High-order transmission conditions in a domain decomposition method for the time-harmonic Maxwell's equations in inhomogeneous media
A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable 3-D objects: the computational domain is partitioned into concentric subdomains and an integral representation (IR) of the electromagnetic fi...
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| Published in | Journal of computational physics Vol. 372; pp. 385 - 405 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge
Elsevier Inc
01.11.2018
Elsevier Science Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2018.06.050 |
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| Abstract | A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable 3-D objects: the computational domain is partitioned into concentric subdomains and an integral representation (IR) of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The corresponding numerical code is efficiently parallelized and the full IR matrices are compressed in order to expedite the solution of very large problems. Exact and approximate high-order transmission conditions (HOTC) are obtained for the model problem of a multi-layer planar structure. Their application to real world objects is investigated in terms of well-posedness and numerical complexity. New well-posed low complexity HOTCs are proposed that speed up the convergence of the DDM algorithm.
•New well posed and numerically cheap high order transmission conditions for inhomogeneous media.•Large full matrices arising from the exact radiation condition are compressed via ACA.•Parallelized numerical code.•Very accurate numerical results obtained on electrically large objects involving up to 160 million unknowns with a reasonable numerical complexity. |
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| AbstractList | A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable 3-D objects: the computational domain is partitioned into concentric subdomains and an integral representation (IR) of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The corresponding numerical code is efficiently parallelized and the full IR matrices are compressed in order to expedite the solution of very large problems. Exact and approximate high-order transmission conditions (HOTC) are obtained for the model problem of a multi-layer planar structure. Their application to real world objects is investigated in terms of well-posedness and numerical complexity. New well-posed low complexity HOTCs are proposed that speed up the convergence of the DDM algorithm. A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable 3-D objects: the computational domain is partitioned into concentric subdomains and an integral representation (IR) of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The corresponding numerical code is efficiently parallelized and the full IR matrices are compressed in order to expedite the solution of very large problems. Exact and approximate high-order transmission conditions (HOTC) are obtained for the model problem of a multi-layer planar structure. Their application to real world objects is investigated in terms of well-posedness and numerical complexity. New well-posed low complexity HOTCs are proposed that speed up the convergence of the DDM algorithm. •New well posed and numerically cheap high order transmission conditions for inhomogeneous media.•Large full matrices arising from the exact radiation condition are compressed via ACA.•Parallelized numerical code.•Very accurate numerical results obtained on electrically large objects involving up to 160 million unknowns with a reasonable numerical complexity. |
| Author | Chanaud, Mathieu Stupfel, Bruno |
| Author_xml | – sequence: 1 givenname: Bruno surname: Stupfel fullname: Stupfel, Bruno email: bruno.stupfel@cea.fr organization: CEA, DAM, CESTA, F-33114 Le Barp, France – sequence: 2 givenname: Mathieu surname: Chanaud fullname: Chanaud, Mathieu organization: CS, 38 Av. Ariane, 33702 Mérignac Cedex, France |
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| Snippet | A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable... |
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| SubjectTerms | Boundary conditions Complexity Computational physics Domain decomposition method Domain decomposition methods Electromagnetic fields Electromagnetic scattering Electromagnetics Electromagnetism Finite elements Inhomogeneous media Integral representation Iterative method Mathematical models Maxwell's equations Multilayers Parallel processing Planar structures Well posed problems |
| Title | High-order transmission conditions in a domain decomposition method for the time-harmonic Maxwell's equations in inhomogeneous media |
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