دورية أكاديمية
ASYMPTOTIC DISPERSION CORRECTION IN GENERAL FINITE DIFFERENCE SCHEMES FOR HELMHOLTZ PROBLEMS
| العنوان: | ASYMPTOTIC DISPERSION CORRECTION IN GENERAL FINITE DIFFERENCE SCHEMES FOR HELMHOLTZ PROBLEMS |
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| المؤلفون: | Cocquet, Pierre-Henri, Gander, Martin, J |
| المساهمون: | Laboratoire des Sciences de l'Ingénieur Appliquées à la Mécanique et au génie Electrique (SIAME), Université de Pau et des Pays de l'Adour (UPPA), Section de mathématiques Genève, Université de Genève = University of Geneva (UNIGE) |
| المصدر: | ISSN: 1064-8275 ; SIAM Journal on Scientific Computing ; https://hal.science/hal-03837707Test ; SIAM Journal on Scientific Computing, 2024, 46 (2), pp.A670-A696. ⟨10.1137/22M1531142⟩. |
| بيانات النشر: | HAL CCSD Society for Industrial and Applied Mathematics |
| سنة النشر: | 2024 |
| المجموعة: | HAL e2s UPPA (Université de Pau et des Pays de l'Adour) |
| مصطلحات موضوعية: | Frequency-Domain wave propagation, Finite difference method, Helmholtz equation, Numerical dispersion, Asymptotic dispersion correction, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| الوصف: | International audience ; Most numerical approximations of frequency-domain wave propagation problemssuffer from the so-called dispersion error, which is the fact that plane waves at the discrete leveloscillate at a frequency different from the continuous one. In this paper, we introduce a new techniqueto reduce the dispersion error in general Finite Difference (FD) schemes for frequency-domainwave propagation using the Helmholtz equation as guiding example. Our method is based on theintroduction of a shifted wavenumber in the FD stencil which we use to reduce the numerical dispersionfor large enough numbers of grid points per wavelength (or for small enough meshsize), andthus we call the method asymptotic dispersion correction. The advantage of this technique is thatthe asymptotically optimal shift can be determined in closed form by computing the extrema of afunction over a compact set. For 1d Helmholtz equations, we prove that the standard 3-point stencilwith shifted wavenumber does not have any dispersion error, and that the so-called pollution effect iscompletely suppressed. For higher dimensional Helmholtz problems, we give easy to use closed formformulas for the asymptotically optimal shift associated to the second order 5-point scheme and asixth-order 9-point scheme in 2d, and the 7-point scheme in 3d that yield substantially less dispersionerror than their standard (unshifted) version. We illustrate this also with numerical experiments. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | hal-03837707; https://hal.science/hal-03837707Test; https://hal.science/hal-03837707v2/documentTest; https://hal.science/hal-03837707v2/file/Shift_general_FD_scheme_MG-last-version-2.pdfTest |
| DOI: | 10.1137/22M1531142 |
| الإتاحة: | https://doi.org/10.1137/22M1531142Test https://hal.science/hal-03837707Test https://hal.science/hal-03837707v2/documentTest https://hal.science/hal-03837707v2/file/Shift_general_FD_scheme_MG-last-version-2.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.220AC297 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1137/22M1531142 |
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