Iterative-solver convergence for loop-star and loop-tree decompositions in method-of-moments solutions of the electric-field integral equation

Method-of-moments (MoM) solutions of the electric-field integral equation using Rao-Wilton-Glisson (RWG) basis functions suffer from the so-called low-frequency breakdown. Introduction of loop-tree or loop-star decompositions of the basis functions can effectively solve this problem, and a number of papers have been published discussing various aspects with respect to these techniques. Several papers imply that loop-tree or loop-star decompositions may help to improve iterative-solver convergence for the solution of the resulting linear-equation systems. Since only a few results with respect to this issue are available, a study of the frequency-dependent iterative-solver convergence for RWG, loop-tree, and loop-star basis functions was performed. Two metallic scattering objects, with meshes comprising up to 21060 unknowns, were considered. RWG functions were found to provide the best convergence behavior, as long as the frequency considered was high enough to prevent the low-frequency breakdown. Among the loop-tree and loop-star bases, the loop-tree functions were found to be superior to the loop-star functions. The loop-tree functions resulted in good and stable convergence behavior if the number of subdivisions per wavelength was larger than a few hundred. Moreover, it is shown that the so-called loop-tree decomposition can also be viewed as a loop-cotree decomposition if an alternative tree of edges connecting the free vertices of the mesh is constructed.