Solving Partial Differential Equations on Surfaces with Fundamental Solutions

Meng Chen; Ka Chun Cheung; Leevan LING

doi:10.1007/978-3-030-52804-1_1

Solving Partial Differential Equations on Surfaces with Fundamental Solutions

Meng Chen, Ka Chun Cheung, Leevan LING^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

Abstract

The aim of this paper is to present partial differential equations (PDEs) on surface to the community of methods of fundamental solutions (MFS). First, we present an embedding formulation to embed surface PDEs into a domain so that MFS can be applied after the PDEs is homogenized with a particular solution. Next, we discuss how the domain-MFS method can be used to directly collocate surface PDEs. Some numerical demonstrations were included to study the effect of basis functions and source point locations.

Original language	English
Title of host publication	Advances in Trefftz Methods and Their Applications
Editors	Carlos Alves, Andreas Karageorghis, Vitor Leitão, Svilen Valtchev
Publisher	Springer Cham
Chapter	1
Pages	1-11
Number of pages	11
Edition	1st
ISBN (Electronic)	9783030528041
ISBN (Print)	9783030528065, 9783030528034
DOIs	https://doi.org/10.1007/978-3-030-52804-1_1
Publication status	Published - 1 Oct 2020

Publication series

Name	SEMA SIMAI Springer Series
Volume	23
ISSN (Print)	2199-3041
ISSN (Electronic)	2199-305X

Scopus Subject Areas

Computational Mechanics
Numerical Analysis
Agricultural and Biological Sciences (miscellaneous)
Physics and Astronomy (miscellaneous)
Fluid Flow and Transfer Processes
Computational Mathematics
Industrial and Manufacturing Engineering
Applied Mathematics

User-Defined Keywords

Collocation
Dual reciprocity method
Embedding method
Laplace-Beltrami

Access to Document

10.1007/978-3-030-52804-1_1

Cite this

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title = "Solving Partial Differential Equations on Surfaces with Fundamental Solutions",

abstract = "The aim of this paper is to present partial differential equations (PDEs) on surface to the community of methods of fundamental solutions (MFS). First, we present an embedding formulation to embed surface PDEs into a domain so that MFS can be applied after the PDEs is homogenized with a particular solution. Next, we discuss how the domain-MFS method can be used to directly collocate surface PDEs. Some numerical demonstrations were included to study the effect of basis functions and source point locations.",

keywords = "Collocation, Dual reciprocity method, Embedding method, Laplace-Beltrami",

author = "Meng Chen and Cheung, {Ka Chun} and Leevan LING",

note = "Funding Information: This work was supported by Hong Kong Research Grant Council GRF Grants.",

year = "2020",

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language = "English",

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booktitle = "Advances in Trefftz Methods and Their Applications",

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Solving Partial Differential Equations on Surfaces with Fundamental Solutions. / Chen, Meng; Cheung, Ka Chun; LING, Leevan.
Advances in Trefftz Methods and Their Applications. ed. / Carlos Alves; Andreas Karageorghis; Vitor Leitão; Svilen Valtchev. 1st. ed. Springer Cham, 2020. p. 1-11 (SEMA SIMAI Springer Series; Vol. 23).

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

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KW - Dual reciprocity method

KW - Embedding method

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Solving Partial Differential Equations on Surfaces with Fundamental Solutions

Abstract

Publication series

Scopus Subject Areas

User-Defined Keywords

Access to Document

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