TY - JOUR

T1 - A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms

AU - Hwang, Feng Nan

AU - Cai, Xiao Chuan

N1 - Funding Information:
The research was supported in part by the Department of Energy, DE-FC02-01ER25479, and in part by the US National Science Foundation, CCR-0219190, ACI-0072089 and ACI-0305666. The first author was also supported in part by the National Science Council in Taiwan, NSC94-2115-M-008-017.

PY - 2007/1/20

Y1 - 2007/1/20

N2 - We propose and test a new class of two-level nonlinear additive Schwarz preconditioned inexact Newton algorithms (ASPIN). The two-level ASPIN combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. This approach is more attractive than the two-level method introduced in [X.-C. Cai, D.E. Keyes, L. Marcinkowski, Nonlinear additive Schwarz preconditioners and applications in computational fluid dynamics, Int. J. Numer. Methods Fluids, 40 (2002), 1463-1470], which is nonlinear on both levels. Since the coarse part of the global function evaluation requires only the solution of a linear coarse system rather than a nonlinear coarse system derived from the discretization of original partial differential equations, the overall computational cost is reduced considerably. Our parallel numerical results based on an incompressible lid-driven flow problem show that the new two-level ASPIN is quite scalable with respect to the number of processors and the fine mesh size when the coarse mesh size is fine enough, and in addition the convergence is not sensitive to the Reynolds numbers.

AB - We propose and test a new class of two-level nonlinear additive Schwarz preconditioned inexact Newton algorithms (ASPIN). The two-level ASPIN combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. This approach is more attractive than the two-level method introduced in [X.-C. Cai, D.E. Keyes, L. Marcinkowski, Nonlinear additive Schwarz preconditioners and applications in computational fluid dynamics, Int. J. Numer. Methods Fluids, 40 (2002), 1463-1470], which is nonlinear on both levels. Since the coarse part of the global function evaluation requires only the solution of a linear coarse system rather than a nonlinear coarse system derived from the discretization of original partial differential equations, the overall computational cost is reduced considerably. Our parallel numerical results based on an incompressible lid-driven flow problem show that the new two-level ASPIN is quite scalable with respect to the number of processors and the fine mesh size when the coarse mesh size is fine enough, and in addition the convergence is not sensitive to the Reynolds numbers.

KW - Domain decomposition

KW - Incompressible Navier-Stokes equations

KW - Inexact Newton

KW - Multilevel nonlinear preconditioning

KW - Nonlinear additive Schwarz

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=33751073924&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2006.03.019

DO - 10.1016/j.cma.2006.03.019

M3 - 期刊論文

AN - SCOPUS:33751073924

SN - 0045-7825

VL - 196

SP - 1603

EP - 1611

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 8

ER -