SOLBOX-22: Solution to problems involving a wide range of scales using the combined potential-field formulation

Abstract

In the area of computational electromagnetics, there is an extensive literature on broadband solvers that were developed to analyze multiscale objects [1-11]. Some of these structures involved small details, the numerical solutions to which with conventional elements - such as triangles - required dense discretizations with respect to wavelength. Some other objects may have needed dense discretizations to accurately model equivalent currents at critical locations, even if their geometric features allowed larger elements. In any case, development and implementation of a broadband solver to handle such relatively large objects with dense discretizations are often associated with maintaining "low-frequency" stability [12-30], since the conventional methods tend to break down when discretization elements become small in comparison to the operating wavelength. Accuracy and efficiency are sought in terms of two components: formulation/ discretization and solution algorithms. In the context of formulation/discretization, alternative formulations have been developed, e.g., the augmented electric-field integral equation [14, 19], potential integral equations (PIEs) [23-26], and other formulations incorporating electric charges, to name a few for perfect electric conductors (PECs). In terms of solution algorithms, low-frequency-stable methods havebeencontinuouslyproposedand implemented. Diverse implementations of the low-frequency Multilevel Fast Multipole Algorithm (MLFMA) using multipoles [1,4], inhomogeneous plane waves [3, 12], or other expansion techniques [9, 11, 28-30] merely form one track on the development ofbroadband solution algorithms.