  In this paper the author introduces a new domain decomposition method for the
solution of discretised integral equation eigenvalue problems. The new domain
decomposition method is motivated by the so-called automated multi-level
substructuring (short AMLS) method. The AMLS method is a domain decomposition
method for the solution of elliptic PDE eigenvalue problems which has been
shown to be very efficient especially when a large number of eigenpairs is
sought. In general the AMLS method is only applicable to these kind of
continuous eigenvalue problems where the corresponding discretisation leads to
an algebraic eigenvalue problem of the form $Kx=\lambda Mx$ where $K,M \in
\mathbb{R}^{N\times N}$ are symmetric sparse matrices. However, the
discretisation of an integral equation eigenvalue problem leads to a discrete
problem where the matrix $K$ is typically dense, since a non-local integral
operator is involved in the equation. In the new method, which is introduced in
this paper, the domain decomposition technique of classical AMLS is generalised
to eigenvalue problems $Kx=\lambda Mx$ where $K,M$ are symmetric and possibly
dense, and which is therefor applicable for the solution of integral equation
eigenvalue problems. To make out of this an efficient eigensolver, the new
domain decomposition method is combined with a recursive approach and with the
concept of hierarchical matrices.
