Can I read Parallel Memory-efficient All-at-once Algorithms for the Sparse Matrix Triple Products in Multigrid Methods on EtoBox?

Parallel Memory-efficient All-at-once Algorithms for the Sparse Matrix Triple Products in Multigrid Methods by Kong, Fande is a scholarly article available to read on EtoBox.

What is Parallel Memory-efficient All-at-once Algorithms for the Sparse Matrix Triple Products in Multigrid Methods about?

Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the multilevel/multigrid methods is to form coarse matrices through a sequence of sparse matrix triple products. A commonly used approach for the triple products explicitly involves two steps, and during each step a sparse matrix-matrix multiplication is employed. This approach works well for many applications with a good computational efficiency, but it has a high memory overhead since some auxiliary matrices need to be temporarily stored for accomplishing the calculations. In this work, we propose two new algorithms that construct a coarse matrix with taking one pass through the input matrices without involving any auxiliary matrices for saving memory. The new approaches are referred to as "all-at-once" and "merged all-at-once", and the traditional method is denoted as "two-step". The all-at-once and the merged all-at-once algorithms are implemented based on hash tables in PETSc as part of this work with a careful consideration on the performance in terms of the

Author

Kong, Fande

Published

2019

Language

EN