A transform-based technique for solving boundary value problems on convex planar domains-Reference-Cited by-同舟云学术

A transform-based technique for solving boundary value problems on convex planar domains

Published:2024-06-18 Issue: Volume: Page:
ISSN:0272-4960
Container-title:IMA Journal of Applied Mathematics
language:en
Short-container-title:

Author:

Hulse Jesse J¹^ORCID,Lanzani Loredana¹²^ORCID,Llewellyn Smith Stefan G³⁴^ORCID,Luca Elena⁵^ORCID

Affiliation:

1. Syracuse University Department of Mathematics, , Syracuse NY 13244-1150, USA

2. University of Bologna Department of Mathematics, , Bologna 40126, Italy

3. Jacobs School of Engineering, UCSD Department of Mechanical and Aerospace Engineering, , 9500 Gilman Drive, La Jolla, CA 92093-0411, USA

4. Scripps Institution of Oceanography , UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0209, USA

5. The Cyprus Institute Climate and Atmosphere Research Center, , Nicosia 2121, Cyprus

Abstract

Abstract A new technique is presented that can be used to solve mixed boundary value problems for Laplace’s equation and the complex Helmholtz equation in bounded convex planar domains. This work is an extension of Crowdy (2015, CMFT, 15, 655–687) where new transform-based techniques were developed for boundary value problems for Laplace’s equation in circular domains. The key ingredient of the method is the analysis of the so-called global relation, which provides a coupling of integral transforms of the given boundary data and of the unknown boundary values. Three problems which involve mixed boundary conditions are solved in detail, as well as numerically implemented, to illustrate how to apply the new approach.

Funder

EPSRC

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imamat/advance-article-pdf/doi/10.1093/imamat/hxae018/58507547/hxae018.pdf

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