We present a massively-parallel solver for large Helmholtz-type inverse scattering problems. The solver employs the distorted Born iterative method for capturing the multiple-scattering phenomena in image reconstructions. This method requires many full-wave forward-scattering solutions in each iteration, constituting the main performance bottleneck with its high computational complexity. As a remedy, we use the multilevel fast multipole algorithm (MLFMA). The solver scales among computing nodes using a two-dimensional parallelization strategy that distributes illuminations in one dimension, and MLFMA sub-trees in the other dimension. Multi-core CPUs and GPUs are used to provide per-node speedup. We demonstrate a 76% efficiency when scaling from 64 GPUs to 4,096 GPUs. The paper provides reconstruction of a 204.8λ×204.8λ image (4M unknowns) executed on 4,096 GPUs in near-real time (almost 2 minutes). To the best of our knowledge, this is the largest full-wave inverse scattering solution to date, in terms of both image size and computational resources.

Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknowns. Some of the complicated real-life problems (such as scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as benchmarking data for many purposes and even as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and National Aeronautics and Space Administration (NASA) Almond geometries are presented, in addition to the solution of complicated objects, such as the Flamme. The parallel implementation is also extended to solve very large dielectric problems, such as dielectric lenses and photonic crystals.

Due to itsO(NlogN) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns.

The finite-difference time-domain (FDTD) method is used to investigate the effects of highly lossy grounds and the frequency-band selection on ground-penetrating-radar (GPR) signals. The ground is modeled as a heterogeneous half space with arbitrary background permittivity and conductivity. The heterogeneities encompass both embedded scatterers and surface holes, which model the surface roughness. The decay of the waves in relation to the conductivity of the ground is demonstrated. The detectability of the buried targets is investigated with respect to the operating frequency of the GPR, the background conductivity of the ground, the density of the conducting inhomogeneities in the ground, and the surface roughness. The GPR is modeled as transmitting and receiving antennas isolated by conducting shields, whose inner walls are coated with absorbers simulated by perfectly matched layers (PML). The feed of the transmitter is modeled by a single-cell dipole with constant current density in its volume. The time variation of the current density is selected as a smooth pulse with arbitrary center frequency, which is referred to as the operating frequency of the GPR.

The versatility of the three-dimensional (3D) finite-difference time-domain (FDTD) method to model arbitrarily inhomogeneous geometries is exploited to simulate realistic ground-penetrating radar (GPR) scenarios for the purpose of assisting the subsequent designs of high-performance GPR hardware and software. The buried targets are modeled by conducting and dielectric prisms and disks. The ground model is implemented as lossy with surface roughness, and containing numerous inhomogeneities of arbitrary permittivities, conductivities, sizes, and locations. The impact of such an inhomogeneous ground model on the GPR signal is demonstrated. A simple detection algorithm is introduced and used to process these GPR signals. In addition to the transmitting and receiving antennas, the GPR unit is modeled with conducting and absorbing shield walls, which are employed to reduce the direct coupling to the receiver. Perfectly matched layer absorbing boundary condition is used for both simulating the physical absorbers inside the FDTD computational domain and terminating the lossy and layered background medium at the borders.

The finite-difference time-domain (FDTD) method is used to simulate three-dimensional (3-D) geometries of realistic ground-penetrating radar (GPR) scenarios. The radar unit is modeled with two transmitters and a receiver in order to cancel the direct signals emitted by the two transmitters at the receiver. The transmitting and receiving antennas are allowed to have arbitrary polarizations. Single or multiple dielectric and conducting buried targets are simulated. The buried objects are modeled as rectangular prisms and cylindrical disk. Perfectly-matched layer absorbing boundary conditions are adapted and used to terminate the FDTD computational domain, which contains a layered medium due to the ground-air interface.