2020/12/01 by Liliana Borcea, Borcea, Liliana, Vladimir Druskin +3 · 2 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #37N30 #65L09 #65N21 #86A22 #Dynamical Systems (math.DS) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.2012.00861
openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a reduced order model (ROM) methodology for inverse\nelectromagnetic wave scattering in layered lossy media, using data gathered by\nan antenna which generates a probing wave and measures the time resolved\nreflected wave. We recast the wave propagation problem as a passive\ninfinite-dimensional dynamical system, whose transfer function is expressed in\nterms of the measurements at the antenna. The ROM is a low-dimensional\ndynamical system that approximates this transfer function. While there are many\npossible ROM realizations, we are interested in one that preserves passivity\nand in addition is: (1) data driven (i.e., is constructed only from the\nmeasurements) and (2) it consists of a matrix with special sparse algebraic\nstructure, whose entries contain spatially localized information about the\nunknown dielectric permittivity and electrical conductivity of the layered\nmedium. Localized means in the intervals of a special finite difference grid.\nThe main result of the paper is to show with analysis and numerical simulations\nthat these unknowns can be extracted efficiently from the ROM.\n