Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming
Schmitt J, Köstler H (2022)
Publication Language: English
Publication Status: Published
Publication Type: Conference contribution, Conference Contribution
Future Publication Type: Conference contribution
Publication year: 2022
Series: GECCO '22
Pages Range: 1009-1018
Conference Proceedings Title: Proceedings of the Genetic and Evolutionary Computation Conference
Event location: Boston, Massachusetts
ISBN: 9781450392372
Abstract
Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we introduce a new approach for evolving efficient preconditioned iterative solvers for Helmholtz problems with multi-objective grammar-guided genetic programming. Our approach is based on a novel context-free grammar, which enables the construction of multigrid preconditioners that employ a tailored sequence of operations on each discretization level. To find solvers that generalize well over the given domain, we propose a custom method of successive problem difficulty adaption, in which we evaluate a preconditioner's efficiency on increasingly ill-conditioned problem instances. We demonstrate our approach's effectiveness by evolving multigrid-based preconditioners for a two-dimensional indefinite Helmholtz problem that outperform several human-designed methods for different wavenumbers up to systems of linear equations with more than a million unknowns.
Authors with CRIS profile
Jonas Schmitt
Lehrstuhl für Informatik 10 (Systemsimulation)
Harald Köstler
Lehrstuhl für Informatik 10 (Systemsimulation)
How to cite
APA:
Schmitt, J., & Köstler, H. (2022). Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming. In Association for Computing Machinery (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference (pp. 1009-1018). Boston, Massachusetts, US.
MLA:
Schmitt, Jonas, and Harald Köstler. "Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming." Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’22), Boston, Massachusetts Ed. Association for Computing Machinery, 2022. 1009-1018.
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