A fast element-free Galerkin method for the fractional diffusion-wave equation
A fast element-free Galerkin method for the fractional diffusion-wave equation
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DOI：
10.1016/j.aml.2021.107529
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发表时间：
2021-12
期刊：
影响因子：
--
通讯作者：
Xiaolin Li;Shuling Li
中科院分区：
文献类型：
--
作者：
Xiaolin Li;Shuling Li
提出了一种用于分数阶扩散-波动方程数值分析的快速无网格Galerkin(EFG)方法。在该方法中，首先利用L1和快速H_2N_2近似离散时间Caputo分数阶导数，然后利用Nitsche技巧和稳定化移动最小二乘近似建立线性代数系统。在再生核梯度平滑积分的基础上，提出了一种有效的数值积分方法，进一步提高了算法的计算速度。给出了快速无网格法的理论误差分析。数值结果验证了该方法的有效性。
A fast element-free Galerkin (EFG) method is proposed for the numerical analysis of the fractional diffusion-wave equation. In this method, a fast time discrete scheme is first derived by applying the L1 and the fast H2N2 approximations to discretize the time Caputo fractional derivative, and then the Nitsche’s technique and the stabilized moving least squares approximation are adopted to establish linear algebraic systems. Based on the reproducing kernel gradient smoothing integration, an efficient numerical integration procedure is also presented to further accelerate the computations of the method. Theoretical error analysis of the fast EFG method is provided. Numerical results verify the efficiency of the method.