University of Illinois, Champaign-Urbana Progress Report 95/96

RECENT_96_ACCOMPLISHMENT

Improvements have been made in all phases of CAPSS, a fully parallel solver for direct solution of large sparse positive definite systems. Complementing the previous ordering, which was based on Cartesian nested dissection using coordinate information, a new ordering algorithm has been added which is based on graph compaction and does not require coordinates. The use of two-dimensional matrix partitioning and higher-level BLAS was investigated for enhancing the performance and scalability of numeric factorization. A new selective inversion scheme was developed that speeds up the triangular solution phase by factor of 6 to 16 on typical test problems. This scheme, which computes inverses of a sequence of submatrices of the factor and uses these to replace substitution steps by more efficient distributed matrix-vector multiplications, is a significant breakthrough for a portion of the computation that was previously a substantial performance and scalability bottleneck. Investiation also began on improving the user interface to make the package easier to use in applications.

FY1997_PLAN

The following new features will be integrated into a complete new version of CAPSS: coordinate and non-coordinate orderings with improved fill reduction and load balance, two-dimensional partitioning and higher level BLAS in the factorization, and selective inversion in the triangular solution. Communication will use MPI for improved portability, and performance will be made tunable for a given platform.

TECHNOLOGY_TRANSITION

CAPSS has been used in solving numerous problems in structural mechanics, including shearing in foam-like materials and crack propagation in extrusion processes.