Benchmark Computations of the Phase Field Crystal and Functionalized Cahn-Hilliard Equations via Fully Implicit,Nesterov Accelerated Schemes

作     者：Jea-Hyun Park Abner J.Salgado Steven M.Wise 

作者机构：Department of MathematicsUniversity of California Santa BarbaraCA 93106USA Department of MathematicsUniversity of Tennessee KnoxvilleTN 37996USA. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2023年第33卷第2期

页      面：367-398页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：NSF grants DMS-1720213,DMS-1719854,and DMS-2012634 NSF grants DMS-1720213 and DMS-2111228.The work of S.M.Wise was partially supported by DMS-1719854 and DMS-2012634 

主　　题：Phase field crystal functionalized Cahn-Hilliard preconditioning Nesterov acceleration nonlinear solver. 

摘      要：We introduce a fast solver for the phase field crystal(PFC)and functionalized Cahn-Hilliard(FCH)equations with periodic boundary conditions on a rectangular domain that features the preconditioned Nesterov’s accelerated gradient descent(PAGD)*** discretize these problems with a Fourier collocation method in space,and employ various second-order schemes in *** observe a significant speedup with this solver when compared to the preconditioned gradient descent(PGD)*** the PAGD solver,fully implicit,second-order-in-time schemes are not only feasible to solve the PFC and FCH equations,but also do so more efficiently than some semi-implicit schemes in some cases where accuracy issues are taken into *** computations of four different schemes for the PFC and FCH equations are conducted and the results indicate that,for the FCH experiments,the fully implicit schemes(midpoint rule and BDF2 equipped with the PAGD as a nonlinear time marching solver)perform better than their IMEX versions in terms of computational cost needed to achieve a certain *** the PFC,the results are not as conclusive as in the FCH experiments,which,we believe,is due to the fact that the nonlinearity in the PFC is milder nature compared to the FCH *** also discuss some practical matters in applying the *** introduce an averaged Newton preconditioner and a sweeping-friction strategy as heuristic ways to choose good preconditioner *** sweeping-friction strategy exhibits almost as good a performance as the case of the best manually tuned parameters.