Eigenvalue
Solve a PDE eigenvalue problem.
Syntax
model.sol(sname).create(fname,"Eigenvalue")
model.sol(sname).feature(fname).set(pname,value)
 
model.sol(sname).feature(fname).create(fname2,LinearType)
 
model.sol(sname).feature(fname).create(fname2,"Advanced")
 
Here LinearType is any of the allowed linear solver feature types.
Description
Operation feature.
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.
The feature eigenvalue accepts the following property/value pairs:
auto | on | off
Rotation angle of the ellipse contour (180 – 180 degrees), when eigsolver is feast and searchcon is wholecon.
Lower bound of search interval, when eigsolver is feast and searchcon is halfcon.
Center of the ellipse contour, when eigsolver is feast and searchcon is wholecon.
Horizontal radius of the ellipse contour, when eigsolver is feast and searchcon is wholecon.
Name of the controlling study step or user if the feature is controlled manually.
Upper bound of search interval, when eigsolver is feast and searchcon is halfcon.
manual | region | all
Eigenvalue search method; the all method finds all eigenvalues for a full matrix and can only be used for small eigenvalue problems when eigsolver is arpack.
arpack | feast
true | false
average | maximum | mass
auto | gaussf | trapez | zolot
Integration type for estimation: automatic, Gauss, or trapezoidal, when eigsolver is feast. Also, you can choose Zolotarev (zolot) when searchcon is halfcon.
on | off
init | solution
zero | solution object
current | solution store
on | off
Approximate number of eigenvalues, when neigsmethodnhm is set to manual.
Size of initial search subspace for estimation, when neigsmethodnhm is stochest or stochestonly.
auto | manual
stochest | manual | stochestonly
auto | manual
Number of integration points, when nintgptsmethodnhm is manual.
halfcon | wholecon
Specify the eigenvalue search contour when eigsolver is feast: a whole contour or a half contour (Hermitian problem).
on | off
Eigenvalue shift (when shiftregselect = manual).
auto | manual
auto | all | positive integer
on | off
true | false
true | false
auto | false
Vertical/horizontal axis ratio of ellipse contour (%), when eigsolver is feast and searchcon is halfcon. The default is 30 for an eigenvalue study and 333 for an eigenfrequency study.
Vertical/horizontal axis ratio of ellipse contour (%), when eigsolver is feast and searchcon is wholecon.
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.