# A Parallel Choleski Solver with Improved Scalabilities

## Xiaoming Zhang

(IBM UK)

Direct system solvers are sometimes quite useful for the solution of linear systems arising from finite element problems. However, it is well known that they are difficult to parallelise on distributed memory platforms to achieve high scalabilities.

This talk will first investigate the isoefficiency scalabilities of a parallel Choleski method (factorization and forward/backward substitutions) based on a conventional substructuring approach and then demonstrate that these scalabilities can be improved upon by further adoption of substructuring for both two- and three-dimensional finite element and finite difference analysis problems. For 2D problems, the isoefficiency scalabilities can be optimized from N=p4 to N=p3 for factorization and from N=p5 to N=p3.67 for forward/backward substitutions, where N is the number of mesh nodes and p the number of parallel processors. For 3D problems, the isoefficiency scalabilities can be improved from N=p5.5 to N=p4.375. for factorization and from N=p7 to N=p5.5 for forward/backward substitutions.

**Tuesday 8th December 1998, 15:00**

Seminar Room 322

Department of Computer Science