Finite volume method for solving the stochastic Helmholtz equation

Advances in Difference Equations

卷:2019

Ruimin Xu¹  Tingting Wu² 

[1] School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences);

[2] School of Mathematics and Statistics, Shandong Normal University;

关键词: Stochastic Helmholtz equation;    White noise;    Finite volume method;   

DOI  :  10.1186/s13662-019-2011-x

来源: DOAJ

【 摘 要 】

Abstract In this paper, we consider the linear finite volume method (FVM) for the stochastic Helmholtz equation, driven by white noise perturbed forcing terms in one-dimension. We first deduce the linear FVM for the deterministic Helmholtz problem. The dispersion equation is presented, and the error between the numerical wavenumber and the exact wavenumber is then analyzed. Comparisons between the linear FVM and the linear finite element method (FEM) are also made. The theoretical analysis and practical calculation indicate that the error of the linear FVM is half of that of the linear FEM. For the stochastic Helmholtz equation, convergence analysis and error estimates are given for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are provided to examine our theoretical results.

【 授权许可】

Unknown