A hybrid formulation is proposed that incorporates finite element substructuring and Galerkin boundary elements in the numerical solution of Poisson's or Laplace's equation with open boundaries. Substructuring the problem can dramatically decreases the size of matrix to be solved. It is shown that the boundary integration that results from application of Green's first theorem to the weighted residual statement can be used to advantage by imposing potential and flux continuity through the contour which separates the interior and exterior regions. In fact, the boundary integration is of exactly the same form as that found in Galerkin boundary elements.
BEATOVIC, D., LEVIN, P.L., GAN, H., KOKERNAK, J.M. and HANSEN, A.J. (1992), "NUMERICAL ANALYSIS OF OPEN BOUNDARY PROBLEMS USING FINITE ELEMENT SUBSTRUCTURING AND GALERKIN BOUNDARY ELEMENTS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 11 No. 2, pp. 295-309. https://doi.org/10.1108/eb010093
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