Optimizing geometric multigrid method computation using a DSL approach

Vasista, Vinay and Narasimhan, Kumudha and Bhat, Siddharth and Bondhugula, Uday (2017) Optimizing geometric multigrid method computation using a DSL approach. In: International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2017, 12 - 17 November 2017, Denver, Colorado, pp. 1-13.

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Abstract

The Geometric Multigrid (GMG) method is widely used in numerical analysis to accelerate the convergence of partial differential equations solvers using a hierarchy of grid discretizations. Multiple grid sizes and recursive expression of multigrid cycles make the task of program optimization tedious. A high-level language that AIDS domain experts for GMG with effective optimization and parallelization support is thus valuable. We demonstrate how high performance can be achieved along with enhanced programmability for GMG, with new language/optimization support in the PolyMage DSL framework. We compare our approach with (a) hand-optimized code, (b) hand-optimized code in conjunction with polyhedral optimization techniques, and (c) the existing PolyMage optimizer adapted to multigrid. We use benchmarks varying in multigrid cycle structure and smoothing steps for evaluation. On a 24-core Intel Xeon Haswell multicore system, our automatically optimized codes achieve a mean improvement of 3.2x over straightforward parallelization, and 1.31x over the PolyMage optimizer.

Item Type:	Conference Paper
Publisher:	Association for Computing Machinery, Inc
Additional Information:	The Copyright of this article belongs to the Association for Computing Machinery, Inc.
Keywords:	Multigrid; Parallelization; Tiling; Codes (symbols); Computer programming languages; Convergence of numerical methods; Digital subscriber lines; DSL; High level languages; Numerical methods; Geometric multigrid methods; Multi-grid; Parallelizations; Partial differential equations solver; Polyhedral optimizations; Program optimization; Recursive expressions; Tiling; C (programming language)
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	17 Jun 2022 05:23
Last Modified:	17 Jun 2022 05:23
URI:	https://eprints.iisc.ac.in/id/eprint/73482

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