A dissection solver with kernel detection for symmetric finite element matrices on shared memory computers

• Published in: International journal for numerical methods in engineering Vol. 100; no. 2; pp. 136 - 164
• Main Authors: Suzuki, A., Roux, F.-X.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 12.10.2014; Wiley Subscription Services, Inc; Wiley
• Subjects: asynchronous task execution; Complement; Computer Science; Computer simulation; finite element matrix; kernel detection; Kernels; level 3 BLAS; Mathematical analysis; Mathematical models; Mathematics; nested dissection; Numerical Analysis; Pivots; Solvers; Thresholds; level 3 BLAS; kernel detection; finite element matrix; asynchronous task execution; nested dissection
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.4729

SUMMARYA direct solver for symmetric sparse matrices from finite element problems is presented. The solver is supposed to work as a local solver of domain decomposition methods for hybrid parallelization on cluster systems of multi‐core CPUs, and then it is required to run on shared memory computers and to have an ability of kernel detection. Symmetric pivoting with a given threshold factorizes a matrix with a decomposition introduced by a nested bisection and selects suspicious null pivots from the threshold. The Schur complement constructed from the suspicious null pivots is examined by a factorization with 1 × 1 and 2 × 2 pivoting and by a robust kernel detection algorithm based on measurement of residuals with orthogonal projections onto supposed image spaces. A static data structure from the nested bisection and a block sub‐structure for Schur complements at all bisection levels can use level 3 BLAS routines efficiently. Asynchronous task execution for each block can reduce idle time of processors drastically, and as a result, the solver has high parallel efficiency. Competitive performance of the developed solver to Intel Pardiso on shared memory computers is shown by numerical experiments. Copyright © 2014 John Wiley & Sons, Ltd.