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Trefftz Methods and Method of Fundamental Solutions (Virtual special issue)

Uscilowska, Anita; Alves, Carlos J. S.; Maciag, Artur

Engineering Analysis with Boundary Elements, 2019

This special issue of Engineering Analysis with Boundary Elements is devoted to the theory and the computational implementation of meshfree methods, with applications to engineering problems, where new research developments in Trefftz Methods and in the Method of Fundamental Solutions are expected.

Trefftz Methods, and in particular the Method of Fundamental Solutions, belong to a class of numerical methods that incorporates, as basis functions, some special solutions of partial differential equations. A main purpose of these methods is to reduce the discretization dimension, from the dimension D of the domain to the dimension D-1 of the boundary. These, and other similar methods, can be called boundary collocation methods, which are “meshless”, in the sense that they avoid an underlying mesh structure in the nodes, as it occurs in the classical finite element method or finite difference method. Although these boundary collocation methods have a long history of development, they are becoming increasingly popular in the last decade.