A High Arithmetic Intensity Krylov Subspace Method Based on Stencil Compiler Programs
Additional information
Authors
Donfack S. .,
Sanan P. .,
Schenk O.,
Reps B. .,
Vanroose W.
Type
Article in conference proceedings
Year
2018
Language
English
Abstract
Stencil calculations and matrix-free Krylov subspace solvers
represent important components of many scientific computing applica-
tions. In these solvers, stencil applications are often the dominant part
of the computation; an efficient parallel implementation of the kernel is
therefore crucial to reduce the time to solution. Inspired by polynomial
preconditioning, we remove upper bounds on the arithmetic intensity
of the Krylov subspace building block by replacing the matrix with a
higher-degree matrix polynomial. Using the latest state-of-the-art stencil
compiler programs with temporal blocking, reduced memory bandwidth
usage and, consequently, better utilization of SIMD vectorization and
thus speedup on modern hardware, we are able to obtain performance
improvements for higher polynomial degrees than simpler cache-blocking
approaches have yielded in the past, demonstrating the new appeal of
polynomial techniques on emerging architectures. We present results in a
shared-memory environment and an extension to a distributed-memory
environment with local shared memory.
Conference proceedings
Proceedings of the International Conference on High Performance Computing in Science and Engineering
Month
May
Publisher
Springer International Publishing. Lecture Notes in Computer Science, vol 9611. Springer, Cham.
Start page number
1
End page number
18
Meeting name
HPCSE2017
Meeting place
Soláň, Czech Republic
Meeting date
May 2017
ISSN
978-3-319-97135-3
Keywords
stencil compilers, performance engineering, Krylov meth- ods, code generation, autotuning, HPC, CG, polynomial preconditioning
