Based on the assumption that solutions from different methods should be the same, the relationship among weakly singular, strongly singular and hypersingular matrices associated with symmetric Galerkin boundary element method (SGBEM) is derived in this paper. Hypersingularity is avoided through matrix manipulations so that only weakly and strongly singularities need to be solved. Compared with the advantages brought about by symmetry, the additional computation caused by matrix manipulations is not so important in many cases, especially for time-domain problems or when one wants to couple BEM with other symmetric schemes. Simplicity is the advantage of the current method over the traditional SGBEM. Both steady-state and time-domain potential problems have been studied, and two numerical examples are included to show the effectiveness and accuracy of the present formulation.
Relationship Among Coefficient Matrices in Symmetric Galerkin Boundary Element Method for Two-Dimensional Scalar Problems
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Apr. 23, 2002; final revision, Dec. 17, 2002. Associate Editor: T. E. Tezduyar. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Yu, G. Y. (August 25, 2003). "Relationship Among Coefficient Matrices in Symmetric Galerkin Boundary Element Method for Two-Dimensional Scalar Problems ." ASME. J. Appl. Mech. July 2003; 70(4): 479–486. https://doi.org/10.1115/1.1598478
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