| Contents |
| We consider time harmonic wave equations in cylindric waveguides
with physical solutions for which the signs of group and
phase velocities differ. In particular, we will consider a
one-dimenisonal fourth order model problem and
two-dimensional elastic waveguides for which this phenomenon occurs.
Standard transparent boundary
conditions, e.g.\ the Perfectly Matched Layers (PML) method select
modes with positive phase velocity, whereas physical modes are characterized by positive group velocity. Hence these methods yield stable,
but unphysical solutions for such problems.
We derive an infinite element method for a
physically correct discretization of such waveguide problems
which is based on a Laplace transform in propagation direction.
In the Laplace domain the space of transformed solutions can be
separated into a sum of a space of incoming and a space of
outgoing functions where both function spaces are
curved Hardy spaces. The curved Hardy space is constructed such
that it contains a simple and convenient Riesz basis with moderate
condition numbers.
Our method does not use a modal separation and works on
an interval of frequencies. In particular, it is well-adapted
for the computation of resonances.
Numerical experiments exhibit super-algebraic convergence
and moderate condition numbers. |
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