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Now showing items 1-9 of 9

#### A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD

(2014-02-04)

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 ...

#### Efficient Iterative Algorithms for Linear Stability Analysis of Incompressible Flows

(2013-11-07)

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 ...

#### Reduced Basis Collocation Methods for Partial Differential Equations with Random Coefficients

(2012-06-18)

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 ...

#### Preconditioning Techniques for Reduced Basis Methods for Parameterized Partial Differential Equations

(2014-05-27)

The reduced basis methodology is an efficient approach to solve
parameterized discrete partial differential equations when the solution
is needed at many parameter values. An offline step approximates the
solution space ...

#### A Stochastic Approach to Uncertainty in the Equations of MHD Kinematics

(2014-07-10)

The magnetohydodynamic (MHD) kinematics model describes the
electromagnetic behavior of an electrically conducting fluid when its
hydrodynamic properties are assumed to be known. In particular, the MHD
kinematics equations ...

#### Stochastic Collocation With Kernel Density Estimation

(2011-09-06)

The stochastic collocation method has recently received much attention for solving partial differential equations posed with uncertainty, i.e., where coefficients in the differential operator, boundary terms or right-hand ...

#### Lyapunov Inverse Iteration for Identifying Hopf Bifurcations in Models of Incompressible Flow

(2011-03-07)

The identification of instability in large-scale dynamical systems
caused by Hopf bifurcation is difficult because of the problem of
identifying the rightmost pair of complex eigenvalues of large sparse
generalized ...

#### Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems

(2011-06-22)

We consider the numerical solution of a steady-state diffusion problem
where the diffusion coefficient is the exponent of a random field. The
standard stochastic Galerkin formulation of this problem is
computationally ...

#### Lyapunov Inverse Iteration for Computing a few Rightmost Eigenvalues of Large Generalized Eigenvalue Problems

(2012-04-20)

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust ...