Control of the accuracy and improvement of the convergence rate of a LATIN-based multiscale strategy for frictional contact problems

This paper deals with the control and improvement of the convergence of the interface contact quantities in the framework of a multiscale strategy for the resolution of time-dependent fric- tional contact problems. The considered strategy is the multiscale mixed domain decomposition method based on the LATIN non-incremental solver, whose specificity is that it generates succes- sive approximations of the solution over the entire space-time domain. In order to highlight this characteristic of the method, in a previous paper [1], the robustness of the strategy was pointed out, but also how challenging it is to control the accurate convergence of microquantities at the interfaces and how the convergence rate of microquantities depends on the parameters of search directions used in the LATIN, in a manner similar to the influence of augmentation parameters in augmented Lagrangian approaches combined with an Uzawa-like solver. The objective of this work is to propose, first of all, a dedicated convergence indicator in order to stop the iterative pro- cess of the resolution strategy for ensuring converged contact quantities with a reasonable level of accuracy. Such a convergence indicator is crucial for the second part of the paper, where a strategy is introduced for the on-the-fly updating of search directions along the LATIN iterations based on the contact status in space and time to improve the convergence rate of the interface quantities. The robustness of the convergence indicator and the updating strategy is tested on several 2D frictional contact problems with multiple contact interfaces and different time-evolving contact conditions (open/closed and stick/slip transitions), allowing for accurate control and improved convergence rate of local microquantities, especially when a high level of accuracy is required.