Implicit parallel processing in structural mechanics

Parallel processors are becoming reality but many engineering disciplines, including finite element structural analysis, are still lagging behind in using this new computing technology. Clearly, programming languages, education, economics, and resistance to changes are important obstacles for the transfer of this technology. However, the unawareness of the impact of parallel architectures on computational mechanics software design principles, and the lack of powerful algorithms that fully exploit the capabilities of these new machines are more important and challenging barriers. The purpose of this monograph is to address the two latter issues. Focusing on finite element implicit computations, we discuss in great details parallel skyline solvers, primal substructuring algorithms, and the dual substructuring method also known as the Finite Element method of Tearing and Interconnecting (FETI). We highlight the concept of numerical scalability for domain decomposition based iterative solvers, the effect and parallel implementation of their coarse grid solvers, and discuss their extension to systems with multiple right-hand sides. We also address the topic of mesh partitioning and the message-passing paradigm.