A scaled wave finite element method for computing scalar wave radiation and scattering in exterior domains

Denis Duhamel (1)

1 ECOLE NATIONALE DES PONTS ET CHAUSSEES PARIS

The calculation of high-frequency wave radiation in exterior domains by finite element methods can lead to large computations. In this paper, it is shown that the solution in the exterior domain can be decomposed as a series expansion of functions with an analytical part made from the product of harmonic waves and polynomials in a scaled variable and a numerical part made of a finite element approximation vectors. The solution of the radiation or scattering problem can be found by solving a sparse linear system which is set from the dynamic stiffness matrices of several scaled layers around the radiating body. These dynamic stiffness matrices are classical finite element matrices obtained from any finite element software. Moreover, accurate results can be obtained from a small number of terms in the series expansion. Several examples are given to estimate the efficiency of the proposed method.

Mots clés: Finite element; scaled domain; wave; Helmholtz equation; radiation; scattering; infinite domain

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Denis Duhamel. A scaled wave finite element method for computing scalar wave radiation and scattering in exterior domains. Computer Methods in Applied Mechanics and Engineering, 2022, 392, pp.114676. ⟨10.1016/j.cma.2022.114676⟩. ⟨hal-03689294⟩