Comparison of Fixed Point Methods and Krylov Subspace Methods Solving Convection-Diffusion Equations

Residual-Minimizing Krylov Subspace Methods for Stabilized Discretizations of Convection-Diffusion Equations

We discuss the behavior of the minimal residual method applied to stabilized discretizations of oneand two-dimensional model problems for the stationary convection-diffusion equation. In the one-dimensional case, it is shown that eigenvalue information for estimating the convergence rate of the minimal residual method is highly misleading due to the strong nonnormality of these operators for la...

Krylov subspace methods for solving linear systems

Krylov subspace methods for projected Lyapunov equations

We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with re...

Preconditioned Krylov Subspace Methods for Transport Equations

Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important p...

Analysis of Coupled Grid Methods for Solving Convection-diffusion Equations

The error behavior of finite difference discretization schemes has been researched. Starting from the onedimensional case, where two particles of a fluidized bed were taken, the diffusion equation was numerically solved on a single grid as reference. Then the diffusion equation, a model equation for the real problem, was solved on a separated grids setup, where the grid spacing of the grid adja...