On Hybrid Multigrid-Schwarz Algorithms
نویسندگان
چکیده
J. Lottes and P. Fischer in [J. Sci. Comput., 24:45–78, 2005] studied many smoothers or preconditioners for hybrid Multigrid-Schwarz algorithms for the spectral element method. The behavior of several of these smoothers or preconditioners are analyzed in the present paper. Here it is shown that the Schwarz smoother that best performs in the above reference, is equivalent to a special case of the weighted restricted additive Schwarz, for which convergence analysis is presented. For other preconditioners which do not perform as well, examples and explanations are presented illustrating why this behavior may occur.
منابع مشابه
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method
We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the origin...
متن کاملMultiplicative Schwarz Algorithms for Some Nonsymmetric and Indefinite Problems
Abstract The classical Schwarz alternating method has recently been generalized in several directions This e ort has resulted in a number of new powerful domain decomposition methods for elliptic problems in new insight into multigrid methods and in the development of a very useful framework for the analysis of a variety of iterative methods Most of this work has focused on positive de nite sym...
متن کاملHybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes
The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...
متن کاملNonuniformly weighted Schwarz smoothers for spectral element multigrid
A hybrid Schwarz/multigrid method for spectral element solvers to the Poisson equation in R2 is presented. It extends the additive Schwarz method studied by J. Lottes and P. Fischer (J. Sci. Comput. 24:45–78, 2005) by introducing nonuniform weight distributions based on the smoothed sign function. Using a V-cycle with only one pre-smoothing, the new method attains logarithmic convergence rates ...
متن کاملSchwarz Methods: to Symmetrize or Not to Symmetrize1
SUMMARY A preconditioning theory for Schwarz methods is presented. The theory establishes suucient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive deenite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Sci. Comput.
دوره 36 شماره
صفحات -
تاریخ انتشار 2008