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Paper
Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations
Presenter
Dinesh Parthasarathy is a PhD student at the Friedrich-Alexander University of Erlangen-Nuremberg (FAU). He completed his Master’s in Computational Engineering at FAU and is an alumnus of the Bavarian Graduate School of Computational Engineering (BGCE) program. His research focuses on applying artificial intelligence (AI) techniques to design efficient numerical methods, particularly using evolutionary algorithms guided by context-free grammars for efficient large scale simulations. More broadly, he is interested in scientific machine learning and its applications to computational science. He interned at Lawrence Livermore National Laboratory with the hypre team and is now an external collaborator, contributing to the AI-driven design of algebraic multigrid methods in hypre.
Description
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal multigrid components using machine learning techniques, we adopt a complementary strategy here, employing evolutionary algorithms to construct efficient multigrid cycles from available individual components.
This technology is applied to finite element simulations of the laser beam welding process. The thermo-elastic behavior is described by a coupled system of time-dependent thermo-elasticity equations, leading to nonlinear and ill-conditioned systems. The nonlinearity is addressed using Newton’s method, and iterative solvers are accelerated with an algebraic multigrid (AMG) preconditioner using hypre BoomerAMG interfaced via PETSc. This is applied as a monolithic solver for the coupled equations.
To further enhance solver efficiency, flexible AMG cycles are introduced, extending traditional cycle types with level-specific smoothing sequences and non-recursive cycling patterns. These are automatically generated using genetic programming, guided by a context-free grammar containing AMG rules. Numerical experiments demonstrate the potential of these approaches to improve solver performance in large-scale laser beam welding simulations.