On monotone iteration and Schwarz methods for nonlinear parabolic PDEs
نویسندگان
چکیده
منابع مشابه
On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
The Schwarz Alternating Method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz Alternating Methods for nonli...
متن کاملOn Schwarz Methods for Monotone Elliptic PDEs
The Schwarz Alternating Method was devised by H. A. Schwarz more than one hundred years ago to solve linear boundary value problems. It has garnered interest recently because of its potential as an efficient algorithm for parallel computers. See [Lio88], and [Lio89], the recent reviews [CM94], [LT94], and [XZ98], and the books [SBG96] and [QV99]. The literature for nonlinear problems is rather ...
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We present overlapping Schwarz methods for the numerical solution of two model problems of delay PDEs: the heat equation with a fixed delay term, and the heat equation with a distributed delay in the form of an integral over the past. We first analyze properties of the solutions of these PDEs and find that their dynamics is fundamentally different from that of regular time-dependent PDEs withou...
متن کاملOn Schwarz Alternating Methods for Nonlinear Elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers several Schwarz alternating methods for nonlinear elliptic p...
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We construct and study a scalable overlapping Additive Schwarz-Richardson (ASR) algorithm for monotone nonlinear parabolic problems discretized implicitly in time. At each time step, the Additive Schwarz preconditioner is built using the linear part of the nonlinear operator, partitioning the domain of the problem into overlapping subdomains, solving local problems on these subdomains and solvi...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/j.cam.2003.06.001