# Computation of Resonances in Open Systems based on the Pole Condition

## Thorsten Hohage

**Oct. 14, 2003, 3:30 p.m. P 215**

Resonances in open systems can be defined as square roots of complex eigenvalues of the negative Laplacian on an unbounded domain with corresponding eigenfunctions which satisfy a radiation condition and typically grow exponentially at infinity. Applications include the modelling of slat noise of air planes. Classical radiation conditions based e.g. on an integral representation of the solution do not lead to feasible algorithms since the unknown eigenvalues $k2$ occur in a complicated way as arguments of a Hankel function. We discuss an alternative radiation condition called pole condition which has been suggested by Frank Schmidt. After discretization it leads to linear generalized eigenvalue problems which can be solved by standard algorithms. The feasibility of this method is illustrated in numerical examples.