Variable order panel clustering (Q1577400)

The author describes a new version of the panel clustering method for sparse representations of boundary integral operators. Instead of applying the clustering separately for each matrix row as in the classical panel clustering method it is applied to more general block partitionings. The variable order panel clustering is studied for the Galerkin discretization of the double layer potential over a sufficiently smooth manifold in \(\mathbb R^3\). By using variable approximation orders of the kernel function depending on the size of blocks it is shown that the complexity of the method depends only linearly on the number of unknowns.