A Domain Decomposition-based Solver for Acoustic Wave propagation in Two-Dimensional Random Media

TL;DR

The paper addresses efficient uncertainty quantification for 2D acoustic wave propagation in random media by combining a sampling-free intrusive stochastic Galerkin method with non-overlapping domain decomposition. It develops a probabilistic two-level Neumann-Neumann preconditioner to accelerate the conjugate gradient solver for the large SPD system arising from the stochastic Galerkin projection, enabling scalable performance with increasing mesh size and stochastic complexity. The approach is validated against Monte Carlo simulations for a log-normal wave-speed field and demonstrates strong and weak scalability with respect to both spatial discretization and stochastic parameters. This yields a practical, high-fidelity framework for UQ in time-dependent wave problems applicable to engineering scenarios requiring high-resolution, probabilistic predictions.

Abstract

An acoustic wave propagation problem with a log normal random field approximation for wave speed is solved using a sampling-free intrusive stochastic Galerkin approach. The stochastic partial differential equation with the inputs and outputs expanded using polynomial chaos expansion (PCE) is transformed into a set of deterministic PDEs and further to a system of linear equations. Domain decomposition (DD)-based solvers are utilized to handle the overwhelming computational cost for the resulting system with increasing mesh size, time step and number of random parameters. A conjugate gradient iterative solver with a two-level Neumann-Neumann preconditioner is applied here showing their efficient scalabilities.

Figures (20)

• Figure 1: A unit square domain with four subdomains showing interior (blue), interface (red + green ), corner (green) and remaining (red) nodes.
• Figure 2: Comparison of DD-based preconditioners applied to acoustic wave propagation problem
• Figure 3: Mean (left) and standard deviation (right) of the acoustic pressure field for three different points in the domain. Top row shows $(x = 0.5, y =0.5)$, middle row $(x = 0.7,y = 0.7)$ and bottom row $(x = 0.2,y = 0.7)$.
• Figure 4: Mean (left) and standard deviation (right) of pressure field at time $0.0065 s, 0.2 s, 0.5s$ and $0.8 s$.
• Figure 5: Strong scalability and memory consumption for acoustic wave propagation problem with 7 input random variables.