# 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…

## One Citation

### Decay of coefficients and approximation rates in Gabor Gaussian frames

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This work analyzes decay properties of the coeﬃcients of functions in these frames in terms of the regularity of the functions and their decay at inﬁnity, and permits to show that a good approximation to any smooth rapidly decaying function is provided.

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