Compression of boundary integral operators discretized by anisotropic wavelet bases

The present article is devoted to wavelet matrix compression for boundary integral equations when using anisotropic wavelet bases for the discretization. We provide a compression scheme for boundary integral operators of order \(2q\) $2q$ on patchwise smooth and globally Lipschitz continuous mainfolds which amounts to only \(\mathcal {O}(N)\) $\mathcal{O}(N)$ relevant matrix coefficients in the system matrix without deteriorating the accuracy offered by the underlying Galerkin scheme. Here, \(N\) $N$ denotes the degrees of freedom in the related trial spaces. By numerical results we validate our theoretical findings.