On a Novel Pivoting Strategy for the Nested Cross Approximation

Surface integral equations are a popular choice for solving electromagnetic scattering and radiation problems. Standard discretizations via the boundary element method, however, lead to dense system matrices. Therefore, in practice, so-called fast methods are used to reduce the complexity in terms of CPU time and memory consumption for the construction of the compressed system matrix as well as the cost for a single matrix-vector product. For electrically small problems, the adaptive cross approximation of H-matrices [1] is a popular choice due to its purely algebraic nature, resulting in quasi-linear complexity with respect to the number of unknowns. The complexity can be reduced to linear by introducing a nested dependency of the low-rank blocks between the levels of the tree-structure, resulting in an H<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>-matrix.