In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …

We introduce a new algorithm for approximation by rational functions on a real or complex
set of points, implementable in 40 lines of MATLAB and requiring no user input parameters …

This paper reviews the equivalent source method (ESM), an attractive alternative to the
standard boundary element method (BEM). The ESM has been developed under different …

In an attempt to introduce application scientists and graduate students to the exciting topic of
positive definite kernels and radial basis functions, this book presents modern theoretical …

This paper develops a novel boundary meshless approach, Laplace transformed boundary
particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It …

The satisfactory location for the sources outside the closure of the domain of the problem
under consideration remains one of the major issues in the application of the method of …

Internet of vehicles (IoV) is a branch of the internet of things (IoT) which is used for
communication among vehicles. As vehicular nodes are considered always in motion …

Trefftz methods are finite element-type schemes whose test and trial functions are (locally)
solutions of the targeted differential equation. They are particularly popular for time …

This paper presents the localized collocation solver based on fundamental solutions to 3D
elastic wave propagation analysis. In the proposed collocation solver, the approximated …

The method of fundamental solutions (MFS) may be seen as one of the simplest methods for
solving boundary value problems for some linear partial differential equations (PDEs). It is a …