Here LinearType is any of the allowed linear solver feature types.

For both linear and nonlinear problems, the eigenvalue problem is that of the linearization about a solution U0. If the eigenvalue appears nonlinearly, COMSOL Multiphysics reduces the problem to a quadratic approximation around a value λ0 specified by the property eigref. The discretized form of the problem reads

where K, D, E, N, and NF are evaluated for U = U0 and λ = λ0. Λ is the Lagrange multiplier vector, and λ is the eigenvalue. The eigenvalue name can be given by the property eigname. The linearization point U0 can be given with the property U. The shift, described below, is compensated according to the linearization point for the eigenvalue. Therefore, changing the linearization point has no effect at all for linear or quadratic eigenvalue problems. The eigenvalue search method can be manual or a region in the complex plane (controlled by the property eigmethod) for the ARPACK eigenvalue solver or by stochastic estimation or a manually defined half or full contour in the complex plane for the FEAST eigenvalue solver. There is also a LAPACK eigenvalue for small filled matrices.

The eigenvalue feature accepts the following properties:

Specify where to look for the desired eigenvalues with the property shift. Enter a real or complex scalar; the default value is 0, meaning that the solver tries to find eigenvalues close to 0.

For more information about the eigenvalue solver, see Eigenvalue Solver in the COMSOL Multiphysics Reference Manual.