Asynchronous domain decomposition method in structure mechanics -- case of the global/local coupling

The analysis and design of complex structures can be time-consuming and computationally intensive, especially for large-scale problems. Domain decomposition methods have become a powerful tool in structural mechanics to address these challenges. They divide a computational task into smaller and independent tasks that can be executed in parallel. Recent work shows many advantages when coupling asynchronous parallel computation with these methods, overcoming the limitations of classical synchronous methods and resulting in more efficient use of computational resources and better parallelism, resulting in faster solution times.This research work presents the first asynchronous version of non-intrusive global/local coupling, capable of efficiently processing multiple possibly adjacent patches. We propose a new interpretation of the coupling by a primal domain decomposition method. We also demonstrate the convergence of relaxed asynchronous iteration in the linear and nonlinear cases using Paracontractions techniques. Subsequently, we propose an implementation based on MPI-RDMA techniques. This implementation is then confronted with an accelerated synchronous method. We illustrate it on several linear elliptic problems, such as those encountered in thermal and elasticity studies, and on nonlinear problems, such as nonlinear elliptic and plasticity problems. The asynchronous paradigm eliminates many global/local coupling performance problems.