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The magnetohydrodynamics (MHD) equations are used to model the flow of electrically conducting fluids in such applications as liquid metals and plasmas. This system of non-self adjoint, nonlinear PDEs couples the Navier-Stokes ...

We describe some new preconditioning strategies for handling the algebraic systems of equations that arise from discretization of the incompressible Navier-Stokes equations. We demonstrate how these methods adapt in ...

Linear stability analysis of a dynamical system entails finding the rightmost eigenvalue for a series of eigenvalue problems. For large-scale systems, it is known that conventional iterative eigenvalue solvers are not ...

We discuss iterative methods for solving the algebraic systems of equations arising from linearization and discretization of primitive variable formulations of the incompressible Navier-Stokes equations. Implicit discretization ...

Boundary conditions are analyzed for a class of preconditioners used for the incompressible Navier-Stokes equations. We consider pressure convection-diffusion preconditioners [8,12] as well as least-square commutator methods ...

We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of Reconditioners ...

We examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional box-shaped domain with Sommerfeld-like boundary conditions. The preconditioners are of two types. The first is derived by ...

In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that ...

In this paper, we study the computational cost of solving the convection-diffusion equation using various discretization strategies and iteration solution algorithms. The choice of discretization influences the properties ...

The sparse grid stochastic collocation method is a new method for solving partial differential equations with random coefficients. However, when the probability space has high dimensionality, the number of points required ...