Paper Info
Title
A MULTIHARMONIC FINITE ELEMENT METHOD FOR SCATTERING PROBLEMS WITH SMALL-AMPLITUDE BOUNDARY DEFORMATIONS
Abstract
A finite element method in the frequency domain is proposed for solving scattering problems with moving or, more generally, deforming boundaries. First, the original problem is rewritten as an equivalent weak formulation set in a fixed domain. Next, this formulation is approximated as a simpler weak form based on asymptotic expansions when the amplitude of the movements or the deformations is small. Fourier series expansions of some geometrical quantities and of the solution, under the assumption that the movement is periodic, are next introduced to obtain a coupled multi harmonic frequency domain formulation. Standard finite element methods can then be applied to solve the resulting problem, and a block diagonal preconditioner is proposed to accelerate the Krylov subspace solution of the linear system for high-frequency problems. The efficiency of the resulting method is demonstrated on a radar sensing application for the automotive industry.
Year
DOI
Venue
2022
10.1137/21M1432363
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
DocType
Volume
high-frequency scattering, moving boundary, Doppler effect, multiharmonic reso-lution, finite element method
Journal
44
Issue
ISSN
Citations 
2
1064-8275
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
David Gasperini100.34
Hans-peter Biese200.34
U. D. O. Schroeder300.34
Xavier Antoine400.34
Christophe Geuzaine500.34