Page 225 - Process Modelling and Simulation With Finite Element Methods

212 Process Modelling and Simulation with Finite Element Methods

modes do not necessarily get excited in systems that have FEM operators that are
non-self-adjoint. I would speculate that this methodology for numerical
computation of stability is far more likely to capture the pseudomodes of [ 101 for
a non-self-adjoint problem than the linear stability theory.
This chapter introduces several new aspects of eigensystem analysis that can
be done by using FEMLAB and MATLAB tools and a little user defined
programming. The ease by which this can be done is a major advantage of the
pde engine and programming language of FEMLAB. It is now common practice
in stability theory, for instance of viscoelastic flows [16], across many
disciplines [ 171, to compute via numerical methods the eigenvalues and
eigenmodes of instabilities in transient conditions. Smith et al. [16] use the
Arnoldi iterative method implemented in ARPACK [ 181 for their computation.
The eigs() sparse eigensolver of MATLABFEMLAB does as well. This
method, based on the Krylov subspace decomposition, becomes computationally
cost effective with larger, sparse systems; the MATLABFEMLAB
implementation of the ARPACK routines is robust and highly accurate.

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