3D metric-based anisotropic mesh adaptation for the fast multipole accelerated boundary element method in acoustics

Faisal Amlani (1) , Stéphanie Chaillat (1) , Samuel P Groth (2) , Adrien Loseille (3)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 UMA - Unité de Mathématiques Appliquées
3 Gamma3 - Automatic mesh generation and advanced methods

We introduce a metric-based anisotropic mesh adaptation strategy for the fast multipole accelerated boundary element method (FM-BEM) applied to exterior boundary value problems of the three-dimensional Helmholtz equation. The present methodology is independent of discretiz-ation technique and iteratively constructs meshes refined in size, shape and orientation according to an " optimal " metric reliant on a reconstructed Hessian of the boundary solution. The resulting adaptation is anisotropic in nature and numerical examples demonstrate optimal convergence rates for domains that include geometric singularities such as corners and ridges.

Mots clés: acoustic scattering; boundary element methods; anisotropic mesh adaptation; fast multipole method

Domaines: Mathématiques [math]

Faisal Amlani, Stéphanie Chaillat, Samuel P Groth, Adrien Loseille. 3D metric-based anisotropic mesh adaptation for the fast multipole accelerated boundary element method in acoustics. WAVES 2017 - 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, May 2017, Minneapolis, United States. ⟨hal-01598238⟩