Title: A symmetric variational finite element-boundary integral equation coupling method
Abstract: This paper is concerned with the development of a mixed variational principle for coupling finite element and boundary integral methods in interface problems, using the generalized Poisson's equation as a prototype situation. One of its primary objectives is to compare the performance of fully variational procedures with methods that use collocation for the treatment of boundary integral equations. A distinctive feature of the new variational principle is that the discretized algebraic equations for the coupled problem are automatically symmetric since they are all derived from a single functional. In addition, the condition that the flux remain continuous across interfaces is satisfied naturally. In discretizing the problem within inhomogeneous or loaded regions, domain finite elements are used to approximate the field variable. On the other hand, only boundary elements are used for regions where the medium is homogeneous and free of external agents. The corresponding integral equations are discretized both by fully variational and by collocation techniques. Results of numerical experiments indicate that the accuracy of the fully variational procedure is significantly greater than that of collocation for the complete interface problem, especially for complex disturbances, at little additional computational cost. This suggests that fully variational procedures may be preferable to collocation, not only in dealing with interface problems, but even for solving integral equations by themselves.
Publication Year: 1993
Publication Date: 1993-03-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 7
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