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

TL;DR

This paper introduces a domain decomposition-based solver for simulating acoustic wave propagation in two-dimensional random media, employing a stochastic Galerkin approach with polynomial chaos expansion to efficiently handle the computational complexity.

Contribution

The paper develops a novel domain decomposition solver combined with a stochastic Galerkin method for efficient simulation of acoustic waves in random media, reducing computational costs.

Findings

Efficient scalability of the conjugate gradient solver with Neumann-Neumann preconditioner.

Successful transformation of stochastic PDEs into deterministic systems for simulation.

Reduction in computational cost for large-scale random media problems.

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.