Evolving Algebraic Multigrid Methods Using Grammar-Guided Genetic Programming

• URL: http://arxiv.org/abs/2412.05852v1
• Date: Sun, 08 Dec 2024 08:21:35 GMT
• Title: Evolving Algebraic Multigrid Methods Using Grammar-Guided Genetic Programming
• Authors: Dinesh Parthasarathy, Wayne Bradford Mitchell, Harald Köstler,
• Abstract summary: We use grammar rules to generate arbitrary-shaped cycles, where smoothers and relaxation weights are chosen independently. These flexible cycles are used in Algebraic Multigrid (AMG) methods with the help of grammar rules and optimized using genetic programming. We observe that the optimized flexible cycles provide higher efficiency and better performance than the standard cycle types.
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• Abstract: Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and W-cycles. We use grammar rules to generate arbitrary-shaped cycles, wherein the smoothers and their relaxation weights are chosen independently at each step within the cycle. We call this a flexible multigrid cycle. These flexible cycles are used in Algebraic Multigrid (AMG) methods with the help of grammar rules and optimized using genetic programming. The flexible AMG methods are implemented in the software library of hypre, and the programs are optimized separately for two cases: a standalone AMG solver for a 3D anisotropic problem and an AMG preconditioner with conjugate gradient for a multiphysics code. We observe that the optimized flexible cycles provide higher efficiency and better performance than the standard cycle types.

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