一种分阶段的有限元方法,用于二维空间分数施罗丁格方程
Xiaogang Zhu1, Haiyang Wan2, Yaping Zhang3
1School of Science, Shaoyang University, Shaoyang, 422000, Hunan, People's Republic of China. zhuxg590@yeah.net.
本研究介绍了一种新的分阶段有限元法 (FEM),用于用瑞兹分数导数解决二维非线性施罗丁格方程 (NLS). 新方法节约了质量和能量,同时降低了波动力学模拟的计算成本.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 量子力学就是量子力学.
背景情况:
- 非线性施罗丁格方程 (NLS) 对于描述各种物理系统中的波浪现象至关重要.
- 分数导数扩展经典模型以捕捉非局部行为,对于复杂的动态至关重要.
- 需要有效的数值方法来解决像空间分数NLS这样的高维分数局部微分方程.
研究的目的:
- 开发和分析一个新的分割步骤有限元素方法 (FEM) 用于二维非线性施罗丁格方程 (NLS) 与里兹分数导数.
- 确保拟议的数值方案保持了诸如质量和能量之类的基本物理量.
- 为了降低与解决分数NLS模型相关的计算成本.
主要方法:
- 使用有限元素方案获得分数NLS的空间离散化,以获得半离散的变量配方.
- 开发一个完全离散的分步FEM,避免在每个时间步骤中进行代计算.
- 数学推导和证明质量保存属性和完全离散方案的误差估计.
主要成果:
- 拟议的半离散FEM计划严格保持质量和能量保存规律.
- 完全离散的分步FEM通过消除时间层代来显著降低计算成本.
- 数字模拟证明了该方案的有效性和能力,能够捕捉波溶液的动态.
结论:
- 开发的分阶段FEM是2D Riesz分数NLS的有效和计算效率高的方法.
- 该方案保存质量和能量的能力使其适用于波浪现象的长期模拟.
- 该方法为研究分数微分方程中的复杂波动学提供了强大的工具.
更多相关视频
10:52Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
Published on: April 12, 2019
06:51Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations
Published on: August 21, 2018
相关概念视频
The Quantum-Mechanical Model of an Atom
State Space Representation
Consider an RLC circuit, a...
Poisson's And Laplace's Equation
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
The Buckingham Pi Theorem
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
