乘性噪声驱动的随机麦克斯韦方程的Parareal算法
Parareal Algorithms for Stochastic Maxwell Equations Driven by Multiplicative Noise
AI总结：
本文提出求解乘性噪声随机麦克斯韦方程的Parareal算法，以随机指数积分器为粗传播子，理论证明均方收敛速率与迭代次数k/2成正比，数值实验验证了增大k和阻尼系数σ可加速收敛，且在长时间模拟中优于传统指数方法。
摘要：
本文研究了用于求解乘性噪声驱动的随机麦克斯韦方程的Parareal算法，重点关注其收敛性、计算效率和数值性能。该算法采用随机指数积分器作为粗传播子，同时使用精确积分器和随机指数积分器作为细传播子。理论分析表明，上述两种算法的均方收敛速率与$k/2$成正比，具体取决于算法的迭代次数。数值实验验证了这些理论结果，表明较大的迭代次数$k$可提高收敛速率，而较大的阻尼系数$σ$可加速算法的收敛。此外，这些算法保持了高精度和计算效率，凸显了它们在长时间模拟中相对于传统指数方法的显著优势。
英文摘要：
This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the stochastic exponential integrator as the coarse propagator, while both the exact integrator and the stochastic exponential integrator are used as fine propagators. Theoretical analysis shows that the mean square convergence rates of the two algorithms selected above are proportional to $k/2$, depending on the iteration number of the algorithms. Numerical experiments validate these theoretical findings, demonstrating that larger iteration numbers $k$ improve convergence rates, while larger damping coefficients $σ$ accelerate the convergence of the algorithms. Furthermore, the algorithms maintain high accuracy and computational efficiency, highlighting their significant advantages over traditional exponential methods in long-term simulations.
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