Lulu Liu, Associate Professor, Nanjing University of Science and Technology

Chensong Zhang, Professor

Nonlinear Preconditioning for Implicit Solution of Discretized PDEs

14:00-15:00 September 30(Monday), Tencent Meeting: 376-112-885

Nonlinear preconditioning refers to transforming a nonlinear algebraic system to a form for which Newton-type algorithms have improved success through quicker advance to the domain of quadratic convergence. We place these methods, which go back at least as far as the Additive Schwarz Preconditioned Inexact Newton (ASPIN, 2002), in the context of a proliferation distinguished by being left- or right-sided, multiplicative or additive, and partitioned by field, subdomain, or other criteria. We present the Nonlinear Elimination Preconditioned Inexact Newton (NEPIN, 2022), which is based on a heuristic “bad/good” heuristic splitting of equations and corresponding degrees of freedom. NEPIN is shown to be fairly insensitive to mesh resolution and ``bad'' subproblem identification based on the local Mach number or the local nonlinear residual for transonic flow over a wing.

个人简介：刘璐璐，南京理工大学数学与统计学院副教授，主要从事大规模科学计算，尤其是非线性预条件并行算法的设计及其在油藏模拟、流体力学、燃烧等领域的应用研究，成果发表在SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing，Journal of Computational Physics,  Journal of the American Chemical Society，IEEE Transactions on Geoscience and Remote Sensing等具有国际影响力的权威期刊上。主持国家自然科学基金面上项目1项，以及国家自然科学基金青年项目和江苏省自然科学基金青年项目等。 2022年获得第五届江苏省工业与应用数学学会科学技术奖青年奖。