Abstract: We present a comprehensive description of numerical methods within the Computational Electromagnetics field, of which include high frequency asymptotic techniques, high performance computing techniques for numerical method optimization, full wave numerical solutions, and regression for use in optimization and uncertainty quantification. We propose and evaluate several improvements to the accuracy of the shooting and bouncing rays (SBR) method for ray-tracing (RT) electromagnetic modeling. We present per-ray cone angle calculation, with the maximum separation angle between rays calculated for every individual ray, based on a set of local neighbors rather than a single global maximum. The results demonstrate that the advanced shooting and bouncing RT method––using both proposed ray cone generation approaches––can perform wireless propagation modeling of tunnel environments with the same accuracy as image theory RT, a dramatically less efficient but traditionally considerably more accurate solver. We additionally present a novel unified parallelization framework, consisting of algorithms, strategies, and data structures, to radically enhance the efficiency of the shooting and bouncing rays (SBR) method for ray tracing (RT) electromagnetic propagation modeling. The massively parallel optimization of the SBR code is achieved by integration of the SBR with NVIDIA OptiX Prime programming interfaces on graphics processing units (GPUs), comprehensive parallelization of all components of the SBR algorithm, including electric field computation and postprocessing tasks being traditionally limited to sequential operation, and addressing and optimizing memory usage and constraints to further advance efficiency of the overall method. Numerical results demonstrate that the new proposed optimized SBR methodology achieves massive parallel vs. serial speedups and upwards of 99% parallelism under Amdahl’s parallelization scaling law. Finally, we present the implementation and use of the Kriging methodology, i.e., surrogate models based on Kriging interpolation, in uncertainty quantification (UQ) in computational electromagnetics (CEM). We provide consistent, unified, and comprehensive description, derivation, implementation, use, validation, and comparative study of accuracy and convergence of several advanced Kriging approaches, namely, the universal Kriging, Taylor Kriging, and gradient-enhanced Kriging methods, for reconstruction of probability-density function in UQ CEM problems. We also propose, derive, and demonstrate the gradient-enhanced Taylor Kriging (GETK) methodology, novel to science and engineering in general. Numerical results using higher-order finite-element scattering modeling show that Kriging methods for UQ in CEM are able to accurately output probability-density function prediction for a quantity of interest (e.g., radar cross-section) given the probability density of stochastic input parameters (e.g., material uncertainties), as very efficient alternatives to Monte Carlo simulations.

Adviser: Branislav Notaros
Co-Adviser: Milan Ilic
Non-ECE Member: Karan Venayagamoorthy
Member 3: Jesse Wilson
Addional Members: NA

Publications:
Advancing Accuracy of Shooting and Bouncing Rays Method for Ray-Tracing Propagation Modeling Based on Novel Approaches to Ray Cone Angle Calculation

Non-Self-Adjacent Ray Classes for Parallelizable Shooting–Bouncing Ray Tracing Double Count Removal

RCS Uncertainty Predictions for Scatterers with Uncertain Material Parameters Using FEM, Adjoints, and HOPS Technique

Some Advances in Shooting-Bouncing-Rays Asymptotic Propagation Methodologies

Advanced Error Estimation, Adaptive Refinement, and Uncertainty Quantification Methodologies in Frequency-Domain Computational Electromagnetics

Kriging Methodology for Predicting Material Uncertainty Impact on FEM Scattering Computations

Shooting-Bouncing-Rays Technique to Model Mine Tunnels: Algorithm Acceleration

Shooting-Bouncing-Rays Technique to Model Mine Tunnels: Theory and Accuracy Validation

Program of Study:
ENGR 550
GRAD 510
ECE 504
MATH 520
ECE 541
ECE 604
MATH 510
ECE 504