A Domain-Decomposition-Based Surface Integral Equation Simulator for Characterizing EM Wave Propagation in Mine Environments

Abstract

A domain decomposition-based surface integral equation (SIE) technique for simulating electromagnetic (EM) wave propagation in large and realistic mine environments is proposed. After partitioning the mine into subdomains, the simulator characterizes EM wave propagation in each subdomain using a butterfly-based direct solver in conjunction with a fast multiple – fast Fourier transform (FMM-FFT) iterative scheme. Next, it constructs and solves a composite system characterizing inter-domain interactions. The simulator requires fewer CPU and memory resources than conventional SIE simulators to analyze EM wave propagation in electrically large mine environments. When applied to mines composed of a small set of identical “building blocks”, the simulator’s computational and memory requirements scale logarithmically as opposed to quasi-linearly with mine size. When used in closed-loop uncertainty quantification or design settings, the simulator realizes additional computational savings by recycling many computations performed offline. Numerical results demonstrate the simulator’s accuracy and applicability to mine tunnels and galleries with arbitrary cross-sections, rough walls, and debris from a partial cave-in.