论文标题
用于用于钢化部分问题的多移民方法的平滑分析
A smoothing analysis for multigrid methods applied to tempered fractional problems
论文作者
论文摘要
我们考虑了时间依赖的空间钢化部分扩散方程的数值解。在时间和二阶准确的加权和变化的Grünwald差异的时间内使用曲柄 - 尼科尔森会导致茂密（多级）toeplitz样线性系统。通过利用相关的结构，我们设计了一个临时的Multigrid求解器和基于Multigrid的预处理，所有这些都以加权的Jacobi更加顺畅。提供了新的平滑分析，可以完善最先进的结果，从而扩大了合适的雅各比权重。此外，我们证明，如果多式方法在非脾气的情况下是有效的，那么同一Multigrid方法在调速中也有效。数值结果证实了理论分析，表明所得的基于多族的求解器对于钢化分数扩散方程具有计算有效。
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Grünwald difference in space leads to dense (multilevel) Toeplitz-like linear systems. By exploiting the related structure, we design an ad-hoc multigrid solver and multigrid-based preconditioners, all with weighted Jacobi as smoother. A new smoothing analysis is provided, which refines state-of-the-art results expanding the set of the suitable Jacobi weights. Furthermore, we prove that if a multigrid method is effective in the non-tempered case, then the same multigrid method is effective also in the tempered one. The numerical results confirm the theoretical analysis, showing that the resulting multigrid-based solvers are computationally effective for tempered fractional diffusion equations.
