Schwarz Methods for Convection-Diffusion Problems
نویسندگان
چکیده
Various variants of Schwarz methods for a singularly perturbed two dimensional stationary convection-diffusion problem are constructed and analysed. The iteration counts, the errors in the discrete solutions and the convergence behaviour of the numerical solutions are analysed in terms of their dependence on the singular perturbation parameter of the Schwarz methods. Conditions for the methods to converge parameter uniformly and for the number of iterations to be independent of the perturbation parameter are discussed.
منابع مشابه
MPI implementation of parallel subdomain methods for linear and nonlinear convection-diffusion problems
The solution of linear and nonlinear convection–diffusion problems via parallel subdomain methods is considered. MPI implementation of parallel Schwarz alternating methods on distributed memory multiprocessors is discussed. Parallel synchronous and asynchronous iterative schemes of computation are studied. Experimental results obtained from IBM-SP series machines are displayed and analyzed. The...
متن کاملOptimized Sponge Layers, Optimized Schwarz Waveform Relaxation Algorithms for Convection-diffusion Problems and Best Approximation
When solving an evolution equation in an unbounded domain, various strategy have to be applied, aiming to reduce the number of unknowns and of computation, from infinite to a finite but not too large number. Among them truncation of domains with a sponge boundary and Schwarz Waveform Relaxation with overlap. These problems are closely related, as they both use the Dirichlet-to-Neumann map as a ...
متن کاملAdditive Schwarz Algorithms for Parabolic Convection-Diffusion Equations
In this paper, we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems. We introduce three additive Schwarz type domain decomposition methods for general, not necessarily selfadjoint, linear, second order, parabolic partial differential equations and also study the convergence rates of these algorithms. The resulting preconditioned lin...
متن کاملTimely Communication a Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems∗
We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods are superior to AS in terms of both iteration counts and CPU time, as well as the communication cost when implemented on distributed memory computers. This is especially true for harder problems such as indefi...
متن کاملA Characteristic Nonoverlapping Domain Decomposition Method for Multidimensional Convection-Diffusion Equations
We develop a quasi-two-level, coarse-mesh-free characteristic nonoverlapping domain decomposition method for unsteady-state convection-diffusion partial differential equations in multidimensional spaces. The development of the domain decomposition method is carried out by utilizing an additive Schwarz domain decomposition preconditioner, by using an Eulerian-Lagrangian method for convection-dif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000