Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise

In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply compact finite difference method and interior penalty discontinuous Galerkin element to discretize space variable present two semi-discrete schemes, respectively. Then make use of discrete gradient Pad\'e approximation propose efficient fully-discrete schemes. These are proved preserve law. particular, also prove that proposed exactly inherit almost surely if considered model is additive Numerical experiments given confirm theoretical findings.