论文标题
通过SAV方法进行随机波方程的半图像节能数值方案
Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach
论文作者
论文摘要
在本文中，我们提出和分析具有一般非线性和乘法噪声的随机波方程（SWE）的半图形数值方案。这些称为随机标量辅助变量（SAV）方案的数值方案是通过将所考虑的SWE转换为具有随机SAV的更高维生的随机系统来构建的。我们证明它们可以明确解决，并保留修改后的能量演化定律和原始系统的规律性结构。这些具有结构的特性是克服噪声和非线性相互作用的关键。通过证明对引入的SAV的新规律性估计，我们建立了随机SAV方案的强收敛速率，以及在空间方向上使用有限元方法的进一步的全差异方案。据我们所知，这是对非线性SWE的半明显呈现能源的构建和强烈收敛的结果。
In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV) schemes, are constructed by transforming the considered SWE into a higher dimensional stochastic system with a stochastic SAV. We prove that they can be solved explicitly and preserve the modified energy evolution law and the regularity structure of the original system. These structure-preserving properties are the keys to overcoming the mutual effect of the noise and nonlinearity. By proving new regularity estimates of the introduced SAV, we establish the strong convergence rate of stochastic SAV schemes and the further fully-discrete schemes with the finite element method in spatial direction. To the best of our knowledge, this is the first result on the construction and strong convergence of semi-implicit energy-preserving schemes for nonlinear SWE.
