A COMBINED BI-CGSTAB (1) AND WAVELET TRANSFORM METHOD FOR EM PROBLEMS USING METHOD OF MOMENTS

• Published in: Electromagnetic waves (Cambridge, Mass.) Vol. 52; pp. 205 - 224
• Main Authors: Zunoubi, Mohammad R., Kishk, Ahmed A.
• Format: Journal Article
• Language: English
• Published: Cambridge Electromagnetics Academy 2005
• Subjects: Integral equations; Wavelet transforms
• ISSN: 1559-8985; 1070-4698; 1559-8985
• DOI: 10.2528/PIER04080903

An efficient technique for the solution of large-scale electromagnetic radiation and scattering problems arising from the surface integral equations and the method of moments is developed. The conventional MoM basis and testing functions are used to discretize the integral equations resulting in a dense impedance matrix. A block-partitioned wavelet transform is then employed to sparsify the matrix. Full advantage is taken of the sparse nature of the mathematical model to solve the system of equations by means of the recently introduced Stabilized Bi-Conjugate Gradient method (Bi-CGSTAB (l)). Various problems are considered involving perfect electric conductor and dielectric material. Results are compared to the corresponding results obtained via the direct solution, or LU decomposition, of the original MoM dense matrix. Excellent results are obtained in a very efficient manner. By block partitioning the MoM impedance matrix as it is built and performing the wavelet transform on the matrix blocks, analysis of very large electromagnetic problems becomes possible in a very efficient and accurate manner.