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Some parallel linear and nonlinear S...

Hwang, Feng-Nan.

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Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics./
Author:	Hwang, Feng-Nan.
Description:	142 p.
Notes:	Director: Xiao-Chuan Cai.
Contained By:	Dissertation Abstracts International65-11B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3153838
ISBN:	9780496143573

Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics.
Hwang, Feng-Nan.

Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics. - 142 p.

Director: Xiao-Chuan Cai.

Thesis (Ph.D.)--University of Colorado at Boulder, 2004.

Domain decomposition methods are widely used and very powerful for solving large sparse linear and nonlinear systems of equations arising from partial differential equations (PDEs). Among different families of domain decomposition methods, we focus primarily on the class of Schwarz type methods. This dissertation proposes and tests some general techniques of linear and nonlinear preconditioning based on a Schwarz framework for two such challenging problems, namely the Stokes problem and incompressible Navier-Stokes equations in computational fluid dynamics. The two-level preconditioners comprise two parts: local additive Schwarz preconditioners, which ate constructed by using the solution of discrete PDEs defined on the overlapping subdomain with some proper boundary conditions, and a global coarse preconditioner, which is defined by the solution on coarse meshes of either original discrete PDEs for the Stokes problem or the linear approximation of PDEs for incompressible Navier-Stokes equations. The two-level preconditioners are applied in conjunction with some linear or nonlinear iterative methods, such as Krylov subspace methods or Newton methods. Numerical results obtained on parallel computers show that (1) for the Stokes problem, the performance of the two-level method with a multiplicative coarse preconditioner is superior to the other two variants of additive Schwarz preconditioners; (2) for incompressible Navier-Stokes equations, the local nonlinear preconditioners make the Newton method more robust in the sense that the method converges within few iterations for a wide range of Reynolds numbers and mesh sizes, and the linear coarse preconditioner makes the method more scalable in the sense that the number of linear iterations depends only slightly on the number of parallel processors.

ISBN: 9780496143573Subjects--Topical Terms:

1018410
Applied Mechanics.

Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics.
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020 $a 9780496143573
035 $a (UMI)AAI3153838
035 $a AAI3153838
040 $a UMI $c UMI
100 1 $a Hwang, Feng-Nan. $3 1264013
245 1 0 $a Some parallel linear and nonlinear Schwarz methods with applications in computational fluid dynamics.
300 $a 142 p.
500 $a Director: Xiao-Chuan Cai.
500 $a Source: Dissertation Abstracts International, Volume: 65-11, Section: B, page: 5765.
502 $a Thesis (Ph.D.)--University of Colorado at Boulder, 2004.
520 $a Domain decomposition methods are widely used and very powerful for solving large sparse linear and nonlinear systems of equations arising from partial differential equations (PDEs). Among different families of domain decomposition methods, we focus primarily on the class of Schwarz type methods. This dissertation proposes and tests some general techniques of linear and nonlinear preconditioning based on a Schwarz framework for two such challenging problems, namely the Stokes problem and incompressible Navier-Stokes equations in computational fluid dynamics. The two-level preconditioners comprise two parts: local additive Schwarz preconditioners, which ate constructed by using the solution of discrete PDEs defined on the overlapping subdomain with some proper boundary conditions, and a global coarse preconditioner, which is defined by the solution on coarse meshes of either original discrete PDEs for the Stokes problem or the linear approximation of PDEs for incompressible Navier-Stokes equations. The two-level preconditioners are applied in conjunction with some linear or nonlinear iterative methods, such as Krylov subspace methods or Newton methods. Numerical results obtained on parallel computers show that (1) for the Stokes problem, the performance of the two-level method with a multiplicative coarse preconditioner is superior to the other two variants of additive Schwarz preconditioners; (2) for incompressible Navier-Stokes equations, the local nonlinear preconditioners make the Newton method more robust in the sense that the method converges within few iterations for a wide range of Reynolds numbers and mesh sizes, and the linear coarse preconditioner makes the method more scalable in the sense that the number of linear iterations depends only slightly on the number of parallel processors.
590 $a School code: 0051.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Computer Science. $3 626642
650 4 $a Mathematics. $3 515831
690 $a 0346
690 $a 0405
690 $a 0984
710 2 $a University of Colorado at Boulder. $3 1019435
773 0 $t Dissertation Abstracts International $g 65-11B.
790 $a 0051
790 1 0 $a Cai, Xiao-Chuan, $e advisor
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3153838