A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914877501603840 |
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| author | Le, Van Chien Cordel, Pierrick Andriulli, Francesco P. Cools, Kristof |
| author_facet | Le, Van Chien Cordel, Pierrick Andriulli, Francesco P. Cools, Kristof |
| contents | This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06367 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors Le, Van Chien Cordel, Pierrick Andriulli, Francesco P. Cools, Kristof Numerical Analysis This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis. |
| title | A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2312.06367 |