Integral and Differential Equation Methods in Electromagnetic Radiation and Scattering

Dear Colleagues,

Mathematical computations related to antenna radiation and target scattering are of extreme interest to electromagnetics engineering; however, they can rely on analytical methods only to a limited extent. Closed form, or even asymptotic solutions, are possible for canonical geometries only, which is usually not the case in the real world, and when arbitrary shapes are involved, space discretization and approximate (instead of exact) calculations are inevitable. Triggered and fueled by the explosive progress of computers since the 80s, numerical techniques have therefore been an indispensable tool in electromagnetics for decades, falling into two main categories: Integral Equation and Differential Equation Methods. Both types are characterized by certain advantages and disadvantages, where their applicability and efficiency depend on the specific features of the problem, and their improvement or optimization has been the topic of literally thousands of papers in the recent literature. Furthermore, several commercial software packages, which are broadly used today by both industry and academia, are based on closely related algorithms. Fundamental computational methods with a long history of continuous development include the Method of Moments (MoM), the Finite Element Method (FEM), the Finite Volume Method (FVM), the Finite Difference Time Domain Method (FDTD), the Method of Auxiliary Sources (MAS), etc. For high frequencies, due to the large electric size of antennas or scatterers, extremely high computational resources are required, in terms of memory and CPU time, to handle even millions of unknowns. Therefore, “fast” variants of the latter techniques were developed to reduce the computational cost, such as the Adaptive Integral Method (AIM), the Adaptive Cross Approximation (ACA), the Fast Multipole Method (FMM), its parallel version called the Multi-Level Fast Multipole Algorithm (MLFMA), its time domain counterpart called the Plane Wave Time Domain (PWTD) method, etc.  Several variants of the above, plus additional approaches, having evolved particularly over the last few years, are designed to suppress the complexity and/or enhance, at the same time, the accuracy of the calculations. For instance, Domain Decomposition (DDM) Methods are a typical example of algorithms exploiting the benefits of parallel processing. The ambition of this Special Issue is to host and promote the most recent advancements made by internationally renowned scholars in this fascinating research area.

Prof. Dr. Hristos T. Anastassiu
Guest Editor

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• MoM
• FEM
• FDTD
• MAS
• AIM
• ACA
• FMM
• MLFMA
• PWTD
• DDM