Asynchronous optimized Schwarz methods with and without overlap
نویسندگان
چکیده
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 conditions on the size of the subdomains, when approximate (non-optimal) interface conditions are utilized. Numerical results are presented on a large three-dimensional problem on modern parallel clusters and supercomputers illustrating the efficiency of the asynchronous approach.
منابع مشابه
Optimized Schwarz Methods for Maxwell equations
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for ...
متن کاملOptimized Schwarz Methods for Maxwell's Equations
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for ...
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 with nonoverlapping circular domain decomposition
While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interf...
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:
- Numerische Mathematik
دوره 137 شماره
صفحات -
تاریخ انتشار 2017