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 …

This paper presents a summary of various localized collocation schemes and their
engineering applications. The basic concepts of localized collocation methods (LCMs) are …

A standard approach for solving linear partial differential equations is to split the solution into
a homogeneous solution and a particular solution. Motivated by the method of fundamental …

Hardy's multiquadric and its related interpolators have been found to be highly efficient for
interpolating continuous, multivariate functions, as well as for the solution of partial …

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 …

Multiquadric (MQ) collocation method is highly efficient for solving partial differential
equations due to its exponential error convergence rate. A special feature of the method is …

A nonlinear formulation, based on the total Lagrange description of the weighted radial
basis collocation method (WRBCM), is proposed for the large deformation analysis of rubber …

The singular boundary method (SBM) is a recent strong-form meshless boundary collocation
method. Like the method of fundamental solutions (MFS), the SBM uses the fundamental …

A weighted strong form collocation method using radial basis functions and explicit time
integration is proposed to solve the incompressible Navier-Stokes equations. The velocities …

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient
acoustic wave equations in arbitrary space dimensions, extending the one-dimensional …