Investigation of Pivoting Strategies for the Application of the Adaptive Cross Approximation to the Magnetic Field Integral Equation

Integral equations such as the electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE) are a popular choice to solve electromagnetic scattering and radiation problems. Standard discretizations via the boundary element method (BEM) lead, however, to dense matrices. Compressed with techniques such as the multilevel fast multipole algorithm (MLFMA) or the adaptive cross approximation (ACA), the cost of a single matrix-vector product can be reduced to quasi-linear complexity [1]. An advantage of the ACA is that the algorithm is purely algebraic. Therefore, the ACA is applicable in a blackbox-like manner to system matrices arising from integral equations where the integral kernel is asymptotically smooth and when a global pivoting strategy is used [2].