Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation

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dc.citation.articleNumber113091en_US
dc.citation.journalTitleJournal of Computational Physicsen_US
dc.citation.volumeNumber511en_US
dc.contributor.authorAnderson, Thomas G.en_US
dc.contributor.authorBonnet, Marcen_US
dc.contributor.authorFaria, Luiz M.en_US
dc.contributor.authorPérez-Arancibia, Carlosen_US
dc.date.accessioned2024-08-07T19:14:59Zen_US
dc.date.available2024-08-07T19:14:59Zen_US
dc.date.issued2024en_US
dc.description.abstractThis article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the ideas of the density interpolation method for boundary integral operators, the proposed methodology leverages Green's third identity and a local polynomial interpolant of the density function to recast the volume potential as a sum of single- and double-layer potentials and a volume integral with a regularized (bounded or smoother) integrand. The layer potentials can be accurately and efficiently evaluated everywhere in the plane by means of existing methods (e.g. the density interpolation method), while the regularized volume integral can be accurately evaluated by applying elementary quadrature rules. Compared to straightforwardly computing corrections for every singular and nearly-singular volume target, the method significantly reduces the amount of required specialized quadrature by pushing all singular and near-singular corrections to near-singular layer-potential evaluations at target points in a small neighborhood of the domain boundary. Error estimates for the regularization and quadrature approximations are provided. The method is compatible with well-established fast algorithms, being both efficient not only in the online phase but also to set-up. Numerical examples demonstrate the high-order accuracy and efficiency of the proposed methodology; applications to inhomogeneous scattering are presented.en_US
dc.identifier.citationAnderson, T. G., Bonnet, M., Faria, L. M., & Pérez-Arancibia, C. (2024). Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation. Journal of Computational Physics, 511, 113091. https://doi.org/10.1016/j.jcp.2024.113091en_US
dc.identifier.digital1-s2-0-S0021999124003401-mainen_US
dc.identifier.doihttps://doi.org/10.1016/j.jcp.2024.113091en_US
dc.identifier.urihttps://hdl.handle.net/1911/117591en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleFast, high-order numerical evaluation of volume potentials via polynomial density interpolationen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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