Fast methods for solving rough contact problems: A comparative study

A realistic description of rough surfaces will generally involve very large arrays of surface height data, which makes the application of conventional numerical methods of contact mechanics to rough contact analyses impractical. Recently, two fast numerical techniques have been applied to rough contact problems: the multi-level multi-summation (MLMS) and the fast Fourier transform (FFT). In this work, the computational efficiency of the two methods is compared by applying them to an example concentrated contact problem. It is shown that to achieve a numerical accuracy comparable to that of MLMS, the grid on,which FFT is performed needs to be extended far beyond the contact area, which results in a dramatic increase in the computation time. When such a high accuracy is unnecessary, FFT can be applied on a smaller grid. However, the computational speed of MLMS can also be increased in this case by modifying certain algorithm parameters. Numerical results demonstrate that MLMS is more advantageous than FFT for solving three-dimensional concentrated contact problems, both when the maximum possible accuracy is desired and when a moderate accuracy goal is specified.