Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2013.01.017 ◽

2013 ◽

Vol 37 (4) ◽

pp. 765-780 ◽

Author(s):

Liping Zhang ◽

Zi-Cai Li ◽

Yimin Wei ◽

John Y. Chiang

Keyword(s):

Fundamental Solutions ◽

Laplace’S Equation ◽

Cauchy Problems ◽

Laplace's Equation ◽

Particular Solutions

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Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries

Numerical Algorithms ◽

10.1007/s11075-021-01150-5 ◽

2021 ◽

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Ming-Gong Lee ◽

Hung-Tsai Huang

Keyword(s):

Stability Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace’s equation; selection of pseudo-boundaries

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112861 ◽

2020 ◽

Vol 377 ◽

pp. 112861 ◽

Author(s):

Fangfang Dou ◽

Li-Ping Zhang ◽

Zi-Cai Li ◽

C.S. Chen

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

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New locations of source nodes for method of fundamental solutions solving Laplace’s equation; pseudo radial-lines

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2021.12.004 ◽

2022 ◽

Vol 136 ◽

pp. 93-115

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Hung-Tsai Huang ◽

Ming-Gong Lee

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

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Convergence analysis for the Cauchy problem of Laplace’s equation by a regularized method of fundamental solutions

Advances in Computational Mathematics ◽

10.1007/s10444-009-9134-7 ◽

2009 ◽

Vol 33 (4) ◽

pp. 491-510 ◽

Author(s):

T. Wei ◽

D. Y. Zhou

Keyword(s):

Cauchy Problem ◽

Convergence Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

The Cauchy Problem ◽

Regularized Method

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A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation

SIAM Journal on Applied Mathematics ◽

10.1137/0151085 ◽

1991 ◽

Vol 51 (6) ◽

pp. 1653-1675 ◽

Author(s):

Michael V. Klibanov ◽

Fadil Santosa

Keyword(s):

Laplace’S Equation ◽

Cauchy Problems ◽

Laplace's Equation

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Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation

Computing ◽

10.1007/s00607-010-0081-4 ◽

2010 ◽

Vol 88 (1-2) ◽

pp. 1-29 ◽

Author(s):

Zi-Cai Li ◽

Jin Huang ◽

Hung-Tsai Huang

Keyword(s):

Stability Analysis ◽

Boundary Value Problems ◽

Mixed Boundary ◽

Boundary Value ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Mixed Boundary Value Problems ◽

Laplace's Equation

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Generation of collocation points in the method of fundamental solutions for 2D Laplace's equation

JSIAM Letters ◽

10.14495/jsiaml.11.49 ◽

2019 ◽

Vol 11 (0) ◽

pp. 49-52

Author(s):

Hiroaki Hirano ◽

Ken'ichiro Tanaka

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Collocation Points

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Combinations of method of fundamental solutions for Laplace's equation with singularities

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2008.01.002 ◽

2008 ◽

Vol 32 (10) ◽

pp. 856-869 ◽

Author(s):

Zi-Cai Li

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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Neumann problems of 2D Laplace's equation by method of fundamental solutions

Applied Numerical Mathematics ◽

10.1016/j.apnum.2017.04.004 ◽

2017 ◽

Vol 119 ◽

pp. 126-145 ◽

Author(s):

Zi-Cai Li ◽

Ming-Gong Lee ◽

Hung-Tsai Huang ◽

John Y. Chiang

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Neumann Problems

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The method of fundamental solutions for solving a Cauchy problem of Laplace's equation in a multi-connected domain

Inverse Problems in Science and Engineering ◽

10.1080/17415970701602614 ◽

2008 ◽

Vol 16 (3) ◽

pp. 389-411 ◽

Author(s):

Dayong Zhou ◽

Ting Wei

Keyword(s):

Cauchy Problem ◽

Connected Domain ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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