Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

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• 作者：Martin Schanz ; Wenjing Ye ; Jinyou Xiao
• 关键词：Convolution quadrature method ; FFT exponential window ; Boundary element method
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：57
• 期：4
• 页码：523-536
• 全文大小：1,316 KB
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• 作者单位：Martin Schanz (1)
  Wenjing Ye (2)
  Jinyou Xiao (3)
  
  1. Institute of Applied Mechanics, Graz University of Technology, Graz, Austria
  2. Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong
  3. School of Astronautics, Northwestern Polytechnical University, Xi’an, China
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.