Summary: Convergence of the domain decomposition finite
element≠boundary element coupling methods
M. El-Gebeily a,*, Wael M. Elleithy b
, Husain J. Al-Gahtani c
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan
Department of Civil Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Received 8 February 2001; received in revised form 23 December 2001; accepted 4 June 2002
In this work, we analyze three available domain decomposition methods. We also establish the convergence con-
ditions. The theoretical analysis provides an interval in which a relaxation parameter has to be chosen in order to
achieve convergence. Moreover, it allows the selection of the relaxation parameter so that convergence is achieved with
the minimum number of iterations. Several example problems are given for elaboration.
” 2002 Elsevier Science B.V. All rights reserved.
Keywords: Finite element method; Boundary element method; Domain decomposition; Coupling; Convergence
Coupling the finite element method (FEM) and the boundary element method (BEM) is well known as