Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity

[2307.09103] Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2307.09103 (math) [Submitted on 18 Jul 2023 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity Authors: Lutz Angermann View a PDF of the paper titled Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity, by Lutz Angermann View PDF HTML (experimental) Abstract: A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model consists of a nonlinear Helmholtz equation that is reduced to a spherical domain. As a specific example, we consider a finite element method consisting of Courant-type elements with curved edges at the boundary of a circular computational domain in the two-dimensional case. We examine this method and more general conforming methods -- including three-dimensional ones -- with comparable properties for their well-posedness; in particular, the validity of a discrete inf-sup condition of the modified sesquilinear form uniformly with respect to both the truncation and the mesh parameters is shown. Under suitable assumptions to the nonlinearities, a quasi-optimal error estimate is obtained. Finally, the satisfiability of the approximation property of the finite element space required for the solvability of a class of adjoint linear problems is discussed. Subjects: Numerical Analysis (math.NA) MSC classes: 35J05, 35Q60, 65N30, 78A45 Cite as: arXiv:2307.09103 [math.NA] (or arXiv:2307.09103v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2307.09103 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Lutz Angermann [ view email ] [v1] Tue, 18 Jul 2023 09:52:35 UTC (23 KB) [v2] Tue, 14 Apr 2026 14:11:02 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled Finite element solution of a radiation/propagation problem for a Helmholtz equation with a compactly supported nonlinearity, by Lutz Angermann View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2023-07 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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