"مراجعة شاملة لتطبيقات التحويل المطابق في حل المسائل الكهرومغناطيسية"

Kameelah Khalleefah  Alnmri

Department of Electrical and Computer Engineering, Faculty of Education, Al-Ajelat, Zawia University, Libya

 k.alnmri@zu.edu.ly

https://share.google/lQisVct9rRCDiFvnP

Abstract—Conformal mapping has evolved from a classical two-dimensional electrostatic analysis tool into a powerful and versatile methodology for solving complex electromagnetic problems. This review synthesizes recent advancements (2024–2025) across multiple domains, including finite-frequency scattering from arbitrarily shaped metallic surfaces [1], rapid electromagnetic computation using conformal energy minimization [2], conformal metasurfaces for enhanced wireless power transfer systems [3], mathematical optimization techniques for accelerating computations [4], time-domain reflectometry combined with conformal mapping for ultrawideband antenna design [5], wearable antennas for biomedical applications [6], advanced ceramic sensors [7], smart antennas for mobile communications [8], and mechanical interference measurement antennas [9]. The reviewed studies demonstrate significant improvements in computational efficiency, achieving speedups of up to three orders of magnitude compared to traditional finite element methods, while maintaining high accuracy in handling complex geometries and practical engineering problems.

The findings indicate that conformal mapping has significantly expanded beyond its traditional scope, now playing a key role in modern applications such as 6G communications, biomedical engineering, and sustainable energy systems. The reviewed works confirm major advancements in computational efficiency, accuracy, and real-world implementation, particularly in reducing computational time and effectively addressing complex singularities. However, challenges remain, especially in extending these methods to fully three-dimensional problems, integrating artificial intelligence, and enabling adaptive and reconfigurable electromagnetic systems. Future research should therefore focus on developing unified theoretical frameworks, enhancing AI-driven computational approaches, and expanding multi-physics modeling that integrates electromagnetic, thermal, and mechanical effects. In addition, practical progress is recommended in areas such as terahertz antenna design for 6G systems, biomedical sensing technologies, wireless power transfer, and sustainable energy applications, supported by standardized validation methods, open-source computational tools, and improved time-domain measurement techniques.

Keywords: Conformal mapping, electromagnetic scattering, computational electromagnetics, metasurfaces, wireless power transfer, antenna design, boundary integral equations, singularity treatment