A DPIM-GFDM-PML framework for the modelling of stochastic response of elastic wave propagation in viscoelastic media

Abstract

The stochastic response analysis of elastic wave propagation in viscoelastic media is critical for applications in seismic engineering, geological exploration, coastal engineering and non-destructive testing of composite materials. Conventional studies predominantly rely on deterministic models, neglecting the spatial inhomogeneity and parameter randomness. This study proposes a non-intrusive stochastic framework, DPIM-GFDM-PML, integrating the Direct Probability Integral Method (DPIM), the Generalized Finite Difference Method (GFDM), and the Perfectly Matched Layer (PML) technique. Parameter uncertainties are modeled via Karhunen-Loève (K-L) expansion and embedding stochastic fields into frequency-domain governing equations using the GFDM discretization and the PML boundary treatment, establishing a mapping between stochastic inputs and physical responses. DPIM further decouples governing equations from probability density integration, enabling efficient computation of response probability density functions (PDFs) through Gaussian kernel smoothing. Three numerical examples, namely infinite-domain cavities, multi-cavity domain, and complex multilayered media, demonstrate that the proposed framework captures the stochastic characteristics of wave propagation accurately and efficiently. Compared to Monte Carlo simulation (MCS), the DPIM achieves consistent probabilistic results with three orders of magnitude fewer samples, thereby achieving high computational efficiency while maintaining accuracy. Key quantitative findings reveal that multi-parameter coupling amplifies displacement variance by nearly two orders of magnitude and significantly increases the coefficient of variation; whereas increasing the spatial correlation length reduces variance by 14–27 %. The results reveal that spatial randomness in material properties significantly affects wave behavior, with the combined effects of multiple stochastic parameters playing a dominant role. This framework provides a novel and effective tool for uncertainty quantification in viscoelastic wave dynamics.