  Boundary element methods (BEM) reduce a partial differential equation in a
domain to an integral equation on the domain's boundary. They are particularly
attractive for solving problems on unbounded domains, but handling the dense
matrices corresponding to the integral operators requires efficient algorithms.
  This article describes two approaches that allow us to solve boundary element
equations on surface meshes consisting of several millions of triangles while
preserving the optimal convergence rates of the Galerkin discretization.
