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In this paper, we propose and analyze semi-implicit numerical schemes for thestochastic wave equation (SWE) with general nonlinearity and multiplicativenoise. These numerical schemes, called stochastic scalar auxiliary variable(SAV) schemes, are constructed by transforming the considered SWE into a higherdimensional stochastic system with a stochastic SAV. We prove that they can besolved explicitly and preserve the modified energy evolution law and theregularity structure of the original system. These structure-preservingproperties are the keys to overcoming the mutual effect of the noise andnonlinearity. By proving new regularity estimates of the introduced SAV, weestablish the strong convergence rate of stochastic SAV schemes and the furtherfully-discrete schemes with the finite element method in spatial direction. Tothe best of our knowledge, this is the first result on the construction andstrong convergence of semi-implicit energy-preserving schemes for nonlinearSWE.

Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach