AN ENERGY-BASED MACRO-ELEMENT METHOD VIA A COUPLED FINITE-ELEMENT ANDBOUNDARY INTEGRAL FORMULATION

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.