Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states

@article{ChaumontFrelet2022EfficientAO,
  title={Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states},
  author={Th{\'e}ophile Chaumont-Frelet and Victorita Dolean and Maxime Ingremeau},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.04851}
}
. We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension d . These discretization spaces are spanned by Gaussian coherent states, that have the key property to be localised in phase space. We carefully select the Gaussian coherent states spanning the approximation space by exploiting the (known) micro-localisation properties of the solution. For a large class of source terms… 
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