## Colloquium-Minghao Wu Rostami (WPI)-Numerical Methods for Linear Stability Analysis

Mathematics - Colloquium

Friday, September 20, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: Linear stability analysis is a standard approach of studying how steady states of a dynamical system respond to small perturbations. I am interested in linear stability analysis for large-scale dynamical systems arising from spacial discretization of systems of PDEs, which entails solving a series of large, sparse and in general, nonsymmetric eigenvalue problems for their rightmost eigenvalues (i.e., eigenvalues with algebraically largest real part). Traditional eigenvalue solvers are not reliable for computing these eigenvalues.

I will show that by reformulating the original eigenvalue problem in a clever way, its rightmost eigenvalues can be found by computing the smallest eigenvalue of a new eigenvalue problem whose structure resembles that of a Lyapunov equation. Such an eigenvalue can be computed in a robust manner by a recently developed eigenvalue solver ''Lyapunov inverse iteration''. This method requires the solution of large-scale Lyapunov equations, which in turn entails solving large, sparse linear systems. Numerical results will be presented for examples from both hydrodynamic and aeroelastic stability analysis.

Suggested Audiences:
Adult, College

E-mail:
ma-chair@wpi.edu

Last Modified: September 19, 2013 at 9:48 AM

## Colloquium-Minghao Wu Rostami (WPI)-Numerical Methods for Linear Stability Analysis

Mathematics - Colloquium

Friday, September 20, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: Linear stability analysis is a standard approach of studying how steady states of a dynamical system respond to small perturbations. I am interested in linear stability analysis for large-scale dynamical systems arising from spacial discretization of systems of PDEs, which entails solving a series of large, sparse and in general, nonsymmetric eigenvalue problems for their rightmost eigenvalues (i.e., eigenvalues with algebraically largest real part). Traditional eigenvalue solvers are not reliable for computing these eigenvalues.

I will show that by reformulating the original eigenvalue problem in a clever way, its rightmost eigenvalues can be found by computing the smallest eigenvalue of a new eigenvalue problem whose structure resembles that of a Lyapunov equation. Such an eigenvalue can be computed in a robust manner by a recently developed eigenvalue solver ''Lyapunov inverse iteration''. This method requires the solution of large-scale Lyapunov equations, which in turn entails solving large, sparse linear systems. Numerical results will be presented for examples from both hydrodynamic and aeroelastic stability analysis.

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: September 19, 2013 at 9:48 AM