A semi-Toeplitz preconditioner for the linearized Navier– Stokes equation for compressible flow is proposed and tested. The preconditioner is applied to the linear system of equations to be solved in each time step of an implicit method. The equations are solved with flat plate boundary conditions and are linearized around the Blasius solution. The grids are stretched in the normal direction to...

2 Hierarchical Preconditioner for Scalar Bases 3 2.1 General Hierarchical Preconditioner Formula . . . . . . . . . . . 3 2.2 Hierarchical Splitting in Case of Nodal Basis Functions . . . . . 4 2.3 Hierarchical Preconditioner Formula for Bases of Nodal Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . ...

In this paper, a relaxed Hermitian and skew-Hermitian splitting (RHSS) preconditioner is proposed for saddle point problems from the element-free Galerkin (EFG) discretization method. The EFG method is one of the most widely used meshfree methods for solving partial differential equations. The RHSS preconditioner is constructed much closer to the coefficient matrix than the well-known HSS preco...

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.