Using an LU recombination method to improve the performance of the boundary element method at very 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 new method for improving the low-frequency performance of boundary element techniques. The proposed method does not require special basis functions and is relatively easy to implement. Numerical errors introduced by the great difference in scale between the vector and scalar electric potential are corrected automatically during the LU decomposition of the impedance matrix.