Classical BEM with linear complexity

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to choose the order of the numerical approximations much lower than for the classical formulations. Low order discretizations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU-time grow only linearly (without any logarithmic terms) with respect to the number of unknowns. AMS Subject Classifications: 65N38, 65R20, 65Y20