A Multi-Resolution FDTD Method for Uncertainty Quantification In the Time-Domain Modeling of Microwave Structures

Recent research on parameter uncertainty quantification via the Finite-Difference Time-Domain (FDTD) method has led to several approaches aimed at outperforming the conventional Monte-Carlo technique. Among those, the use of polynomial chaos (PC) is characterized by mathematical robustness and computational efficiency. However, it still requires either multiple FDTD runs (in non-intrusive PC methods) or the execution of one large simulation to compute the PC expansion coefficients for all field nodes and time steps (in the intrusive case). This paper presents an intrusive PC-FDTD method stemming from a wavelet-based PC expansion of field components, with respect to the uncertain parameters. This multi-resolution expansion implements a sparse adaptive grid in the uncertain parameter space, which produces significant performance gains, without sacrificing accuracy.