===firstname:
Pieter
===firstname3:

===affil6:

===lastname3:

===email:
pghysels@lbl.gov
===keyword_other2:

===lastname6:

===affil5:

===lastname4:

===lastname7:

===affil7:

===postal:
1 Cyclotron Road MS 50F-1630A
Berkeley, CA 94720
===ABSTRACT:
We present an effective preconditioner for linear systems that arise from PDE discretizations. The preconditioner is constructed from an incomplete factorization, based on a multifrontal version of classical Gaussian elimination. The fill-in introduced during the factorization is compressed or approximated by rank-structured matrices.  Rank-structured matrices are matrices which have sub-blocks that are of low rank. We consider Hierarchically Semi-Separable (HSS) matrices, a specific type of rank-structured or hierarchical matrices. The compression of matrix sub-blocks into a low-rank product representation in the HSS format is performed with a novel randomized sampling techniques.

We apply the incomplete factorization as a preconditioner for GMRES or BiCGStab and compare with a number of other common preconditioners such as ILU and AMG. We look at linear and nonlinear elasticity problems, Maxwell's equation and a number of large-scale applications which are of key importance to the DOE.

Code for this preconditioner is developed as the package STRUMPACK and is released online with a BSD license. The code exploits hybrid parallelism through OpenMP and MPI. We present results obtained on large distributed memory parallel machines from the National Energy Research Scientific Computing Center (NERSC).


===affil3:

===title:
Evaluation of a preconditioner using low-rank approximation and randomized sampling
===affil2:
Lawrence Berkeley National Laboratory
===lastname2:
Li
===firstname4:

===keyword1:
APP_OTHER
===workshop:
no
===lastname:
Ghysels
===firstname5:

===keyword2:
Hybrid direct-iterative solvers
===otherauths:

===affil4:

===competition:
no
===firstname7:

===firstname6:

===keyword_other1:
Preconditioning
===lastname5:

===affilother:

===firstname2:
Xiaoye S.