|
Adaptive Boundary Element Methods Using Anisotropic Wavelets
Third-party funded project |
Project title |
Adaptive Boundary Element Methods Using Anisotropic Wavelets |
Principal Investigator(s) |
Harbrecht, Helmut
|
Project Members |
Barendrecht, Pieter Jaap von Rickenbach, Remo
|
Organisation / Research unit |
Departement Mathematik und Informatik / Computational Mathematics (Harbrecht) |
Department |
Departement Mathematik und Informatik / Computational Mathematics (Harbrecht) |
Project start |
01.04.2020 |
Probable end |
31.03.2023 |
Status |
Completed |
Abstract |
This project aims at developing wavelet methods that adaptively solve boundary integral equations posed in three space dimensions. Since isotropic refinement is not optimal for the approximation of singularities which are of anisotropic nature, we will use (anisotropic) tensor wavelets for the discretization. Tensor wavelets are known to be able to resolve anisotropic singularities in an optimal way. Especially they are able to optimally resolve edge singularities which arise in case of non-smooth geometries and are typically of anisotropic nature. Therefore, the classical, isotropic adaptive wavelet algorithm has to be extended to this more general setting and necessary building blocks such as quadrature and compression routines have to be further developed. We will construct an adaptive algorithm which is optimal in the sense that it computes the approximate solution at an expense that scales proportional to the best $N$-term approximation of the unknown solution. |
Financed by |
Swiss National Science Foundation (SNSF)
|
|
|
|
MCSS v5.8 PRO. 0.402 sec, queries - 0.000 sec
©Universität Basel | Impressum
| |
19/04/2024
Research Database / FORSCHUNGSDATENBANK
|