\documentclass[a4paper,11pt]{article}

\title{Eigenvalue solvers for electromagnetic fields in cavities}

\author{\underline{Peter Arbenz} and Roman Geus \\
  Swiss Federal Institute of Technology (ETH) \\
  Institute of Scientific Computing \\
  CH-8092 Zurich, Switzerland \\[.5cm]
  Email: \texttt{[arbenz,geus]@inf.ethz.ch} \\
  WWW: \texttt{http://www.inf.ethz.ch/personal/arbenz/}
}
\date{}

\begin{document}

\maketitle
\thispagestyle{empty}

\begin{abstract}
  We investigate algorithms for computing steady state electromagnetic waves
  in cavities.  The Maxwell equations for the strength of the electric field
  are solved by (1) a penalty method using common linear and quadratic
  Lagrange (node-based) tetrahedral finite elements, and (2) a mixed method
  with linear and quadratic finite edge elements for the field values and
  corresponding node-based finite elements for the Lagrange multiplier.

  These are two approaches that avoid so-called spurious modes which are
  introduced if the di\-ver\-gence-free condition for the electric field is
  not treated properly.  The resulting large sparse matrix eigenvalue
  problems have been solved (1) implicitly restarted Lanczos algorithm and
  (2) Jacobi-Davidson algorithm.  For all finite element approximations we
  compare the amount of work it takes each solver to compute a few of the
  smallest positive eigenvalues and corresponding eigenmodes to a given
  accuracy.  Numerical results obtained on an HP Exemplar X-Class System are
  presented.
\end{abstract}

\end{document}