Algebraic description and automatic generation of multigrid methods inSPIRAL

摘要

SPIRAL is an autotuning, program generation, and code synthesis system that offers a fully automaticgeneration 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. Weopen SPIRAL up to a new, practically relevant and challenging domain: multigrid solvers. SPIRAL is drivenby algebraic transformation rules. We specify a set of such rules for a simple multigrid solver with aRichardson smoother for a discretized square 2D Poisson equation with Dirichlet boundary conditions. Wepresent 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, morecomplex multigrid solvers may require small adaptations.