Evaluation of singular integrals in the symmetric Galerkin boundary element method

Authors:
Zhiye Zhao;Weifeng Yuan
Affiliations:
School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798;School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore 639798
Venue:
Advances in Engineering Software
Year:
2004

Citing 1
Cited 1

An energy approach to the boundary element method. Part I: elastic solids

Computer Methods in Applied Mechanics and Engineering

Frequency domain analysis by the exponential window method and SGBEM for elastodynamics

Computational Mechanics

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Abstract

The implementation of the symmetric Galerkin boundary element method (SGBEM) involves extensive work on the evaluation of various integrals, ranging from regular integrals to hypersingular integrals. In this paper, the treatments of weak singular integrals in the time domain are reviewed, and analytical evaluations for the spatial double integrals which contain weak singular terms are derived. A special scheme on the allocation of Gaussian integration points for regular double integrals in the SGBEM is developed to improve the efficiency of the Gauss-Legendre rule. The proposed approach is implemented for the two-dimensional elastodynamic problems, and two numerical examples are presented to verify the accuracy of the numerical implementation.