Full-wave and asymptotic computational electromagnetics methods: on their use and implementation in received signal strength, radar-cross-section, and uncertainty quantification predictions

Abstract

We propose and evaluate several improvements to the accuracy of the shooting and bouncing rays (SBR) method for ray-tracing (RT) electromagnetic modeling. A per-ray cone angle calculation is introduced, with the maximum separation angle determined for each individual ray based on local neighbors, allowing the smallest theoretical error in SBR. This enables adaptive ray spawning and provides a unique analysis of the effect of ray cone sizes on accuracy. For conventional uniform angular distribution, we derive an optimal cone angle to further enhance accuracy. Both approaches are integrated with icosahedral ray spawning geometry and a double-counted ray removal technique, which avoids complex ray path searches. The results demonstrate that the advanced SBR method can perform wireless propagation modeling of tunnel environments with accuracy comparable to the image theory RT method, but with much greater efficiency. To further advance the efficiency of the SBR method, we propose a unified parallelization framework leveraging NVIDIA OptiX Prime programming interfaces on graphics processing units (GPUs). The framework achieves comprehensive parallelization of all components of the SBR algorithm, including traditionally sequential tasks like electric field computation and postprocessing. Through optimization of memory usage and GPU resources, the new SBR method achieves upwards of 99% parallelism under Amdahl's scaling law. This innovative parallelization yields dramatic speedups without sacrificing the previously enhanced accuracy of the SBR method, demonstrating an unparalleled level of computational efficiency for large-scale electromagnetic propagation simulations. Finally, we implement and validate several advanced Kriging methodologies for uncertainty quantification (UQ) in computational electromagnetics (CEM). The universal Kriging, Taylor Kriging, and gradient-enhanced Kriging methods are applied to reconstruct probability density functions, offering efficient alternatives to Monte Carlo simulations. We further propose the novel gradient-enhanced Taylor Kriging (GETK) method, which combines the advantages of gradient information and basis functions, yielding superior surrogate function accuracy and faster convergence. Numerical results using higher-order finite-element scattering modeling show that GETK dramatically outperforms other Kriging and non-Kriging methods in UQ problems, accurately predicting the impact of stochastic input parameters, such as material uncertainties, on quantities of interest like radar cross-section.