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Multiscale Approximation of Vortex Patches

We propose an adaptive scheme, based on multiscale decomposition into interpolatory wavelet bases, to simulate the evolution of vortex patches associated with solutions of the two-dimensional Euler equations. This scheme is based on fast algorithms that relate the numerically significant wavelet coefficients with the irregular sampling of the boundary of the patch on an adaptive grid. This method allows analysis of the evolution of the singularities on this boundary at a low computational cost.