Hardy space infinite elements for time-harmonic two-dimensional elastic waveguide problems
For computational mechanics researchers, this provides a method to handle waveguides with backward waves, though it is an adaptation of an existing technique to a new problem class.
The authors tackle time-harmonic elastic waveguide problems in semi-infinite strips where standard methods fail due to modes with opposite group and phase velocities. They apply a Hardy space infinite element method based on a Laplace transform, achieving frequency-independent operators and linear eigenvalue problems for resonances.
We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer (PML) as well as standard Hardy space infinite element methods fail. We apply a recently developed 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 certain Hardy spaces. The Hardy space is chosen such that the construction of a simple infinite element is possible. The method does not use a modal separation and works on intervals of frequencies. On those intervals the involved operators are frequency independent and hence lead to linear eigenvalue problems when computing resonances. Numerical experiments containing convergence tests and resonance problems are included.