Synchronous and asynchronous optimized Schwarz methods for Poisson's equation in rectangular domains
نویسندگان
چکیده
Convergence results for optimized Schwarz methods (OSM) applied as solvers Poisson's equation in a bounded rectangular domain with Dirichlet (physical) boundary conditions and zeroth-order (Robin) artificial transmission between subdomains are presented. The analysis presented applies to continuous formulation on an arbitrary number of cross points. Both synchronous asynchronous versions OSM discussed. theorems presented, it is shown numerically that the hypotheses these satisfied certain configurations subdomains. Additional numerical experiments illustrate practical behavior
منابع مشابه
Asynchronous optimized Schwarz methods with and without overlap
An asynchronous version of the optimized Schwarz method for the solution of differential equations on a parallel computational environment is studied. In a one-way subdivision of the computational domain, with and without overlap, the method is shown to converge when the optimal artificial interface conditions are used. Convergence is also proved for the Laplacian operator under very mild condi...
متن کاملOptimized Schwarz Methods for Domains with an Arbitrary Interface
Optimized Schwarz methods form a class of domain decomposition methods for the solution of partial differential equations. Optimized Schwarz methods employ a first or higher order boundary condition along the artificial interface to accelerate its convergence. In the literature, analysis of optimized Schwarz methods rely on Fourier analysis and so the domains are restricted to be regular (recta...
متن کاملOptimized Schwarz Methods without Overlap for the Helmholtz Equation
The classical Schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel. Convergence is achieved through overlap of the subdomains. We study in this paper a variant of the Schwarz method which converges without overlap for the Helmholtz equation. We show that the key ingredients for such an algorithm are the transmission conditions. We derive o...
متن کاملOptimized Schwarz Methods with Overlap for the Helmholtz Equation
For the Helmholtz equation, simple absorbing conditions of the form ∂n − iω were proposed as transmission condition (TC) in Schwarz methods first without overlap in [4], and later also with overlap, see [3, 12]. More advanced TCs can also be used, see e.g. [11, 14, 2]. Furthermore, parameters can be introduced into TCs and then optimized for rapid convergence, which led to the so called optimiz...
متن کاملOptimized Schwarz Methods
Optimized Schwarz methods are a new class of Schwarz methods with greatly enhanced convergence properties. They converge uniformly faster than classical Schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical Schwarz methods if the overlap is of the order of the mesh parameter, which is often the case in practical applications. They ac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Transactions on Numerical Analysis
سال: 2022
ISSN: ['1068-9613', '1097-4067']
DOI: https://doi.org/10.1553/etna_vol55s744