The Schwarz alternating method for multi-scale coupling and contact in solid mechanics.

Abstract

Multi-scale methods are essential for the understanding and prediction of behavior of engineering systems when a small-scale event will eventually determine the performance of the entire system. In this talk, we will discuss a novel recently-proposed [1,2] approach that enables concurrent multi-scale coupling in finite deformation quasistatic and dynamic solid mechanics by leveraging the domain-decomposition-based Schwarz alternating method. The approach is based on the simple idea that if the solution to a partial differential equation is known in two or more regularly shaped domains comprising a more complex domain, these local solutions can be used to iteratively build a solution for the more complex domain. The proposed methodology has a number of advantages over competing multiscale coupling methods, most notably its concurrent nature, its ability to couple non-conformal meshes with different element topologies and different time integrators with different time steps for dynamic problems all without introducing non-physical artifacts into the solution, and its non-intrusive implementation into existing codes. In the first part of the talk, we will describe the formulation and theoretical properties of the Schwarz alternating method as a means for concurrent multiscale coupling in quasistatic and dynamic solid mechanics. We will show several large-scale numerical examples demonstrating the method’s numerical properties and convergence based on its implementation in two massively-parallel HPC codes: Albany/LCM and Sierra/Solid Mechanics. In the second part of the talk, we will describe some more recent work in extending the Schwarz alternating method to multi-scale contact mechanics problems. Unlike the original formulation of the method for multi-scale coupling, which relies on an overlapping domain decomposition with Dirichlet transmission conditions, the contact formulation requires a non-overlapping domain decomposition with Dirichlet-Neumann or Robin-Robin transmission conditions. After describing our Schwarz contact formulation, we will demonstrate on several collision problems that