On the compressibility of integral operators in anisotropic wavelet coordinates

Abstract The present article is concerned with the $s^\star$-compressibility of classical boundary integral operators, which are discretized by using anisotropic tensor-product wavelets as trial functions. Having the $s^\star$-compressibility at hand one can design adaptive wavelet algorithms that 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 realizing that target accuracy if full knowledge about the unknown solution were given. As we consider anisotropic wavelet bases we can achieve higher convergence rates compared with the standard, isotropic setting. Especially, edge singularities of anisotropic nature can be resolved.