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Non-symmetric isogeometric FEM-BEM couplings

Elasmi, Mehdi ; Erath, Christoph ; Kurz, Stefan (2024)
Non-symmetric isogeometric FEM-BEM couplings.
In: Advances in Computational Mathematics, 2021, 47 (5)
doi: 10.26083/tuprints-00023483
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Non-symmetric isogeometric FEM-BEM couplings
Language: English
Date: 30 April 2024
Place of Publication: Darmstadt
Year of primary publication: 2021
Place of primary publication: Dordrecht
Publisher: Springer Science
Journal or Publication Title: Advances in Computational Mathematics
Volume of the journal: 47
Issue Number: 5
DOI: 10.26083/tuprints-00023483
Corresponding Links:
Origin: Secondary publication DeepGreen

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform h- and p-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide a priori error estimates. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results.

Uncontrolled Keywords: Finite element method, Boundary element method, Non-symmetric coupling, Isogeometric analysis, Non-linear operators, Laplacian interface problem, Boundary value problems, Multiple domains, Well-posedness, a priori estimate, Super-convergence, Electromagnetics, Electric machines
Identification Number: Artikel-ID: 61
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-234830
Additional Information:

Mathematics Subject Classification (2010): 65N12 · 65N30 · 65N38 · 78M10 · 78M15

Classification DDC: 600 Technology, medicine, applied sciences > 621.3 Electrical engineering, electronics
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields
Date Deposited: 30 Apr 2024 12:42
Last Modified: 30 Apr 2024 12:42
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23483
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