Farhat, Charbel; Roux, François-Xavier Implicit parallel processing in structural mechanics. (English) Zbl 0805.73062 Comput. Mech. Adv. 2, No. 1, 1-124 (1994). Focusing on finite element implicit computations, we discuss in great detail parallel skyline solvers, primal substructuring algorithms, and the dual substructuring method also known as the finite element method of tearing and interconnecting. 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. Cited in 1 ReviewCited in 100 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 74K99 Thin bodies, structures 65Y05 Parallel numerical computation 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs Keywords:parallel skyline solvers; primal substructuring; dual substructuring; finite element method of tearing and interconnecting; numerical scalability; iterative solvers; coarse grid solvers; message passing paradigm PDFBibTeX XMLCite \textit{C. Farhat} and \textit{F.-X. Roux}, Comput. Mech. Adv. 2, No. 1, 1--124 (1994; Zbl 0805.73062)