Add upwind operators of C. Williams and K. Duru #284
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Additional details and impacted files@@ Coverage Diff @@
## main #284 +/- ##
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+ Coverage 91.59% 91.80% +0.21%
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Files 35 36 +1
Lines 5364 5530 +166
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+ Hits 4913 5077 +164
- Misses 451 453 +2
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| upper_coef_plus = SVector(T(205//143), | ||
| T(-873//2860), | ||
| T(-133//4290), | ||
| T(3//130), ) | ||
| central_coef_plus = T(-889//858) | ||
| lower_coef_plus = SVector(T(57//1430), | ||
| T(-443//2860), | ||
| T(2//65), ) |
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I haven't read the paper in detail yet. Looking at the arXiv version, these coefficients should be the ones from the table in the appendix, Section A.1, correct? If so, could you please explain the differences?
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The 4th order accurate interior stencil was updated since the 2021 version was uploaded to arXiv. The coefficients I used should match the version on SIAM.
| T=Float64, mode=FastMode()) | ||
| if order == 4 | ||
| left_boundary_plus = ( | ||
| DerivativeCoefficientRow{T,1, 6}(SVector( T(-7244216288712856142349841908536610983621117531423//4383417301651166629768772548289373010602184474830), |
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I guess these coefficients are rational approximations of the floating point values from the paper. Do they still satisfy the accuracy conditions exactly?
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I got the rational coefficients directly from Kenneth Duru. I added some rational tests that show they satisfy the dual-pairing SBP property and accuracy conditions exactly.
| T=Float64, mode=FastMode()) | ||
| if order == 4 | ||
| left_boundary_plus = ( | ||
| DerivativeCoefficientRow{T,1, 6}(SVector( T(-7244216288712856142349841908536610983621117531423//4383417301651166629768772548289373010602184474830), |
| upper_coef_plus = SVector(T(205//143), | ||
| T(-873//2860), | ||
| T(-133//4290), | ||
| T(3//130), ) | ||
| central_coef_plus = T(-889//858) | ||
| lower_coef_plus = SVector(T(57//1430), | ||
| T(-443//2860), | ||
| T(2//65), ) |
The arXiv paper "Provably stable full-spectrum dispersion relation preserving schemes" is now on the SIAM Journal on Numerical Analysis as "Full-Spectrum Dispersion Relation Preserving Summation-by-Parts Operators" (https://epubs.siam.org/doi/10.1137/23M1586471).
This should close #269