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.

翻译：本文采用无采样侵入式随机伽辽金方法，求解了波速采用对数正态随机场近似的声波传播问题。通过多项式混沌展开对输入输出进行展开，将随机偏微分方程转化为一组确定性偏微分方程，并进一步转化为线性方程组系统。为应对网格尺寸、时间步长及随机参数数量增加所导致的巨大计算开销，研究采用了基于域分解的求解器。本文应用了结合两层诺伊曼-诺伊曼预条件子的共轭梯度迭代求解器，其高效的可扩展性得到了验证。