Acceleration of numerical solution of elastic contact problems by a dual-grid approach

Abstract

Finer meshes employed in the numerical simulation of contact problems provide better accuracy, assuring that the effect of specific features of the initial contact geometry on the stress and displacement field are faithfully captured. Efficient implementation of finer meshes may benefit from a dual-grid scheme, involving a lower level and a desired level. The main idea is to use the lower level for the preparation of a better initial guess for the desired level, obtained by interpolation of results derived on the lower level. A dual-grid scheme involves three steps: (a) solution on the lower level (the coarser grid) with a standard initial guess, (b) interpolation of results into the desired level mesh, providing a more accurate initial approximation for the subsequent step, and (c) the solution of the desired level (the finer mesh) with the improved initial guess. As demonstrated by the conducted numerical simulations, this approach provides important computational advantages, as the solution of the lower mesh is obtained more rapidly than that of the finer mesh, whereas the number of iterations in the upper level is reduced due to the quality of the improved initial guess. The optimal ratio between the lower and the upper levels is investigated through numerical examples and an optimal value is proposed. The proposed dual-grid method should promote faster solutions of the contact problems, and therefore can be implemented in a variety of contact scenarios that rely on the considered algorithm. The improvements should be more beneficial for the contact processes involving the reproduction of the loading path, such as the elastic-plastic or the viscoelastic contact.