Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number
| Autor: | Lorenzo Mascotto, Alexander Pichler |
|---|---|
| Přispěvatelé: | Mascotto, L, Pichler, A |
| Rok vydání: | 2020 |
| Předmět: |
Degrees of freedom (statistics)
010103 numerical & computational mathematics Space (mathematics) 01 natural sciences Nonconforming virtual element method Helmholtz problem FOS: Mathematics Applied mathematics Wavenumber Polygon mesh Mathematics - Numerical Analysis 0101 mathematics Plane and evanescent wave 35J05 65N12 65N30 74J20 Mathematics Numerical Analysis Applied Mathematics Piecewise constant wave number Numerical Analysis (math.NA) 010101 applied mathematics Computational Mathematics Range (mathematics) Special functions Piecewise Constant (mathematics) Polygonal meshe Trefftz methods |
| Zdroj: | Applied Numerical Mathematics. 155:160-180 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2019.04.005 |
| Popis: | We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original approach, we address two additional issues: firstly, we define the coupling of local approximation spaces with piecewise constant wave numbers, secondly, we enrich such local spaces with special functions capturing the physical behaviour of the solution to the target problem. As these two issues are directly related to an increase of the number of degrees of freedom, we use a reduction strategy inspired by arXiv:1807.11237, which allows to mitigate the growth of the dimension of the approximation space when considering $h$- and $p$-refinements. This renders the new method highly competitive in comparison to other Trefftz and quasi-Trefftz technologies tailored for the Helmholtz problem with piecewise constant wave number. A wide range of numerical experiments, including the $p$-version with quasi-uniform meshes and the $hp$-version with isotropic and anisotropic mesh refinements, is presented. Comment: 23 pages, 15 figures |
| Databáze: | OpenAIRE |
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