 = [0 0 0 0 0 0 0 -1//1260 5//504 -5//84 5//21 -5//6 0 5//6 -5//21]
q15 = [0 0 0 0 0 0 0 0 -1//1260 5//504 -5//84 5//21 -5//6 0 5//6]

Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12, q13, q14, q15)

D1 = H \ (Q - 1//2*e*e'); display(D1)



# order 12
h = [
1.0000000000011e-01,
5.9616216757547e-01,
9.9065699844442e-01,
1.2512548713913e+00,
1.3316678989403e+00,
1.2093375037721e+00,
1.0236491595704e+00,
9.9685258909811e-01,
1.0004766563923e+00,
9.9993617879146e-01,
1.0000063122914e+00,
9.9999966373260e-01,
1, 1, 1, 1, 1, 1]
e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
H = Diagonal(h)

q1 = [-5,
6.7597560728423e-01,
-2.6859785384416e-01,
1.4850302678903e-01,
-8.7976689586154e-02,
4.1833336322613e-02,
-2.2216684976993e-03,
-1.5910034062022e-02,
1.1296706376589e-02,
-3.1823678285130e-03,
2.4843594063649e-04,
3.1501105449828e-05,
0, 0, 0, 0, 0, 0]'
q2 = [-6.7597560728423e-01,
0,
9.5424013647146e-01,
-4.3389334603464e-01,
2.4285669347653e-01,
-1.1443465137214e-01,
8.5942765682435e-03,
4.0290424215772e-02,
-2.9396383714543e-02,
8.5601827834256e-03,
-7.8128092862319e-04,
-6.0444181254875e-05,
0, 0, 0, 0, 0, 0]'
q3 = [2.6859785384416e-01,
-9.5424013647146e-01,
0,
9.7065114311923e-01,
-4.3205328628292e-01,
1.9549970932735e-01,
-2.4406885385172e-02,
-5.5737279079895e-02,
4.3772338637753e-02,
-1.3727655130726e-02,
1.6271304373071e-03,
1.7066984372933e-05,
0, 0, 0, 0, 0, 0]'
q4 = [-1.4850302678903e-01,
4.3389334603464e-01,
-9.7065114311923e-01,
0,
9.5375878629204e-01,
-3.6113954384951e-01,
6.9749289223875e-02,
6.5161366516465e-02,
-6.0325702283960e-02,
2.1188913621662e-02,
-3.2632650250470e-03,
1.3097937809499e-04,
0, 0, 0, 0, 0, 0]'
q5 = [8.7976689586154e-02,
-2.4285669347653e-01,
4.3205328628292e-01,
-9.5375878629204e-01,
0,
8.8676146394834e-01,
-2.1292503103800e-01,
-4.6037018833218e-02,
7.4338719466734e-02,
-3.1217656663809e-02,
6.1239492854797e-03,
-4.5892226603067e-04,
0, 0, 0, 0, 0, 0]'
q6 = [-4.1833336322613e-02,
1.1443465137214e-01,
-1.9549970932735e-01,
3.6113954384951e-01,
-8.8676146394834e-01,
0,
7.7461223007026e-01,
-1.0609547334165e-01,
-4.4853791547749e-02,
3.2436468405486e-02,
-8.4387621360184e-03,
8.5964292632428e-04,
0, 0, 0, 0, 0, 0]'
q7 = [2.2216684976993e-03,
-8.5942765682435e-03,
2.4406885385172e-02,
-6.9749289223875e-02,
2.1292503103800e-01,
-7.7461223007026e-01,
0,
7.4758103262966e-01,
-1.5730779067906e-01,
2.6517620342970e-02,
-4.3175367549700e-03,
1.1092605832824e-03,
-1.8037518037522e-04,
0, 0, 0, 0, 0]'
q8 = [1.5910034062022e-02,
-4.0290424215772e-02,
5.5737279079895e-02,
-6.5161366516465e-02,
4.6037018833218e-02,
1.0609547334165e-01,
-7.4758103262966e-01,
0,
8.0975719267918e-01,
-2.3568822398349e-01,
6.9373143801571e-02,
-1.6606121869177e-02,
2.5974025974031e-03,
-1.8037518037522e-04,
0, 0, 0, 0]'
q9 = [-1.1296706376589e-02,
2.9396383714543e-02,
-4.3772338637753e-02,
6.0325702283960e-02,
-7.4338719466734e-02,
4.4853791547749e-02,
1.5730779067906e-01,
-8.0975719267918e-01,
0,
8.4765775072084e-01,
-2.6369594097148e-01,
7.8759594625702e-02,
-1.7857142857146e-02,
2.5974025974031e-03,
-1.8037518037522e-04,
0, 0, 0]'
q10 = [3.1823678285130e-03,
-8.5601827834256e-03,
1.3727655130726e-02,
-2.1188913621662e-02,
3.1217656663809e-02,
-3.2436468405486e-02,
-2.6517620342970e-02,
2.3568822398349e-01,
-8.4765775072084e-01,
0,
8.5631774953989e-01,
-2.6769768119702e-01,
7.9365079365093e-02,
-1.7857142857146e-02,
2.5974025974031e-03,
-1.8037518037522e-04,
0, 0]'
q11 = [-2.4843594063649e-04,
7.8128092862319e-04,
-1.6271304373071e-03,
3.2632650250470e-03,
-6.1239492854797e-03,
8.4387621360184e-03,
4.3175367549700e-03,
-6.9373143801571e-02,
2.6369594097148e-01,
-8.5631774953989e-01,
0,
8.5712580212095e-01,
-2.6785714285718e-01,
7.9365079365093e-02,
-1.7857142857146e-02,
2.5974025974031e-03,
-1.8037518037522e-04,
0]'
q12 = [-3.1501105449828e-05,
6.0444181254875e-05,
-1.7066984372933e-05,
-1.3097937809499e-04,
4.5892226603067e-04,
-8.5964292632428e-04,
-1.1092605832824e-03,
1.6606121869177e-02,
-7.8759594625702e-02,
2.6769768119702e-01,
-8.5712580212095e-01,
0,
8.5714285714289e-01,
-2.6785714285718e-01,
7.9365079365093e-02,
-1.7857142857146e-02,
2.5974025974031e-03,
-1.8037518037522e-04]'
q13 = [0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7 -15//56 5//63 -1//56 1//385 -1//5544]
q14 = [0 0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7 -15//56 5//63 -1//56 1//385]
q15 = [0 0 0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7 -15//56 5//63 -1//56]
q16 = [0 0 0 0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7 -15//56 5//63]
q17 = [0 0 0 0 0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7 -15//56]
q18 = [0 0 0 0 0 0 0 0 0 0 1//5544 -1//385 1//56 -5//63 15//56 -6//7 0 6//7]

Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12, q13, q14, q15, q16, q17, q18)

D1 = H \ (Q - 1//2*e*e'); display(D1)
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