A Modified LU Recombination Technique for Improving the Performance of Boundary Element Methods at Low Frequencies

Many numerical electromagnetic modeling techniques that work very well at high frequencies do not work well at lower frequencies. This is directly or indirectly due to the weak coupling between the electric and magnetic fields at low frequencies. One technique for improving the performance of boundary element techniques at low frequencies is through the use of loop-tree basis functions, which decouple the contributions from the vector and scalar electric potential. However, loop-tree basis functions can be difficult to define for large, complex geometries. This paper describes a method for improving the low-frequency performance of boundary element techniques that does not require the explicit definition of loop-tree basis functions. The method is a modified version of an LU recombination method proposed earlier. It automatically detects the linear space spanned by the scalar electric potential and corrects numerical errors during the LU decomposition of the impedance matrix. This method does not require special basis functions and is relatively easy to implement. Several examples are presented to demonstrate the effectiveness of this method.