Adaptive Nonlinear Preconditioning for PDEs

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:2022-09-28 10:00


时  间:928日上午10:00

地  点:腾讯会议ID784158870(无密码)


Nonlinear preconditioning is a globalization technique for Newton's method applied to systems of equations with unbalanced nonlinearities, in which nonlinear residual norm reduction stagnates due to slowly evolving subsets of the degrees of freedom. Even though the Newton corrections may effectively be sparse, a standard Newton method still requires large ill-conditioned linear systems resulting from global linearizations of the nonlinear residual to be solved at each step. Nonlinear preconditioners may enable faster global convergence by shifting work to where it is most strategic, on subsets of the original system. They require additional computation per outer iteration while aiming for many fewer outer iterations and correspondingly fewer global synchronizations. In this work, we improve upon previous nonlinear preconditioning implementations by introducing parameters that allow turning off nonlinear preconditioning during outer Newton iterations where it is not needed. Numerical experiments show that the adaptive nonlinear preconditioning algorithm has performance similar to monolithically applied nonlinear preconditioning, preserving robustness for some challenging problems representative of several PDE-based applications while saving work on nonlinear subproblems.


刘璐璐,南京理工大学数学与统计学院副教授,分别于2007年、2010年、2015年在大连理工大学、复旦大学,沙特阿卜杜拉国王科技大学获得数学学士、硕士、博士学位。主要从事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 ComputingJournal of Computational Physics,  Journal of the American Chemical Society等具有国际影响力的权威期刊上。主持国家和江苏省自然科学基金青年项目各一项。