FEM–BEM coupling for the thermoelastic wave equation with transparent boundary conditions in 3D

  • We consider the thermoelastic wave equation in three dimensions with transparent boundary conditions on a bounded, not necessarily convex domain. In order to solve this problem numerically, we introduce a coupling of the thermoelastic wave equation in the interior domain with time-dependent boundary integral equations. Here, we want to highlight that this type of problem differs from other wave-type problems that dealt with FEM–BEM coupling so far, e.g., the acoustic as well as the elastic wave equation, since our problem consists of coupled partial differential equations involving a vector-valued displacement field and a scalar-valued temperature field. This constitutes a nontrivial challenge which is solved in this paper. Our main focus is on a coercivity property of a Calderón operator for the thermoelastic wave equation in the Laplace domain, which is valid for all complex frequencies in a half-plane. Combining Laplace transform and energy techniques, this coercivity in the frequency domain is used to prove the stability of a fully discrete numerical method in the time domain. The considered numerical method couples finite elements and the leapfrog time-stepping in the interior with boundary elements and convolution quadrature on the boundary. Finally, we present error estimates for the semi- and full discretization.

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Author:Sarah Maria EberleORCiDGND
Parent Title (German):Zeitschrift für angewandte Mathematik und Physik
Publisher:Springer International Publishing AG
Place of publication:Cham (ZG)
Document Type:Article
Date of Publication (online):2022/07/12
Date of first Publication:2022/07/12
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2023/11/20
Boundary elements; Calderón operator; Convolution quadrature; Finite elements; Thermoelastic wave equation; Transparent boundary conditions
Issue:art. 163
Article Number:163
Page Number:27
First Page:1
Last Page:27
Open Access funding enabled and organized by Projekt DEAL.
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M38 Boundary element methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F05 Thermal effects
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International