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Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllability

Year of publication

2025

Authors

Saksa, Tytti

Abstract

This paper discusses computation of time-harmonic wave problems using a mixed formulation and the controllability method introduced by Roland Glowinski. As an example, a scattering problem (in an exterior domain) is considered, and the continuous problem is first formulated in terms of differential forms. Based on the continuous formulation, we write the discrete problem and the controllability algorithm for methods based on both the finite element exterior calculus (FEEC) and the discrete exterior calculus (DEC). As the discrete exterior calculus method provides us with a diagonal ”mass matrix”, time-stepping in the DEC approach is remarkably more efficient than in the FEEC approach. For the computations in this paper, we choose the lowest order Whitney elements (a.k.a. Raviart–Thomas elements) for the FEEC approach, and in the DEC discretization we use different diagonal approximations for the Hodge star. Especially, in the DEC approach, a ”harmonic Hodge” approximation is used, the derivation of which is based on the time-harmonicity of the problem. Different type of grids are used to study the sensitivity of the solution to the quality of the grid. Putting an effort on meshes regular enough, the computed DEC-solution is as accurate as the FEEC-solution, but reached in the fraction of the time. Both methods seem to be able to keep the solution accuracy rather well in computations with a high wave number (corresponding to a high frequency and a small wave length).
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Organizations and authors

Publication type

Publication format

Article

Parent publication type

Journal

Article type

Original article

Audience

Scientific

Peer-reviewed

Peer-Reviewed

MINEDU's publication type classification code

A1 Journal article (refereed), original research

Publication channel information

Publisher

Elsevier

Volume

457

Article number

116154

​Publication forum

59989

Open access

Open access in the publisher’s service

No

Self-archived

No

Other information

Fields of science

Mathematics; Computer and information sciences

Keywords

[object Object],[object Object],[object Object],[object Object]

Publication country

Belgium

Internationality of the publisher

International

Language

English

International co-publication

No

Co-publication with a company

No

DOI

10.1016/j.cam.2024.116154

The publication is included in the Ministry of Education and Culture’s Publication data collection

Yes