Multigrid Computation of Maxwell Eigenvalues
- Ralf Hiptmair (Universität Tübingen)
Abstract
We consider the problem of solving the discrete Maxwell eigenvalue
problem
,
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in a closed simply connected cavity . For
related
eigenvalue problems for symmetric second order elliptic operators,
efficient
iterative schemes for the computation of a couple of the smallest
eigenvalues/eigenvectors have been proposed [1]. They are based on a
preconditioned inverse iteration and a comprehensive analysis has been
presented in
[3].
In the case of the Maxwell eigenvalue problem the large kernel of the
-operator thwarts the straightforward appli
cation of
these algorithms.
However, when the discretization is based on edge elements, we have an
explicit
representation of through gradients of
linear finite
element functions. This paves the way for a fast approximate projection
onto
, which can be coupled with the
edge element
multigrid scheme developed by the author [2]. Numerical experiments
confirm the
good performance of this approach for large scale problems.