Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

Shidong Jiang; Bo Ren; Paul Tsuji; Lexing Ying

doi:10.1016/j.jcp.2011.06.015

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

Shidong Jiang
, Bo Ren
, Paul Tsuji
, Lexing Ying

Mathematical Sciences

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

10 Scopus citations

Abstract

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.

Original language	English (US)
Pages (from-to)	7488-7501
Number of pages	14
Journal	Journal of Computational Physics
Volume	230
Issue number	19
DOIs	https://doi.org/10.1016/j.jcp.2011.06.015
State	Published - Aug 10 2011

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

Biharmonic equation
Dirichlet problem
Second kind integral equation

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10.1016/j.jcp.2011.06.015

Cite this

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title = "Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions",

abstract = "A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.",

keywords = "Biharmonic equation, Dirichlet problem, Second kind integral equation",

author = "Shidong Jiang and Bo Ren and Paul Tsuji and Lexing Ying",

note = "Funding Information: S.J. was supported in part by NSF under Grant CCF-0905395 and would like to thank Prof. Leslie Greengard at Courant Institute for stimulating discussions. L.Y. was supported in part by the Sloan Foundation under a Sloan Research Fellowship and by NSF under grant DMS-0708014 and CAREER Grant DMS-0846501 . ",

year = "2011",

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doi = "10.1016/j.jcp.2011.06.015",

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pages = "7488--7501",

journal = "Journal of Computational Physics",

issn = "0021-9991",

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TY - JOUR

T1 - Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

AU - Jiang, Shidong

AU - Ren, Bo

AU - Tsuji, Paul

AU - Ying, Lexing

N1 - Funding Information: S.J. was supported in part by NSF under Grant CCF-0905395 and would like to thank Prof. Leslie Greengard at Courant Institute for stimulating discussions. L.Y. was supported in part by the Sloan Foundation under a Sloan Research Fellowship and by NSF under grant DMS-0708014 and CAREER Grant DMS-0846501 .

PY - 2011/8/10

Y1 - 2011/8/10

N2 - A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.

AB - A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.

KW - Biharmonic equation

KW - Dirichlet problem

KW - Second kind integral equation

UR - https://www.scopus.com/pages/publications/79960835196

UR - https://www.scopus.com/pages/publications/79960835196#tab=citedBy

U2 - 10.1016/j.jcp.2011.06.015

DO - 10.1016/j.jcp.2011.06.015

M3 - Article

AN - SCOPUS:79960835196

SN - 0021-9991

VL - 230

SP - 7488

EP - 7501

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 19

ER -

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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