Title
Algebraic description and automatic generation of multigrid methods in SPIRAL.
Abstract
SPIRAL is an autotuning, program generation, and code synthesis system that offers a fully automatic generation of highly optimized target codes, customized for the specific execution platform at hand. Initially, SPIRAL was targeted at problem domains in digital signal processing, later also at basic linear algebra. We open SPIRAL up to a new, practically relevant and challenging domain: multigrid solvers. SPIRAL is driven by algebraic transformation rules. We specify a set of such rules for a simple multigrid solver with a Richardson smoother for a discretized square 2D Poisson equation with Dirichlet boundary conditions. We present the target code that SPIRAL generates in static single-assignment form and discuss its performance. While this example required no changes of or extensions to the SPIRAL system, more complex multigrid solvers may require small adaptations.
Year
DOI
Venue
2017
10.1002/cpe.4105
CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE
Keywords
Field
DocType
high-performance computing,PDE solvers,multigrid,SPIRAL,program transformation
Linear algebra,Discretization,Digital signal processing,Spiral,Algebraic number,Poisson's equation,Computer science,Parallel computing,Computational science,Solver,Multigrid method,Distributed computing
Journal
Volume
Issue
ISSN
29
SP17
1532-0626
Citations 
PageRank 
References 
0
0.34
11
Authors
5
Name
Order
Citations
PageRank
Matthias Bolten1509.28
Franz Franchetti297488.39
Paul H. J. Kelly31361112.65
Christian Lengauer41738117.05
M. Mohr5102.85