The coupling of the finite element method and boundary solution procedures

Abstract

SUMMARYThe finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems-structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.

The development of the Trefftzian methodology for engineering design analysis

“…Once {u}r2 is formed, the boundary condition vector { iin} can be completed so that {S) = IT'@d (29) and hence {ul = PI{SI it) = [ms) (30) The flow chart in Fig. 8 presents the algorithm and is self-explanatory.…”

Sliding frame-solid interaction using BEM/FEM coupling

“…The combination of the finite element method FEM and boundary element method BEM to solve structural analysis is attractive because it allows for an optimal exploitation of the respective advantage of the methods Zienkiewicz et al, 1977 . The main strength of the BEM for boundary-value problems governed by linear, homogenous, and elliptic differential equations with constant coefficients is the reduction of the dimensionality of the problem by one unit for linear constitutive relations Brebbia, 1978;Brebbia, 1980 .…”

“…The idea of combining these two methods goes back to Zienkiewicz et al 1977 . One branch of BEM/FEM coupling is the iterative coupling in which the individual sub-domains are treated independently by either method.…”

Parallelizing a hybrid finite element-boundary integral method for the analysis of scattering and radiation of electromagnetic waves

“…This has led to several hybrid schemes FEM-BI (see, for example, [2][3][4], or, more recently, [5]). However, in contrast with standard FEM-BI approaches, FE-IIEE preserves the original sparse and banded structure of the FEM matrices, allowing the use of efficient FEM solvers.…”