Projected Krylov Methods for Solving Non-Symmetric Two-by-Two Block Linear Systems Arising from Fictitious Domain Formulations

On Solving Non-symmetric Saddle-point Systems Arising from Fictitious Domain Approaches∗

where the diagonal block A is an (n × n) matrix, the off-diagonal blocks B1 and B2 are (m× n) matrices with full row-rank and vectors f , g are of order n, m, respectively. Our contribution is inspired by a class of saddle-point systems arising from fictitious domain formulations of PDEs [3, 4]. Therefore we will be interested especially in systems (1) with n large, A singular and B1, B2 sparse...

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

Krylov subspace methods for solving linear systems

Comparison of some Preconditioned Krylov Methods for Solving Sparse Non-symmetric Linear Systems of Equations

Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical exa...

Numerical Investigation of Krylov Subspace Methods for Solving Non-symmetric Systems of Linear Equations with Dominant Skew-symmetric Part

Numerical investigation of BiCG and GMRES methods for solving non-symmetric linear equation systems with dominant skew-symmetric part has been presented. Numerical experiments were carried out for the linear system arising from a 5-point central difference approximation of the two dimensional convection-diffusion problem with different velocity coefficients and small parameter at the higher der...