Precorrected FFT accelerated BEM for large-scale transient elastodynamic analysis using frequency-domain approach

• Published in: International journal for numerical methods in engineering Vol. 90; no. 1; pp. 116 - 134
• Main Authors: Xiao, Jinyou, Ye, Wenjing, Cai, Yaxiong, Zhang, Jun
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 06.04.2012; Wiley
• Subjects: Algebra; boundary element method; elastodynamics; Exact sciences and technology; exponential window method; frequency-domain approach; Fundamental areas of phenomenology (including applications); Linear and multilinear algebra, matrix theory; Mathematics; Physics; precorrected FFT; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Performance evaluation; exponential window method; Fast Fourier transformation; Discrete Fourier transformation; Krylov subspace method; Windows; Polynomial method; Elastic wave; Modeling; Convolution; Least squares method; Elastodynamics; Boundary element method; Minimum residual method; Transient response; Frequency domain method; Experimental study; precorrected FFT; Plate; Dimension reduction; Reduction method; frequency-domain approach; Cube; Large scale; Porosity; Mechanical shock
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3316

SUMMARY A precorrected fast Fourier transform (pFFT) accelerated boundary element method (BEM) for large‐scale transient elastodynamic analysis is developed and described in this paper. The frequency‐domain approach is used. To overcome the ‘wrap‐around’ problem associated with the discrete Fourier transform, the exponential window method (EWM) is employed and incorporated in the frequency‐domain BEM. An improved implementation scheme of the pFFT method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic BEM. This new scheme reduces the memory required to save the convolution matrix by a factor of 8. To further improve the efficiency of the code, a newly developed linear system solver based on the induced dimension reduction method is employed. Its performance is investigated and compared with that of the well‐known GMRES. The accuracy and computational efficiency of the method are evaluated and demonstrated by three examples: a classical benchmark, a plate subject to an impact loading and a porous cube with nearly half million DOFs subject to a step traction loading. Both analytical and experimental results are employed to validate the method. It has been found that the EWM can effectively resolve the wrap‐around problem and accurate time responses for an arbitrarily chosen time period can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.