In this note, we introduce a special extension of the
Jacobi-Davidson-Method (JD-Method) which is used to solve generalized
eigenvalue
problems in topology optimization. The not well known idea of residual
minimization in standard eigenvalue problems is modified for use in
the generalized case here. Furthermore, a similar but new concept of
orthogonalization minimization will be explained as well.

The runtime behaviour of the well known Arnoldi-based
eigensolver ARPACK is illustrated and
compared with an implementation of the JD-Method by the
author called JDPack. The efficiency of the performed modifications
is shown by means of a special benchmark example.