The Dual Reciprocity Boundary Element Method

Abstract

Computational Engineering has grown in power and diversity in recent years, and for the engineering community the advances are matched by their wider accessibility through modern workstations.The aim of this series is to provide a clear account of computational methods in engineering analysis and design, dealing with both established methods as well as those currently in a state of rapid development.The series will cover books on the state-of-the-art development in computational engineering and as such will comprise several volumes every year covering the latest developments in the application of the methods to different engineering topics. Each volume will consist of authored work or edited volumes of several chapters written by the leading researchers in the field. The aim will be to provide the fundamental concepts of advances in computational methods as well as outlining the algorithms required to implement the techniques in practical engineering analysis.The scope of the series covers almost the entire spectrum of solid mechanics, fluid mechanics and electromagnetics.

Compactly supported kernels method of approximate particular solutions for solving elliptic problems

“…The idea to extend the method of approximate particular solution (MAPS) in [1] for locally supported radial kernel is similar to the construction of the DRBEM [14], in which the operator of Laplacian is retain as main operator on the left, and all the other terms are shifted to right side. We consider the following elliptic partial differential equation in 2D…”

The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity

“…In order to obtain a particular solution for the displacements in the case when instead of equation (2) we have its inhomogeneous version, namely the Poisson equation ∆T = Q, where Q is a given heat source, or the heterogeneous conductivity equation ∇ · (κ(x)∇T ) = 0, one would have to use a more general purpose method such asthe multiple reciprocity [21] or the dual reciprocity BEMs [22].…”

Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation

“…On the other hand, for the anisotropic Brinkman equation, Khor et al [26] deduced fundamental solutions in the transformed Fourier space, which reduce to the isotropic fundamental solutions in the real space when χ 1 = χ 2 [27,62]. However, the transformation of these functions to the real space in the anisotropic case is not a trivial problem and to avoid these difficulties, a boundary-domain integral formulation in terms of the Stokes fundamental solutions is considered for the Brinkman equation and the resulting domain integral is transformed into a boundary integral using DR-BEM [42]. The integral formulation is as follows:…”