A new torus-like mapping for parallel sparse matrix factorization

Conference · Fri Dec 31 04:00:00 EST 1993

OSTI ID:55318

Cleary, A J

A new family of mappings of the elements of a sparse matrix to the processors of a distributed memory parallel computer is presented. The new mapping is based on torus wrap mappings used for dense matrices and differs from previous sparse mappings in that it is not column oriented. Nonetheless, the new mappings generalize subtree-to-subset column-oriented mappings. Two algorithms for computing the Cholesky factorization using the new mapping are given. The communication volume for these algorithms on the classical k {times} k grid ordered by nested dissection is analyzed theoretically. It is shown that the first algorithm reduces the communication volume to O(k{sup 2}p{sup 1/2}), compared to O(k{sup 2}p) for previously published algorithms. The second reduces the volume to O9k{sup 2}p{sup 1/3} while requiring redundant memory of the same order. An order-of-magnitude argument shows that these algorithms scale much better than column-oriented algorithms.

• OSTI ID: 55318
• Report Number(s): DOE/ER/25151--1-Vol.1; CONF-930331--Vol.1
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPUTER ARCHITECTURE
FACTORIZATION
MATRICES
MEMORY MANAGEMENT
NUMERICAL SOLUTION
PARALLEL PROCESSING