BCCG+FAI

A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner. This paper presents our new solver BCCG+FAI for solving elastic normal contact problems. This is a comprehensible approach that is based on the Conjugate Gradients (CG) algorithm and that uses FFTs. A first novel aspect is the definition of the “FFT-based Approximate Inverse” preconditioner. The underlying idea is that the inverse matrix can be approximated well using a Toeplitz or block-Toeplitz form, which can be computed using the FFT of the original matrix elements. This preconditioner makes the total number of CG iterations effectively constant in 2D and very slowly increasing in 3D problems. A second novelty is how we deal with a prescribed total force. This uses a deflation technique in such a way that CGs convergence and finite termination properties are maintained. Numerical results show that this solver is more effective than existing CG-based strategies, such that it can compete with Multi-Grid strategies over a much larger problem range. In our opinion it could be the new method of choice because of its simple structure and elegant theory, and because robust performance is achieved independently of any problem specific parameters,


References in zbMATH (referenced in 10 articles )

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  1. Vollebregt, Edwin: Detailed wheel/rail geometry processing with the conformal contact approach (2021)
  2. Bruni, Stefano; Meijaard, J. P.; Rill, Georg; Schwab, A. L.: State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches (2020)
  3. van der Wekken, C. D.; Vollebregt, E. A. H.: Numerical calculation of the elastic field in a half-space using bilinear elements (2019)
  4. Wu, Min-Hua; Li, Chen-Liang: A preconditioned modulus-based matrix multisplitting block iteration method for the linear complementarity problems with Toeplitz matrix (2019)
  5. Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.: Extending the BEM for elastic contact problems beyond the half-space approach (2016)
  6. Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.: A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems (2015)
  7. Vollebregt, E. A. H.: A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner (2014)
  8. Vollebregt, Edwin A. H.: The bound-constrained conjugate gradient method for non-negative matrices (2014)
  9. Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.: A full multigrid method for linear complementarity problems arising from elastic normal contact problems (2014)
  10. Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.: Multigrid with FFT smoother for a simplified 2D frictional contact problem. (2014)