{'fraction_non_alphanumeric': 0.01860920666013712, 'fraction_numerical': 0.0, 'mean_word_length': 5.768211920529802, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Effective Preconditioners for the Solution of Hybrid FEM/MoM Matrix Equations using Combined Formulations

Hybrid FEM/MoM modeling codes generate large systems of equations that are generally solved using inward-looking, outward-looking or combined formulations. For many types of problems, the combined formulation is preferred because it does not require a direct inversion of the coefficient matrices and can be solved using iterative solution techniques. An effective preconditioner is a crucial part of the solution process in order to guarantee convergence. However, it can be difficult to generate effective, memory-efficient preconditioners for large problems. This paper investigates preconditioners that use the FEM solution and an absorbing boundary condition (ABC). Various techniques are explored to reduce the memory required by the preconditioner while maintaining effectiveness. Practical problems are presented to evaluate the effectiveness of these preconditioners in various situations. I. INTRODUCTION