An overview of the method of fundamental solutions—Solvability, uniqueness, convergence, and stability
AHD Cheng, Y Hong - Engineering Analysis with Boundary Elements, 2020 - Elsevier
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 …
heuristic numerical method. It is truly meshless. Its concept and numerical implementation …
Trefftz method: a general theory
I Herrera - Numerical Methods for Partial Differential Equations …, 2000 - Wiley Online Library
A precise definition of Trefftz method is proposed and, starting with it, a general theory is
briefly explained. This leads to formulating numerical methods from a domain decomposition …
briefly explained. This leads to formulating numerical methods from a domain decomposition …
Trefftz, collocation, and other boundary methods—a comparison
ZC Li, TT Lu, HT Huang… - Numerical Methods for …, 2007 - Wiley Online Library
In this article we survey the Trefftz method (TM), the collocation method (CM), and the
collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal …
collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal …
Theory of differential equations in discontinuous piecewise‐defined functions
I Herrera - Numerical Methods for Partial Differential Equations …, 2007 - Wiley Online Library
A truly general and systematic theory of finite element methods (FEM) should be formulated
using, as trial and test functions, piecewise‐defined functions that can be fully discontinuous …
using, as trial and test functions, piecewise‐defined functions that can be fully discontinuous …
A multiple-scale Trefftz method for an incomplete Cauchy problem of biharmonic equation
CS Liu - Engineering Analysis with Boundary Elements, 2013 - Elsevier
In this paper we numerically solve both the direct and the inverse Cauchy problems of
biharmonic equation by using a multiple-scale Trefftz method (TM). The approximate …
biharmonic equation by using a multiple-scale Trefftz method (TM). The approximate …
The Trefftz method for the Helmholtz equation with degeneracy
ZC Li - Applied Numerical Mathematics, 2008 - Elsevier
The Trefftz method (TM)[E. Trefftz, Ein Gegenstuck zum Ritz'schen Verfahren, in: Proc. 2nd
Ind. Congr. Appl. Mech., Zurich, 1926, pp. 131–137](ie, Boundary approximation method) is …
Ind. Congr. Appl. Mech., Zurich, 1926, pp. 131–137](ie, Boundary approximation method) is …
The collocation Trefftz method for biharmonic equations with crack singularities
The purpose of this paper is to extend the boundary approximation method proposed by Li
et al.[SIAM J. Numer. Anal. 24 (1987) 487], ie the collocation Trefftz method called in this …
et al.[SIAM J. Numer. Anal. 24 (1987) 487], ie the collocation Trefftz method called in this …
General theory of domain decomposition: indirect methods
According to a general theory of domain decomposition methods (DDM), recently proposed
by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz …
by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz …
The singular function boundary integral method for a two-dimensional fracture problem
M Elliotis, G Georgiou, C Xenophontos - Engineering Analysis with …, 2006 - Elsevier
The singular function boundary integral method (SFBIM) originally developed for Laplacian
problems with boundary singularities is extended for solving two-dimensional fracture …
problems with boundary singularities is extended for solving two-dimensional fracture …