On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates

The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are asymptotically optimal, meaning that any target accuracy can be achieved at a computational expense that stays proportional to the number of degrees of freedom (within the setting determined by an underlying wavelet basis) that would ideally be necessary for realising that target accuracy if full knowledge about the unknown solution were given. As we consider here anisotropic wavelet coordinates, we can achieve higher convergence rates compared to the standard, isotropic setting. Especially, edge singularities of anisotropic nature can be resolved.