  We present a fast algorithm that constructs a data-sparse approximation of
matrices arising in the context of integral equation methods for elliptic
partial differential equations.
  The new algorithm uses Green's representation formula in combination with
quadrature to obtain a first approximation of the kernel function and then
applies nested cross approximation to obtain a more efficient representation.
  The resulting $\mathcal{H}^2$-matrix representation requires $\mathcal{O}(n
k)$ units of storage for an $n\times n$ matrix, where $k$ depends on the
prescribed accuracy.
