An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916390088212480 |
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| author | Ganesh, Mahadevan Hawkins, Stuart C. Volkov, Darko |
| author_facet | Ganesh, Mahadevan Hawkins, Stuart C. Volkov, Darko |
| contents | We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the underlying linear operator has a uniformly bounded inverse as the frequency approaches zero, ensuring that there is no low-frequency breakdown. The system is derived from a formulation we introduced in our previous work, which required additional integral constraints to ensure well -posedness across all frequencies. In this study, we eliminate those constraints and demonstrate that our new self adjoint, constraints-free linear system expressed in the desirable form of an identity plus a compact weakly-singular operator is stable for all frequencies. Furthermore, we propose and analyze a fully discrete numerical method for these systems and provide a proof of spectrally accurate convergence for the computational method. We also computationally demonstrate the high-order accuracy of the algorithm using benchmark scatterers with curved surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis Ganesh, Mahadevan Hawkins, Stuart C. Volkov, Darko Numerical Analysis Analysis of PDEs We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the underlying linear operator has a uniformly bounded inverse as the frequency approaches zero, ensuring that there is no low-frequency breakdown. The system is derived from a formulation we introduced in our previous work, which required additional integral constraints to ensure well -posedness across all frequencies. In this study, we eliminate those constraints and demonstrate that our new self adjoint, constraints-free linear system expressed in the desirable form of an identity plus a compact weakly-singular operator is stable for all frequencies. Furthermore, we propose and analyze a fully discrete numerical method for these systems and provide a proof of spectrally accurate convergence for the computational method. We also computationally demonstrate the high-order accuracy of the algorithm using benchmark scatterers with curved surfaces. |
| title | An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17713 |