- 教授
- 博士生导师
- 硕士生导师
- 电子邮箱：
- 入职时间：1997-07-01
- 学历：博士研究生毕业
- 性别：男
- 学位：博士
- 在职信息：在职
- 毕业院校：西安交通大学
- 所属院系：数学与统计学院
- 学科：数学
Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains
- 发布时间：2025-04-30
- 论文名称：Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains
- 发表刊物：Journal of Scientific Computing
- 摘要：This paper aims at developing a dissipation-preserving, linearized, and time-stepping-varying spectral method for strongly damped nonlinear wave system in multidimensional unbounded domains Rd(d=1,2, and 3), where the nonlocal nature is described by the mixed fractional Laplacians. Because the underlying solutions of the problem involving mixed fractional Laplacians decay slowly with certain power law at infinity, we employ the rational spectral-Galerkin method using rational basis (or mapped Gegenbauer functions) for the spatial approximation. To capture the intrinsic dissipative properties of the model equations, we combine the Crank-Nicolson scheme with exponential scalar auxiliary variable (ESAV) approach for the temporal discretization. Based on the rate of nonlocal energy dissipation, we design a novel time-stepping-varying strategy to enhance the efficiency of the scheme. We present the detailed implementation of the scheme, where the main building block of the stiffness matrices is based on the Laguerre-Gauss quadrature rule for the modified Bessel functions of the second kind. The existence, uniqueness, and nonlocal energy dissipation law of the fully discrete scheme are rigourously established. Numerical examples in 3D case are carried out to demonstrate the accuracy and efficiency of the scheme. Finally, we simulate the nonlinear behaviors of 2D/3D dissipative
vector solitary waves for damped sine-Gordon system I, for damped sine-Gordon system II, and for damped Klein-Gordon system to provide a deeper understanding of nonlocal physics. - 合写作者：S. Guo, W. Yan, C. Li, L. Mei
- 是否译文：否
- 发表时间：2022-09-04
- 合写作者：S. Guo, W. Yan, C. Li, L. Mei