The Multiple Reciprocity Boundary Element Method

The boundary element method (BEM) is a numerical technique which is now emerging as a viable alternative to finite difference and finite element methods for solving a wide range of engineering problems. The main advantage of the BEM is its unique ability to confine the dependence of the problem solution to the boundary values only. However, the main drawback of BEM occurs in problems such as those with body forces, time-dependent effects or non-linearities. In these cases, the domain integrals, that appear in the integral equation, can be evaluated by using cell integration. Although this technique is effective in general, it affects the overall efficiency of the BEM and detracts from its elegance owing to the additional internal discretization. In an effort to avoid the internal discretization, many different approaches have been developed. One of the more successful, is the multiple reciprocity method (MRM). This method employs a sequence of higher-order fundamental solutions which permit the application of the reciprocity theorem recurrently. This book presents recent developments in MRM as it applies to BEM, with contributions from researchers worldwide.