Lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions
نویسندگان
چکیده
Lower bounds for the condition numbers of the preconditioned systems are obtained for the Bramble-Pasciak-Schatz substructuring preconditioner and the Neumann-Neumann preconditioner in two dimensions. They show that the known upper bounds are sharp.
منابع مشابه
A NOTE ON OPTIMAL SPECTRAL BOUNDS FOR NONOVERLAPPING DOMAIN DECOMPOSITION PRECONDITIONERS FOR hp–VERSION DISCONTINUOUS GALERKIN METHODS
In this article, we consider the derivation of hp–optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second–order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):12...
متن کاملBlock Diagonal Preconditioners for the Schur Complement Method Block Diagonal Preconditioners for the Schur Complement Method
We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial diierential equations. We are interested in diierential equations that describe heterogeneous and anisotropic phenomena. We use a nonoverlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interf...
متن کاملDomain Decomposition Preconditioners for Spectral Nédélec Elements in Two and Three Dimensions
In this paper, we present several domain decomposition preconditioners for high-order Spectral Nédélec element discretizations for a Maxwell model problem in H(curl), in particular overlapping Schwarz preconditioners and Balancing Neumann-Neumann preconditioners. For an efficient and fast implementation of these preconditioners, fast matrix-vector products and direct solvers for problems posed ...
متن کاملShifted Laplacian RAS Solvers for the Helmholtz Equation
where Ω is a bounded polygonal region in <, and the ∂ΩD, ∂ΩN and ∂ΩS correspond to subsets of ∂Ω where the Dirichlet, Neumann and Sommerfeld boundary conditions are imposed. The main purpose of this paper is to introduce novel two-level overlapping Schwarz methods for solving the Helmholtz equation. Among the most effective parallel two-level domain decomposition solvers for the Helmholtz equat...
متن کاملConvergence of some two-level overlapping domain decomposition preconditioners with smoothed aggregation coarse space
We study two-level overlapping preconditioners with smoothed aggregation coarse spaces for the solution of sparse linear systems arising from finite element discretizations of second order elliptic problems. Smoothed aggregation coarse spaces do not require a coarse triangulation. After aggregation of the fine mesh nodes, a suitable smoothing operator is applied to obtain a family of overlappin...
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:
- Math. Comput.
دوره 69 شماره
صفحات -
تاریخ انتشار 2000