Fast direct solution of standard moment-method matrices

All of the matrices which arise in the Method-of-Moments solution of scattering and antenna problems have a hidden structure. This structure is due to the physics of electromagnetic interactions. Matrix-algebra routines are used to uncover this structure in Moment-Method matrices, after they have been calculated. This structure is used to create a sparse representation of the matrix. Although this step involves an approximation, the error involved can be nearly as small as the precision of the calculation. Then, without further approximation, a sparse representation of the LU factorization of this matrix is computed. A significant speed improvement is realized over that of the standard LU factorization of this matrix. The resulting method can be added to any of a variety of Moment-Method programs to solve the matrix problem more quickly, and with less computer memory. For large problems this is the time-critical operation, so this allows larger problems to be solved. The computer program we have written can be used immediately with most Moment-Method programs, since it amounts to simply a better matrix-inversion package. The method presented here will be referred to as the LU Sparse Integral FactorEd Representation (LUSIFER).