Support: United States — Israel Binational Science Foundation (BSF)

Period of Performance: October 1, 2021 — September 30, 2025

Budget: $200,000 (NCSU share $100,000)

Summary: We propose to develop a numerical capability to simulate the propagation of unsteady electromagnetic waves in three space dimensions. It will offer high order accuracy when solving the transmission and scattering problems for various geometries. This scheme will allow the simulation of short pulses (broadband signals) in the time domain, with pulse length comparable to the problem characteristic size. The computational complexity will scale slower than linear as the discretization grid is refined. This sub-linear scaling translates into considerable performance gains, especially when integrating the problem over a long time or solving multiple similar problems (e.g., different impinging signals scattering about the same shape). The core of the proposed methodology is the method of difference potentials (MDP) combined with compact high order accurate finite difference schemes. High order accuracy provides an efficient means for reducing the dispersion error. Compact schemes offer an inexpensive venue toward high order accuracy on regular structured grids and require no additional boundary conditions beyond those in the continuous formulation. The MDP extends the high order accuracy to non-conforming boundaries and interfaces while incurring no adverse effects due to the “cut cells.’’ In doing so, it transforms the original problem to an equivalent boundary formulation, where the boundary operators are independent of the boundary conditions. Therefore, changing the boundary condition entails only a minor additional cost. This greatly improves the overall efficiency when computing different components of electromagnetic field and/or altering the physical setting, e.g., changing the angle of incidence. When the Huygens’ principle is taken into account, the methodology yields a sub linear computational complexity with respect to the grid dimension while retaining its high order accuracy, and requires no special treatment of artificial outer boundaries. The range of computational capabilities offered by the proposed methodology will be beneficial for a variety of applications. Those include remote sensing (detection, surveillance, navigation, imaging, target recognition), telecommunications, non-destructive evaluation of materials, and others. A radar image is formed by processing the returns, i.e., scattered signals, from the same target illuminated at different angles of incidence. Our scheme solves the solution of multiple similar problems at a low individual cost. Hence, the proposed scheme would be very efficient for the simulation of radar reconstruction (imaging).