Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes
نویسندگان
چکیده
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 that spectral element based smoothers are superior to those based upon finite element discretizations. Results for several large 3D Navier-Stokes applications are presented.
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 کاملEfficient Algorithms for High-Order Discretizations of the Euler and Navier-Stokes Equations
Higher order discretizations have not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to highly tuned lower order methods, such as finite-volume schemes. In this paper we investigate efficient Spectral Difference discretization...
متن کاملOn Hybrid Multigrid-Schwarz Algorithms
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 th...
متن کاملAMGe - Coarsening Strategies and Application to the Oseen Equations
We provide some extensions to the AMGe method (algebraic multigrid method based on element interpolation), concerning the agglomeration process, the application to non-conforming elements, and the application to the mixed finite element discretization of the Oseen-linearized Navier-Stokes equations. This last point, using AMGe for mixed finite elements, gets straight-forward because of the avai...
متن کاملParallel Multilevel Restricted Schwarz Preconditioners with Pollution Removing for PDE-Constrained Optimization
We develop a class of V-cycle type multilevel restricted additive Schwarz (RAS) methods and study the numerical and parallel performance of the new fully coupled methods for solving large sparse Jacobian systems arising from the discretization of some optimization problems constrained by nonlinear partial differential equations. Straightforward extensions of the one-level RAS to multilevel do n...
متن کامل