On improving the low-frequency performance of full-wave modeling techniques

The method of moments and the finite element method are very powerful methods for solving electromagnetic problems in the frequency domain. However, the direct application of these techniques at low frequencies results in instability and significant errors. This is due to the divergence operation on the surface current density in the method of moments formulation and the curl operation on the electric field in the finite element formulation. Although this phenomenon has different physical meanings in these two methods, it can be interpreted in the same way in terms of their matrix equations. Both the moment method matrix and the finite element matrix have a singular component that dominates at low frequencies. Thus the problem can be solved in a similar way.; This dissertation addresses the low frequency problems in the method of moments and the finite element method. It discusses the physical explanations for both methods and shows the mathematical source of these problems in the matrix formulations. The relationship between the physical and mathematical explanations is analyzed. Based on this analysis, an LU recombination method is presented to improve the low frequency performance of the two methods. The LU recombination method utilizes linear transformations of the matrices to eliminate numerical errors in the singular components and preserve the information that otherwise would be lost due to these errors. The LU recombination method can be easily incorporated into existing methods. The dissertation also demonstrates that the full-wave moment methods can be used to solve static field problems with the help of LU recombination.