We present a new version of the panel clustering method for a sparse representation of boundary integral equations. Instead of applying the algorithm separately for each matrix row (as in the classical version of the algorithm) we employ more general block partitionings. Furthermore, a variable order of approximation is used depending on the size of blocks.
We apply this algorithm to a second kind Fredholm integral equation and show that the complexity of the method only depends linearly on the number, say n, of unknowns. The complexity of the classical matrix oriented approach is O(n 2) while, for the classical panel clustering algorithm, it is O(nlog7 n).