We present an efficient block preconditioner for the two-dimensional biharmonic Dirichlet problem discretized by C1 bicubic Hermite finite elements. In this formulation each node in the mesh has four different degrees of freedom (DOFs). Grouping DOFs of the same type together leads to a natural blocking of the Galerkin coefficient matrix. Based on this block structure, we develop two preconditi...

(ABSTRACT) The primary motivation of this research is to develop and investigate parallel precondi-tioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. ...

Parallel preconditioners are considered for improving the convergence rate of the conjugate gradient method for solving sparse symmetric positive deenite systems generated by nite element models of subsurface ow. The diiculties of adapting eeective sequential preconditioners to the parallel environment are illustrated by our treatment of incomplete Cholesky preconditioning. These diiculties are...

Two Krylov subspace iterative methods, GMRES and QMR, were studied in conjunction with several preconditioning techniques for solving the linear system raised from the finite element discretisation of incompressible Navier-Stokes equations for hydrodynamic problems. The preconditioning methods under investigation were the incomplete factorisation methods such as ILU(0) and MILU, the Stokes prec...

113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant Z-matrices with a preconditioner I + S α is superior to that of the basic iterative method. In this paper, we present a new preconditioner I + K β which is different from the preconditioner given by Kohno et al. and prove the convergence theory about two preconditioned iterati...

In this paper we design and analyze a uniform preconditioner for a class of high–order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high–order conforming subspace and results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the ...

SUMMARY Strang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {e iϕ }-circulant Strang-type preconditioner.

We present a preconditioner for the linearised Navier-Stokes equations which is based on the combination of a fast transform approximation of an advection diiusion problem together with the recently introduced`BF B T ' resulting preconditioner when combined with an appropriate Krylov subspace iteration method yields the solution in a number of iterations which appears to be independent of the R...

Abstract. A preconditioning technique to improve the convergence of the Gauss-Seidel method applied to symmetric linear systems while preserving symmetry is proposed. The preconditioner is of the form I + K and can be applied an arbitrary number of times. It is shown that under certain conditions the application of the preconditioner a finite number of steps reduces the matrix to a diagonal. A ...

We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterative method. For example, the standard GPBi-CG algorithm itself can be used as a preconditioner, as can other Krylov subspace methods or splitting methods. Numerical e...