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Scalable nonlinear iterative methods for partial differential equations [electronic resource].

Published:
Washington, D.C. : United States. Dept. of Energy, 2000.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description:
4 pages 135 Kbytes : digital, PDF file
Additional Creators:
Lawrence Berkeley National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary:
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of ∥F∥, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
Report Numbers:
E 1.99:ucrl-cr-141368
ucrl-cr-141368
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Other Subject(s):
Note:
Published through SciTech Connect.
10/29/2000.
"ucrl-cr-141368"
Cai, X-C.
Funding Information:
W-7405-ENG-48
View MARC record | catkey: 14350153