Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914877902159872 |
|---|---|
| author | Imbert-Gerard, Lise-Marie Sylvand, Guillaume |
| author_facet | Imbert-Gerard, Lise-Marie Sylvand, Guillaume |
| contents | Trefftz methods are numerical methods for the approximation of solutions to boundary and/or initial value problems. They are Galerkin methods with particular test and trial functions, which solve locally the governing partial differential equation (PDE). This property is called the Trefftz property. Quasi-Trefftz methods were introduced to leverage the advantages of Trefftz methods for problems governed by variable coefficient PDEs, by relaxing the Trefftz property into a so-called quasi-Trefftz property: test and trial functions are not exact solutions but rather local approximate solutions to the governing PDE. In order to develop quassi-Trefftz methods for aero-acoustics problems governed by the convected Helmholtz equation, the present work tackles the question of the definition, construction and approximation properties of three families of quasi-Trefftz functions: two based on generalizations on plane wave solutions, and one polynomial. The polynomial basis shows significant promise as it does not suffer from the ill-conditioning issue inherent to wave-like bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_12993 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties Imbert-Gerard, Lise-Marie Sylvand, Guillaume Numerical Analysis Trefftz methods are numerical methods for the approximation of solutions to boundary and/or initial value problems. They are Galerkin methods with particular test and trial functions, which solve locally the governing partial differential equation (PDE). This property is called the Trefftz property. Quasi-Trefftz methods were introduced to leverage the advantages of Trefftz methods for problems governed by variable coefficient PDEs, by relaxing the Trefftz property into a so-called quasi-Trefftz property: test and trial functions are not exact solutions but rather local approximate solutions to the governing PDE. In order to develop quassi-Trefftz methods for aero-acoustics problems governed by the convected Helmholtz equation, the present work tackles the question of the definition, construction and approximation properties of three families of quasi-Trefftz functions: two based on generalizations on plane wave solutions, and one polynomial. The polynomial basis shows significant promise as it does not suffer from the ill-conditioning issue inherent to wave-like bases. |
| title | Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2201.12993 |