We present a modification of a tangential frequency filtering decomposition (TFFD) preconditioner [1]. The key idea is to add a “lumping term” ch whose influence can be determined by means of Fourier analysis [2, 3]. For the standard five-point stencil, we derive an optimal order q = 4 3 , and constant c = (2π) 4 3 . With the choice of optimal order of modification, the Fourier results show tha...

In this paper we propose a substructuring preconditioner for solving three-dimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner introduced in Bramble, Pasiack and Schatz (1989), with simpler coarse solvers. We will show that, although the preconditioned system may not have a good...

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

In this paper, we analyze the convergence of the preconditioned GMRESmethod for the first order finite element discretizations of the Helmholtz equation in media with losses. We consider a Laplace preconditioner, an inexact Laplace preconditioner and a two-level preconditioner. Our analysis is based on bounding the field of values of the preconditioned system matrix in the complex plane. The an...

We propose a substructuring preconditioner for solving threedimensional elliptic equations with strongly discontinuous coefficients. The new preconditioner can be viewed as a variant of the classical substructuring preconditioner proposed by Bramble, Pasiack and Schatz (1989), but with much simpler coarse solvers. Though the condition number of the preconditioned system may not have a good boun...

In the past two decades, the FETI method introduced in [10] and its variants have become a class of popular methods for the parallel solution of large-scale finite element problems, see e.g. [11], [9], [14], [15], [8]. A key ingredient in this class of methods is a good preconditioner for the dual Schur complement system whose operator is a weighted sum of subdomain Neumann to Dirichlet (NtD) m...

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The n 2 th column of our circulant preconditioner Sn is equal to the n 2 th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be deened as (S n Sn)...

In this paper, we introduce a new Schwarz preconditioner and with a new coarse space. We construct the preconditioner by grouping together, in one preconditioner, features from the additive overlapping Schwarz methods, from iterative substructuring methods and from a class of restricted additive Schwarz methods. The preconditioner is symmetric and considered as a symmetrized version of restrict...

The paper proposes a preconditioner for the conjugate gradient method CG that is designed for solving systems of equations Ax bi with di erent right hand side vec tors or for solving a sequence of slowly varying systems Akx bk The preconditioner has the form of a limited memory quasi Newton matrix and is generated using infor mation from the CG iteration The automatic preconditioner does not re...

We investigate the use of sparse approximate inverse techniques in a multilevel block ILU preconditioner to design a robust and efficient parallelizable preconditioner for solving general sparse matrices. The resulting preconditioner retains robustness of the multilevel block ILU preconditioner (BILUM) and offers a convenient means to control the fill-in elements when large size blocks (subdoma...