Variable order panel clustering. (English) Zbl 0959.65135

Sauter, S. A.

Computing 64, No. 3, 223-261 (2000).

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.

Reviewer: Gunther Schmidt (Berlin)

MSC:

65N38	Boundary element methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65Y20	Complexity and performance of numerical algorithms

Keywords:

panel clustering method; variable order approximation; boundary integral equations; Galerkin discretization; double layer potential