Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
We consider the sequence of sparse matrix-matrix multiplications performed during the setup phase of algebraic multigrid. In particular, we show that the most commonly used parallel algorithm is often not the most communication-efficient one for all of the matrix-matrix multiplications involved. By using an alternative algorithm, we show that the communication costs are reduced (in theory and practice), and we demonstrate the performance benefit for both model (structured) and more realistic unstructured problems on large-scale distributed-memory parallel systems. Our theoretical analysis shows that we can reduce communication by a factor of up to 5.4 for a model problem, and we observe in our empirical evaluation communication reductions of factors up to 4.7 for structured problems and 3.7 for unstructured problems. These reductions in communication translate to run-time speedups of up to factors of 2.3 and 2.5, respectively.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1504845
- Report Number(s):
- SAND--2015-3275; 603395
- Country of Publication:
- United States
- Language:
- English
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