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Coupling finite and boundary element methods for two‐dimensional potential problems
Author(s) -
Krishnamurthy T.,
Raju I. S.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620362103
Subject(s) - finite element method , boundary (topology) , coupling (piping) , mathematical analysis , boundary value problem , laplace transform , mathematics , remainder , laplace's equation , method of fundamental solutions , poisson's equation , domain (mathematical analysis) , boundary element method , boundary knot method , physics , materials science , thermodynamics , arithmetic , metallurgy
Abstract A finite‐element‐boundary‐element (FE‐BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modelled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effect of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE‐TR interface and zero values on the FE‐TR interface. The present FE‐BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.