A $p$-version of convolution quadrature in wave propagation
<|reference_start|>A $p$-version of convolution quadrature in wave propagation: We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size ($h$-method), we achieve accuracy by increasing the order of the method ($p$-method). We base this method on discontinuous Galerkin timestepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observes(root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the findings.<|reference_end|>
@article{rieder2024a,
    title={A $p$-version of convolution quadrature in wave propagation},
    author={Alexander Rieder},
    journal={arXiv preprint arXiv:2402.17712},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17712},
    primaryClass={math.NA cs.NA}
}