Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus

Shidong Jiang; Vladimir Rokhlin

doi:10.1016/S0021-9991(03)00304-8

Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus

Shidong Jiang
, Vladimir Rokhlin

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A stable second kind integral equation formulation has been developed for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples.

Original language	English (US)
Pages (from-to)	40-74
Number of pages	35
Journal	Journal of Computational Physics
Volume	191
Issue number	1
DOIs	https://doi.org/10.1016/S0021-9991(03)00304-8
State	Published - Oct 10 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Keywords

Dirichlet problem
Finite Hilbert transform
Laplace equation
Open surface problems
Second kind integral equation

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10.1016/S0021-9991(03)00304-8

Cite this

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title = "Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus",

abstract = "A stable second kind integral equation formulation has been developed for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples.",

keywords = "Dirichlet problem, Finite Hilbert transform, Laplace equation, Open surface problems, Second kind integral equation",

author = "Shidong Jiang and Vladimir Rokhlin",

year = "2003",

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doi = "10.1016/S0021-9991(03)00304-8",

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T1 - Second kind integral equations for the classical potential theory on open surfaces I

T2 - Analytical apparatus

AU - Jiang, Shidong

AU - Rokhlin, Vladimir

PY - 2003/10/10

Y1 - 2003/10/10

N2 - A stable second kind integral equation formulation has been developed for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples.

AB - A stable second kind integral equation formulation has been developed for the Dirichlet problem for the Laplace equation in two dimensions, with the boundary conditions specified on a collection of open curves. The performance of the obtained apparatus is illustrated with several numerical examples.

KW - Dirichlet problem

KW - Finite Hilbert transform

KW - Laplace equation

KW - Open surface problems

KW - Second kind integral equation

UR - https://www.scopus.com/pages/publications/0141794005

UR - https://www.scopus.com/pages/publications/0141794005#tab=citedBy

U2 - 10.1016/S0021-9991(03)00304-8

DO - 10.1016/S0021-9991(03)00304-8

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SN - 0021-9991

VL - 191

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EP - 74

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

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Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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