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