Approximation of integral operators by Green quadrature and nested cross approximation (Q726716)

The paper presents a fast algorithm for constructing data-sparse approximations of matrices arising in boundary element methods. In particular, the authors describe an efficient algorithm to construct \(\mathcal H^2\)-matrix approximations of Galerkin discretizations of boundary integral operators. First, a quadrature-based approximation of kernel functions using Green's representation formula combined with Gauss quadrature leads to a factorized approximation of certain matrix blocks. Then a cross approximation method is applied to the factors to compress further this approximation. The authors derive an algebraic interpolation operator that can be used to compute the final matrix approximation very rapidly. The performance of the new approximation method is testet by numerical experiments for the harmonic single and double layer integral operators over the unit sphere and over the nonsmooth boundary of a crankshaft.