Effective construction of divergence-free wavelets on the square

• Autores: S. Kadri Harouna, Valérie Perrier
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 240, Nº 1, 2013, págs. 74-86
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.07.029
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• Resumen

  • We present an effective construction of divergence-free wavelets on the square, with suitable boundary conditions. Since 2D divergence-free vector functions are the curl of scalar stream-functions, we simply derive divergence-free multiresolution spaces and wavelets by considering the curl of standard biorthogonal multiresolution analyses (BMRAs) on the square. The key point of the theory is that the derivative of a 1D BMRA is also a BMRA, as established by Jouini and Lemarié-Rieusset (1993) [16]. We propose such construction in the context of generic compactly supported wavelets, which allows fast algorithms. Examples illustrate the practicality of the method.