Dinesh Parthasarathy
ABSTRACT
We formulate a formal grammar to generate Full Approximation Scheme multigrid solvers. Then, using Grammar-Guided Genetic Programming we perform a multiobjective optimization to find optimal instances of such solvers for a given nonlinear system of equations. This approach is evaluated for a two-dimensional Poisson problem with added nonlinearities. We observe that the evolved solvers outperform the baseline methods by having a faster runtime and a higher convergence rate.
- Félix-Antoine Fortin, François-Michel De Rainville, Marc-André Gardner, Marc Parizeau, and Christian Gagné. 2012. DEAP: Evolutionary Algorithms Made Easy. Journal of Machine Learning Research 13 (jul 2012), 2171--2175.Google Scholar
Digital Library
- Jonas Schmitt, Sebastian Kuckuk, and Harald Köstler. 2020. Constructing Efficient Multigrid Solvers with Genetic Programming. In Proceedings of the 2020 Genetic and Evolutionary Computation Conference (Cancún, Mexico) (GECCO '20). Association for Computing Machinery, New York, NY, USA, 1012--1020. Google ScholarDigital Library
- Jonas Schmitt, Sebastian Kuckuk, and Harald Köstler. 2021. EvoStencils: a grammar-based genetic programming approach for constructing efficient geometric multi-grid methods. Genetic Programming and Evolvable Machines 22, 4 (Sept. 2021), 511--537. Google ScholarDigital Library
- Ulrich Trottenberg, Cornelis W. Oosterlee, and Anton Schüller. 2001. Multigrid. Texts in Applied Mathematics. Bd., Vol. 33. Academic Press, San Diego [u.a.]. With contributions by A. Brandt, P. Oswald and K. Stüben.Google Scholar
Index Terms
Evolving Nonlinear Multigrid Methods With Grammar-Guided Genetic Programming
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