The multiple reciprocity boundary element method.

*(English)*Zbl 0868.73006
International Series on Computational Engineering. Southampton: Computational Mechanics Publications. 256 p. (1994).

(Publisher’s description.) 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 nonlinearities. 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 most successful is the multiple reciprocity method. This method employs a sequence of higher-order fundamental solutions which permit the application of the reciprocity theorem recurrently.

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 nonlinearities. 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 most successful is the multiple reciprocity method. This method employs a sequence of higher-order fundamental solutions which permit the application of the reciprocity theorem recurrently.

##### MSC:

74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |

74S15 | Boundary element methods applied to problems in solid mechanics |