Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations
Parthasarathy D, Bevilacqua T, Lanser M, Klawonn A, Köstler H (2025)
Publication Type: Conference contribution
Publication year: 2025
Publisher: Association for Computing Machinery, Inc
Conference Proceedings Title: PASC 2025 - Platform for Advanced Scientific Computing Conference, Proceedings
Event location: Brugg-Windisch
ISBN: 9798400718861
Abstract
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.
Authors with CRIS profile
Dinesh Parthasarathy
Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)
Harald Köstler
Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)
Involved external institutions
Germany (DE)How to cite
APA:
Parthasarathy, D., Bevilacqua, T., Lanser, M., Klawonn, A., & Köstler, H. (2025). Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations. In PASC 2025 - Platform for Advanced Scientific Computing Conference, Proceedings. Brugg-Windisch, CH: Association for Computing Machinery, Inc.
MLA:
Parthasarathy, Dinesh, et al. "Towards Automated Algebraic Multigrid Preconditioner Design Using Genetic Programming for Large-Scale Laser Beam Welding Simulations." Proceedings of the 2025 Platform for Advanced Scientific Computing Conference, PASC 2025, Brugg-Windisch Association for Computing Machinery, Inc, 2025.
BibTeX: Download