Implicitly Restarted Arnoldi Methods and Eigenvalues of the Discretized Navier Stokes Equations

Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations. Abstract We are concerned with nding a few eigenvalues of the large sparse nonsymmetric generalized eigenvalue problem Ax = Bx that arises in stability studies of incompressible uid ow. The matrices have a block structure that is typical of mixed nite-element discretizations for such problems. We examine the use of shift-invert and Cayley transformations in conjunction with the implicitly restarted Arnoldi method along with using a semi-inner product induced by B and puriication techniques. Numerical results are presented for some model problems arising from the ENTWIFE nite-element package. Our conclusion is that, with careful implementation, implicitly restarted Arnoldi methods are reliable for linear stability analysis.