{"title":"Evolving Nonlinear Multigrid Methods With Grammar-Guided Genetic Programming","authors":"Dinesh Parthasarathy, J. Schmitt, H. Köstler","doi":"10.1145/3583133.3590734","DOIUrl":null,"url":null,"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.","PeriodicalId":422029,"journal":{"name":"Proceedings of the Companion Conference on Genetic and Evolutionary Computation","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Companion Conference on Genetic and Evolutionary Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3583133.3590734","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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