Dr. Li LUO
King Abdullah University of Science and Technology
Parallel linear and nonlinear preconditioning techniques are critical to the numerical solution of large algebraic systems arising from the discretization of partial differential equations. We present some scalable and robust linear and nonlinear preconditioners for the application of computational fluid dynamics. For the linear preconditioners, we focus on a class of overlapping domain decomposition methods that is naturally suitable for parallel processing. The popular one-level and two-level additive Schwarz preconditioners are presented with scalable performance for the application of microfluidics and geophysical flows in 3D. For the nonlinear preconditioners, we introduce some new nonlinear elimination algorithms based on single-layer or multilayer subspace correction to improve the convergence of the global nonlinear solver. For nonlinearly difficult problems such as blood flows in human artery or steady-state cavity flows at large Reynolds numbers, the Newton-type methods often suffer from slow convergence or not converge at all. We show that using the proposed nonlinear preconditioners with a highly parallel domain decomposition framework can significantly improve the robustness and efficiency of the Newton-type methods.
Dr. Li LUO is currently a Postdoc Fellow at the King Abdullah University of Science and Technology. He received his Ph.D. in Applied Mathematics in 2017 from the Hong Kong University of Science and Technology.
His research interests are parallel solution algorithms for linear and nonlinear partial differential equations, computational fluid dynamics, and heterogeneous computing. He received the 1st Prize of the 2017 East Asia SIAM Student Paper Competition and the Best Paper Award of HPC China 2017.