Nonlinear parallel-in-time Schur complement solvers for ordinary differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:344

Article; Proceedings Paper

Badia, Santiago¹ 

[1] Ctr Int Metodes Numer Engn, Parc Mediterrani Tecnol,Esteve Terrades 5, E-08860 Castelldefels, Spain

关键词: Time parallelism;    Ordinary differential equations;    Domain decomposition;    Nonlinear solver;    Scalability;   

DOI  :  10.1016/j.cam.2017.09.033

来源: Elsevier

【 摘 要 】

In this work, we propose a parallel-in-time solver for linear and nonlinear ordinary differential equations. The approach is based on an efficient multilevel solver of the Schur complement related to a multilevel time partition. For linear problems, the scheme leads to a fast direct method. Next, two different strategies for solving nonlinear ODEs are proposed. First, we consider a Newton method over the global nonlinear ODE, using the multilevel Schur complement solver at every nonlinear iteration. Second, we state the global nonlinear problem in terms of the nonlinear Schur complement (at an arbitrary level), and perform nonlinear iterations over it. Numerical experiments show that the proposed schemes are weakly scalable, i.e., we can efficiently exploit increasing computational resources to solve for more time steps the same problem. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free