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Discrete null field equation methods for solving Laplace's equation: Boundary layer computations

Numerical methods for partial differential equations, 2024-07, Vol.40 (4), p.n/a

2024

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Lower and upper bounds of condition number for Vandermonde‐wise matrices and method of fundamental solutions using pseudo radial‐lines

Numerical linear algebra with applications, 2023-03, Vol.30 (2), p.n/a

2023

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Null Field and Interior Field Methods for Laplace's Equation in Actually Punctured Disks

Abstract and Applied Analysis, 2013-01, Vol.2013, p.1-15

2013

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

Applied numerical mathematics, 2017-09, Vol.119, p.126-145

2017

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Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations

Numerical linear algebra with applications, 2011-03, Vol.18 (2), p.205-221

2011

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New regularization techniques for ill-conditioning problems and their applications: Choices of regularization parameters

Engineering analysis with boundary elements, 2023-07, Vol.152, p.347-361

2023

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The method of fundamental solutions for the Helmholtz equation

Applied numerical mathematics, 2019-01, Vol.135, p.510-536

2019

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The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions

Applied numerical mathematics, 2020-08, Vol.154, p.47-69

2020

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Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation

Applied mathematics letters, 2020-07, Vol.105, p.106333, Article 106333

2020

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Trefftz, collocation, and other boundary methods-A comparison

Numerical methods for partial differential equations, 2007-01, Vol.23 (1), p.93-144

2007

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Effective condition number for finite difference method

Journal of computational and applied mathematics, 2007, Vol.198 (1), p.208-235

2007

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The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals

Applied numerical mathematics, 2019-11, Vol.145, p.236-260

2019

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Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis

Engineering analysis with boundary elements, 2021-02, Vol.123, p.182-199

2021

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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, 2022-03, Vol.136, p.93-115

2022

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Analysis of the method of fundamental solutions for the modified Helmholtz equation

Applied mathematics and computation, 2017-07, Vol.305, p.262-281

2017

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Effective condition number for numerical partial differential equations

Numerical linear algebra with applications, 2008-09, Vol.15 (7), p.575-594

2008

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Effective condition number for the finite element method using local mesh refinements

Applied numerical mathematics, 2009-08, Vol.59 (8), p.1779-1795

2009

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Numerical Experiments of the Dual Null Field Method for Dirichlet Problems of Laplace’s Equation in Elliptic Domains with Elliptic Holes

The Bulletin of Irkutsk State University. Series Mathematics, 2022-01, Vol.39 (1), p.80-95

2022

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Effective Condition Number of Finite Difference Method for Poisson's Equation Involving Boundary Singularities

Numerical functional analysis and optimization, 2011-06, Vol.32 (6), p.659-681

2011

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Superconvergence and stability for boundary penalty techniques of finite difference methods

Numerical methods for partial differential equations, 2008-05, Vol.24 (3), p.972-990

2008

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Error analysis of the method of fundamental solutions for linear elastostatics

Journal of computational and applied mathematics, 2013-10, Vol.251, p.133-153

2013

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New expansions of numerical eigenvalues for -\Delta u=\lambda \rho u by nonconforming elements

Mathematics of computation, 2008-10, Vol.77 (264), p.2061-2084

2008

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

Computing, 2010-06, Vol.88 (1-2), p.1-29

2010

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Neumann problems of Laplace's equation in circular domains with circular holes by methods of field equations

Engineering analysis with boundary elements, 2015-02, Vol.51, p.156-173

2015

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Algorithm singularity of the null-field method for Dirichlet problems of Laplace's equation in annular and circular domains

Engineering analysis with boundary elements, 2014-04, Vol.41, p.160-172

2014

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Discrete null field equation methods for solving Laplace's equation: Boundary layer computations

Lower and upper bounds of condition number for Vandermonde‐wise matrices and method of fundamental solutions using pseudo radial‐lines

Null Field and Interior Field Methods for Laplace's Equation in Actually Punctured Disks

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

Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations

New regularization techniques for ill-conditioning problems and their applications: Choices of regularization parameters

The method of fundamental solutions for the Helmholtz equation

The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions

Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation

Trefftz, collocation, and other boundary methods-A comparison

Effective condition number for finite difference method

The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals

Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis

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

Analysis of the method of fundamental solutions for the modified Helmholtz equation

Effective condition number for numerical partial differential equations

Effective condition number for the finite element method using local mesh refinements

Numerical Experiments of the Dual Null Field Method for Dirichlet Problems of Laplace’s Equation in Elliptic Domains with Elliptic Holes

Effective Condition Number of Finite Difference Method for Poisson's Equation Involving Boundary Singularities

Superconvergence and stability for boundary penalty techniques of finite difference methods

Error analysis of the method of fundamental solutions for linear elastostatics

New expansions of numerical eigenvalues for -\Delta u=\lambda \rho u by nonconforming elements

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

Neumann problems of Laplace's equation in circular domains with circular holes by methods of field equations

Algorithm singularity of the null-field method for Dirichlet problems of Laplace's equation in annular and circular domains

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