Constructing Efficient Multigrid Solvers with Genetic Programming

Schmitt J, Kuckuk S, Köstler H (2020)

Publication Language: English

Publication Type: Conference contribution, Conference Contribution

Publication year: 2020

City/Town: New York, NY, USA

Pages Range: 1012 - 1020

Conference Proceedings Title: Proceedings of the 2020 Genetic and Evolutionary Computation Conference

Event location: Cancún MX

ISBN: 9781450371285

DOI: 10.1145/3377930.3389811

Abstract

For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of geometric multigrid methods that is based on evolutionary computation, a generic program optimization technique inspired by the principle of natural evolution. A multigrid solver is represented as a tree of mathematical expressions which we generate based on a tailored grammar. The quality of each solver is evaluated in terms of convergence and compute performance using automated local Fourier analysis (LFA) and roofline performance modeling, respectively. Based on these objectives a multi-objective optimization is performed using grammar-guided genetic programming with a non-dominated sorting based selection. To evaluate the model-based prediction and to target concrete applications, scalable implementations of an evolved solver can be automatically generated with the ExaStencils framework. We demonstrate the effectiveness of our approach by constructing multigrid solvers for a linear elastic boundary value problem that are competitive with common V- and W-cycles.

Authors with CRIS profile

Jonas Schmitt Lehrstuhl für Informatik 10 (Systemsimulation) (LSS) Sebastian Kuckuk Lehrstuhl für Informatik 10 (Systemsimulation) (LSS) Harald Köstler Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)

How to cite

APA:

Schmitt, J., Kuckuk, S., & Köstler, H. (2020). Constructing Efficient Multigrid Solvers with Genetic Programming. In Association for Computing Machinery (Eds.), Proceedings of the 2020 Genetic and Evolutionary Computation Conference (pp. 1012 - 1020). Cancún, MX: New York, NY, USA.

MLA:

Schmitt, Jonas, Sebastian Kuckuk, and Harald Köstler. "Constructing Efficient Multigrid Solvers with Genetic Programming." Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '20), Cancún Ed. Association for Computing Machinery, New York, NY, USA, 2020. 1012 - 1020.

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