Parallel computation of pseudospectra by fast descent

Abstract

The pseudospectrum descent method ( PsDM) is proposed, a new parallel method for the computation of pseudospectra. The idea behind the method is to use points from an already existing pseudospectrum level curve ∂ Λ ϵ to generate in parallel the points of a new level curve ∂ Λ δ such that δ< ϵ. This process can be continued for several steps to approximate several pseudospectrum level curves lying inside the original curve. It is showed via theoretical analysis and experimental evidence that PsDM is embarrassingly parallel, like GRID, and that it adjusts to the geometric characteristics of the pseudospectrum; in particular it captures disconnected components. Results obtained on a parallel system using MPI validate the theoretical analysis and demonstrate interesting load-balancing issues.