Efficient solution of the dry contact of rough surfaces: a comparison of fast Fourier transform and multigrid methods

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Numerical tools are required to improve our understanding of tribological experiments. In order to represent all the details of rough surface contacts, such calculations require many grid points. Hence, high-performance tools are necessary to obtain precision and limit computing time and memory requirement. This article compares the precision, convergence speed, computing time, memory requirement, and robustness of two solvers for three different cases: a smooth Hertzian contact, a wavy Hertzian contact, and a rough Hertzian contact. The first solver is based around the conjugate gradient method and the deformation integrals are computed using the fast Fourier transform (FFT). The second solver is based on the distributed Gauss–Seidel relaxation, using multigrid (MG) techniques to accelerate convergence and multilevel multi integration (MLMI) for a fast computation of the deformation. The overall conclusion is that the MG method excels in terms of computing speed and memory requirement, whereas the FFT-based code excels in robustness and implementation time.