Hyper-reduction methods for accelerating nonlinear finite element simulations: open source implementation and reproducible benchmarks
Explore the source record for details and available documents.
Mathematics and Computing↗
Engineering topics
Kim, Minji
Publications and source records attributed to Kim, Minji.
Preconditioning for Hyper-reduction in Reduced Order Models
Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.
97 MATHEMATICS AND COMPUTING↗