2021/03/31 by Maximilian Klumpp, Klumpp, Maximilian, Guido Schneider +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #35E15 #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Geophysics and Sensor Technology #Optical and Acousto-Optic Technologies #Photonic and Optical Devices #Quantum and Classical Electrodynamics #Seismic Waves and Analysis
paper · pdf · doi:10.48550/arxiv.2104.00133
openalex publication_date 2021/03/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Time-harmonic electromagnetic waves in vacuum are described by the Helmholtz\nequation \Δ u+\ω 2u=0 for (x,y,z) \∈ \ℝ3 . For the\nevolution of such waves along the z-axis a Schr "odinger equation can be\nderived through a multiple scaling ansatz. It is the purpose of this paper to\njustify this formal approximation by proving bounds between this formal\napproximation and true solutions of the original system. The challenge of the\npresented validity analysis is the fact that the Helmholtz equation is\nill-posed as an evolutionary system along the z-axis.\n