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

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
63/2018
Title:
Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations
Date:
Monday 24th December 2018
Author(s):
Brugiapaglia, S.; Micheletti, S.; Nobile, F.; Perotto, S.
Download link:
Abstract:
We present and analyze a wavelet-Fourier technique for the numerical treatment of multi-dimensional advection-diffusion-reaction equations with periodic boundary condi- tions. 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 tech- niques. 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 pro- posed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case.