Applications of Symplectic Geometry Theory in Electromagnetic Simulations and Signal Processing

This paper primarily introduces the applications of symplectic geometry theory in high-frequency approximations of electromagnetic fields, construction of high-precision numerical algorithms, and radar signal processing. It focuses on summarizing how symplectic high-frequency approximation solves the caustic problem in high-frequency approximations through ray lifting in phase space. The paper also discusses the specific applications of high-precision, highly stable, and high-fidelity time-domain numerical algorithms such as symplectic finite-difference time-domain (SFDTD) and multi-symplectic algorithm (MSA) in electromagnetic simulation, and multi-physics problem modeling and analysis. Finally, it introduces the application of symplectic geometric mode decomposition (SGMD) technique in radar signal denoising and mixed signal separation.