Barycentric interpolation of interface solution for solving stochastic partial differential equations on non-overlapping subdomains with additive multi-noises

ABSTRACT

The purpose of this paper is to develop a new numerical method for solving a class of stochastic partial differential equations with additive multi-noise. Based on the domain decomposition method, we combine the deterministic method of lines and the stochastic Itô-Taylor method to construct high-order stochastic numerical method. For numerical approximation of the interface solutions, we introduce the Barycentric interpolation method. The solution is then carried out by collecting the interior solutions on the subdomains and the updated interface solutions. Finally, we computationally analyse on meaningful subdomains with linear and nonlinear interfaces, the case of a stochastic advection–diffusion with additive multi-noise and Dirichlet boundary conditions.

KEYWORDS:

• Stochastic partial differential equations
• stochastic advection–diffusion
• method of lines
• interfaces solution
• Itô-Taylor
• domain decomposition
• non-overlapping
• multi-noise

2010 AMS SUBJECT CLASSIFICATIONS:

• 35K57
• 35R60
• 60H15
• 60H35

Disclosure statement

No potential conflict of interest was reported by the authors.