Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a wavelet-Fourier technique for the numerical treatment of multi-dimensional advection-diffusion-reaction equations with periodic boundary conditions. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques. The proposed theoretical analysis is based on the local a-coherence and provides effective recipes for a practical implementation. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case.

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IMA Journal of Numerical Analysis
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 Record created 2019-01-07, last modified 2020-05-11

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