Scalable Multigrid Methods for Nonlinear Shell Problems on GPUs: Performance and Locking Mitigation

To improve fuel efficiency, commercial airlines are increasingly using high-aspect ratio and flexible wings, leading to aeroelastic coupling and geometric nonlinearity. Robust and scalable geometric nonlinear structural solvers are needed to enable high-fidelity aeroelastic design optimizations. Thus, GPU-acceleration and multigrid linear solvers are used to speedup the TACS finite element software for nonlinear Reissner-Mindlin shell elements. Performance comparisons are done for several shell problems and multigrid smoothers. Then the multigrid solvers are demonstrated on geometric nonlinear analysis and optimizations of plate, cylinder, and wingbox structures, achieving significant speedups to the baseline CPU code. A key finding in the paper is the impact of various locking mitigation methods on multigrid performance for a linear plate. In particular, selective reduced integrated shells introduce nonphysical low energy modes that degrade the smoother. High order p-refined elements had good mesh convergence per unit time, but their performance degrades significantly for thin shells. Recently developed asymptotic isogeometric elements had the best convergence per unit time, as their weak form is independent of shell thickness. Future work should investigate asymptotic isogeometric shells for curvilinear structures such as flexible wings.