COMSOL Multiphysics™

femeig
Purpose
femeig
Solve eigenvalue PDE problem.
Syntax
Description
fem.sol = femeig(fem,...)
[u,lambda] = femeig(fem,...)
fem = femeig(fem,'Out',{'fem'},...)
fem.sol = femeig('In',{'D' D 'K' K 'N' N},...)
fem.sol = femeig(fem,...) assembles and solves the eigenvalue PDE problem
described by the (possibly extended) FEM structure fem.
fem.sol = femeig('In',{'D' D 'K' K 'N' N},...) solves the eigenvalue
problem given by the matrices D, K, and N.
For both linear and nonlinear PDE problems, the eigenvalue problem is that of the
linearization about a solution U 0 . If the eigenvalue appears nonlinearly, COMSOL
Multiphysics reduces the problem to a quadratic approximation around a value λ 0
specified by the property eigref. The discretized form of the problem reads
where K, D, E, and N are evaluated for U = U 0 and λ = λ 0 . Λ is the Lagrange
multiplier vector, λ is the eigenvalue. The eigenvalue name can be given by the
property eigname. The linearization point U 0 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 function femeig accepts the following property/value pairs:
TABLE 1-24: VALID PROPERTY/VALUE PAIRS
KU – ( λ – λ 0
)DU + ( λ–
λ 0
) 2 EU = – N T
NU = M
PROPERTY VALUES DEFAULT DESCRIPTION
Eigname string lambda Name of eigenvalue
variable
Eigref string 0 Linearization point for
the eigenvalue
Etol positive scalar 0 Eigenvalue tolerance
In
cell array of names and N is empty Input matrices
matrices K | N | D | E E=0, D=0
Itol positive real 1e-10 Relative tolerance for
linear iterative solver
121