Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis

TL;DR

This paper enhances the frequency-domain boundary element method for elastodynamic analysis by introducing strategies that improve computational efficiency and response accuracy, enabling faster and more reliable simulations of large-scale problems.

Contribution

It proposes three novel strategies—large damping exponential window, frequency domain windowing, and solution extrapolation—to significantly improve the efficiency and accuracy of the frequency-domain BEM.

Findings

Reduced computational time with the first and third strategies.

Elimination of Gibbs oscillations with the second strategy.

Successful application to large-scale problems with up to 0.7 million unknowns.

Abstract

The frequency-domain fast boundary element method (BEM) combined with the exponential window technique leads to an efficient yet simple method for elastodynamic analysis. In this paper, the efficiency of this method is further enhanced by three strategies. Firstly, we propose to use exponential window with large damping parameter to improve the conditioning of the BEM matrices. Secondly, the frequency domain windowing technique is introduced to alleviate the severe Gibbs oscillations in time-domain responses caused by large damping parameters. Thirdly, a solution extrapolation scheme is applied to obtain better initial guesses for solving the sequential linear systems in the frequency domain. Numerical results of three typical examples with the problem size up to 0.7 million unknowns clearly show that the first and third strategies can significantly reduce the computational time. The second strategy can effectively eliminate the Gibbs oscillations and result in accurate time-domain responses.