F. Zhao et Xg. Zeng, AN ENERGY-BASED MACRO-ELEMENT METHOD VIA A COUPLED FINITE-ELEMENT ANDBOUNDARY INTEGRAL FORMULATION, Computers & structures, 56(5), 1995, pp. 813-824
An energy-based, systematic method for the coupling of the finite elem
ent (FE) method and the boundary integral equation (BIE) method is des
cribed in this paper. This method allows the use of the BIE method to
represent those subdomains of a structure that are best suited to BIE
method, and the use of the FE method to represent the rest of the stru
cture. Different subdomains and their associated FE or BIE representat
ions are coupled naturally through the total potential energy function
al of the system. The associated discretized problem from the proposed
method consists of a linear system of equations with a symmetric and
blockwise banded matrix. As in regular FE methods, the derivation is s
tarted from the total potential energy principle. However, in those su
bdomains that are best suited to the BIE method, the exact solution of
the associated free field equation is used to represent the true solu
tion. The size and shape of each BIE subdomain, called ''macro-element
'' in this paper, may be designed freely to meet various practical req
uirements concerning, for example, numerical efficiency, machine stora
ge limitations, mesh generations, etc. Most significantly, unlike the
existing BIE techniques, the present method does not seem to require s
pecial treatments for corner effects, thus reducing the computational
complexity. Numerical experiments have been performed for generalized
Poisson's equation as a prototype situation. The extension to 2D-3D el
astic problems is straightforward.