Development and implementation of some BEM variants—A critical review

Abstract

a b s t r a c tDue to rapid development of boundary element method (BEM), this article explores the evolution of BEM over the past half century. We here summarize the overall development and implementation of several well-known BEM variants that includes collocation BEM, galerkin BEM, dual reciprocity BEM, complex variable BEM and analog equation method. Their theoretical and mathematical backgrounds are carefully described and a generalized Laplace's equation (and Poisson's equation) is utilized in demonstrating the different approaches involved. An up-to-date review on characteristics and implementation for each of the five variants is presented and also highlighted their significant contributions in boundary element research. In addition, this article tries to cover whole aspect of interests including efficiency, applicability and accuracy in order to give better understanding of BEM evolution. Comparisons and techniques of improvement for these variants are also discussed.

BEM‐based models to simulate the resin flow at macroscale and microscale in LCM processes

“…It should be mentioned that Eq . is valid for any point source placed in the plane, in particular for internal points . Therefore, pressure can be computed in the whole domain provided that both and are known along its boundary .…”

Effectiveness of nonsingular solutions of the boundary problems based on Trefftz methods

“…In this method the bases and the weights are the same, so it is Galerkin version; (in [2] Galerkin version is defined more generally). In this case, the solution has the form…”

“…Since both direct and indirect formulations lead to the BIE so TMs are BEM. As mentioned above, an excellent survey of the BEM is given in [1,2]. But the survey does not include details and TMs are not perceived as separate method.…”

“…In particular, it permits a simple treatment of infinite domains where full field methods such as finite element method or finite difference method are difficult to operate [1,2]. Additionally, an economy is that of data preparation, i.e.…”

Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method

“…So far, the BEM applied to the potential problem has been investigated in many branches of engineering applications [5][6][7][8].…”