The adaptive cross-approximation technique for the 3D boundary-element method

It is well known that the classical boundary-element method (BEM) yields fully populated matrices. Their manipulation is cumbersome with respect to memory consumption and computational costs. This paper describes a novel approach where the matrices are split into collections of blocks of various sizes. Those blocks which describe remote interactions are adaptively approximated by low rank submatrices. This procedure reduces the algorithmic complexity for matrix setup and matrix-by-vector products to approximately O(N). The proposed method has been examined in a testing environment and implemented into an existing BEM-finite-element method (FEM) code for electromagnetic and electromechanical problems. The advantages of the new method are demonstrated by means of several examples.