Kernel techniques: from machine learning to meshless methods

R Schaback, H Wendland - Acta numerica, 2006 - cambridge.org
Kernels are valuable tools in various fields of numerical analysis, including approximation,
interpolation, meshless methods for solving partial differential equations, neural networks …

A fundamental solution method for inverse heat conduction problem

YC Hon, T Wei - Engineering analysis with boundary elements, 2004 - Elsevier
In this paper, we develop a new meshless and integration-free numerical scheme for solving
an inverse heat conduction problem. The numerical scheme is developed based on the use …

A new method of fundamental solutions applied to nonhomogeneous elliptic problems

CJS Alves, CS Chen - Advances in Computational Mathematics, 2005 - Springer
The classical method of fundamental solutions (MFS) has only been used to approximate
the solution of homogeneous PDE problems. Coupled with other numerical schemes such …

Identification of source locations in two-dimensional heat equations

L Ling, M Yamamoto, YC Hon, T Takeuchi - Inverse Problems, 2006 - iopscience.iop.org
In this paper, we show the uniqueness of the identification of unknown source locations in
two-dimensional heat equations from scattered measurements. Based on the assumption …

[HTML][HTML] A numerical technique for solving IHCPs using Tikhonov regularization method

R Pourgholi, M Rostamian - Applied Mathematical Modelling, 2010 - Elsevier
This study is intended to provide a numerical algorithm for solving a one-dimensional
inverse heat conduction problem. The given heat conduction equation, the boundary …

Inverse source identification for Poisson equation

L Ling, YC Hon, M Yamamoto - Inverse problems in science and …, 2005 - Taylor & Francis
A numerical method for identifying the unknown point sources for a two-dimensional
Poisson problem from Dirichlet boundary data is proposed. Under an assumption that the …

On the application of the method of fundamental solutions to nonlinear partial differential equations

CJS Alves, AL Silvestre - Engineering Analysis with Boundary Elements, 2018 - Elsevier
This paper addresses the application of a domain-type method of fundamental solutions
(MFS-D) together with a Picard iteration scheme for solving nonlinear elliptic partial …

Solving partial differential equations by meshless methods using radial basis functions

Y Zhang - Applied mathematics and computation, 2007 - Elsevier
Solving partial differential equations by meshless methods using radial basis functions -
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The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

GSA Fam, YF Rashed - Computational Mechanics, 2005 - Springer
This paper presents the Method of Fundamental Solutions for three-dimensional
elastostatics with body forces. The gravitational body loading is considered as an example …

Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions

C Gáspár - Open Mathematics, 2013 - degruyter.com
The method of fundamental solutions and some versions applied to mixed boundary value
problems are considered. Several strategies are outlined to avoid the problems due to the …