Preconditioning Helmholtz linear systems

Preconditioning Helmholtz linear systems

Linear systems which originate from the simulation of wave propagation phenomena can be very difficult to solve by iterative methods. These systems are typically complex valued and they tend to be highly indefinite, which renders the standard ILU-based preconditioners ineffective. This paper presents a study of ways to enhance standard preconditioners by altering the diagonal by imaginary shift...

Incomplete block factorization preconditioning for linear systems arising in the numerical solution of the Helmholtz equation

The application of the finite difference method to discretize the complex Helmholtz equation on a bounded region in the plane produces a linear system whose coefficient matrix is block tridiagonal and is some (complex) perturbation of an M-matrix. The matrix is also complex symmetric, and its real part is frequently indefinite. Conjugate gradient type methods are available for this kind of line...

Preconditioning the Helmholtz Equation via Row- projections

Approximate Inverse Preconditioning for Shifted Linear Systems

In this paper we consider the problem of preconditioning symmetric positive definite matrices of the form Aα = A+αI where α > 0. We discuss how to cheaply modify an existing sparse approximate inverse preconditioner for A in order to obtain a preconditioner for Aα. Numerical experiments illustrating the performance of the proposed approaches are presented. AMS subject classification (2000): 65F...

Some Preconditioning Techniques for Linear Systems

New convergence intervals of parameters αi are derived and applied for solving the modified linear systems, which enables a better understanding of how parameters should be chosen. The convergence theorem for H-matrix is given. Meanwhile, we discuss the convergence results forM -matrices linear systems and give some new preconditioners. Numerical examples are used to illustrate our results. Key...