A novel efficient numerical solution of Laplace equation with mixed boundary conditions

This paper describes a new type of method to solve Laplace equation subject to mixed boundary conditions in two-dimensional domains for electrostatics. The electric potential ϕ is represented by harmonic Steklov eigenfunctions, obtained from a certain Steklov eigenproblem. Error estimates for this m...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 99; no. 6; pp. 1272 - 1280
Main Author Cho, Manki
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.06.2022
Taylor & Francis Ltd
Subjects
Boundary conditions
Domains
Eigenvectors
electrostatic
Electrostatics
Harmonic functions
Laplace equation
Primary 65M70
Secondary 31A25
Steklov eigenfunctions
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ISSN0020-7160
1029-0265
DOI10.1080/00207160.2021.1967939

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Summary:This paper describes a new type of method to solve Laplace equation subject to mixed boundary conditions in two-dimensional domains for electrostatics. The electric potential ϕ is represented by harmonic Steklov eigenfunctions, obtained from a certain Steklov eigenproblem. Error estimates for this method are provided in terms of given boundary data of solutions. The key idea of the method is that Steklov eigenfuncitons could construct the orthonormal basis of the space of solutions. Some results of computational simulations on polygonal domains are presented to support the effectiveness of the new method.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2021.1967939