COMSOL Multiphysics™

femeig
where Ω is the L-shaped membrane. Start by setting up the problem:
clear fem
fem.geom = poly2([-1 0 0 1 1 -1],[0 0 1 1 -1 -1]);
fem.mesh = meshinit(fem,'hmax',0.1);
fem.shape = 2;
fem.equ.c = 1; fem.equ.da = 1;
fem.bnd.h = 1;
fem.xmesh = meshextend(fem);
fem.sol = femeig(fem,'neigs',16);
Display the first and sixteenth eigenmodes. The membrane function is available in
MATLAB and not in COMSOL Script.
postsurf(fem,'u')
% first eigenmode
membrane(1,20,9,9)
% the MATLAB function
postsurf(fem,'u','solnum',16) % sixteenth eigenmode
Cautionary
Consider the case of a linear eigenvalue problem, E=0.Write the generalized
eigenvalue problem as (A-λB)u=0. In the standard case the coefficients c and d a are
positive in the entire region. All eigenvalues are positive, and 0 is a good choice for
the shift (eigenvalue search location). The cases where either c or d a is zero are
discussed below.
• If d a = 0 in a subregion, the mass matrix B becomes singular. This does not cause
any trouble, provided that c > 0 everywhere. The pencil (A,B) has a set of infinite
eigenvalues.
• If c = 0 in a subregion, the stiffness matrix A becomes singular, and the pencil
(A,B) has many zero eigenvalues. Choose a positive shift below the smallest
nonzero eigenvalue.
• If there is a region where both c = 0 and d a = 0, we get a singular pencil. The
whole eigenvalue problem is undetermined, and any value is equally plausible as
an eigenvalue.
Compatibility The property Variables has been renamed to Const in FEMLAB 2.3.
The properties Epoint and Tpoint are obsolete from FEMLAB 2.2. Use
fem.***.gporder to specify integration order.
See Also
femsolver, assemble, femlin
123