A new parallel sparse direct solver: Presentation and numerical experiments in large-scale structural mechanics parallel computing

• Published in: International journal for numerical methods in engineering Vol. 88; no. 4; pp. 370 - 384
• Main Authors: Guèye, I., Arem, S. El, Feyel, F., Roux, F.-X., Cailletaud, G.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 28-10-2011; Wiley
• Subjects: Algebra; Computation; DDM; Dissection; Engineering Sciences; Exact sciences and technology; Factorization; FETI; finite element method; Fundamental areas of phenomenology (including applications); Linear and multilinear algebra, matrix theory; linear sparse direct solver; Linear systems; Materials and structures in mechanics; Mathematics; Mechanics; Mumps; nested dissection; Numerical analysis; Parallel processing; Physics; Sciences and techniques of general use; Solid mechanics; Solvers; Structural and continuum mechanics; Structural mechanics; Performance evaluation; Matrix factorization; DDM; Distributed computing; Modeling; Finite element method; linear sparse direct solver; FETI; Massive parallelism; Sparse matrix; Parallel processing; Large scale system; High performance; Parallel algorithm; LU factorization; structural mechanics; Matrix decomposition; Experimental study; Linear system; Parallel computation; Large scale; Domain decomposition; Parallelization; nested dissection; Structural analysis; Finite Element Method; Structural Mechanics; Dissection
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3179

The main purpose of this work is to present a new parallel direct solver: Dissection solver. It is based on LU factorization of the sparse matrix of the linear system and allows to detect automatically and handle properly the zero‐energy modes, which are important when dealing with DDM. A performance evaluation and comparisons with other direct solvers (MUMPS, DSCPACK) are also given for both sequential and parallel computations. Results of numerical experiments with a two‐level parallelization of large‐scale structural analysis problems are also presented: FETI is used for the global problem parallelization and Dissection for the local multithreading. In this framework, the largest problem we have solved is of an elastic solid composed of 400 subdomains running on 400 computation nodes (3200 cores) and containing about 165 millions dof. The computation of one single iteration consumes less than 20 min of CPU time. Several comparisons to MUMPS are given for the numerical computation of large‐scale linear systems on a massively parallel cluster: performances and weaknesses of this new solver are highlighted. Copyright © 2011 John Wiley & Sons, Ltd.