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 …
interpolation, meshless methods for solving partial differential equations, neural networks …
A fundamental solution method for inverse heat conduction problem
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 …
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
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 …
the solution of homogeneous PDE problems. Coupled with other numerical schemes such …
Identification of source locations in two-dimensional heat equations
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 …
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 heat conduction problem. The given heat conduction equation, the boundary …
Inverse source identification for Poisson equation
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 …
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 …
(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
This paper presents the Method of Fundamental Solutions for three-dimensional
elastostatics with body forces. The gravitational body loading is considered as an example …
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 …
problems are considered. Several strategies are outlined to avoid the problems due to the …