This paper is devoted to the derivation and analysis of accurate and efficient perfectly matched layers (PMLs) or efficient absorbing layers for solving fractional Laplacian equations within initial boundary value problems (IBVP). Two main approaches are derived: we first propose a Fourier-based pseudospectral method, and then present a real space method based on an efficient computation of the fractional Laplacian with PML. Some numerical experiments and analytical results are proposed along the paper to illustrate the presented methods.

中文翻译：

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带有吸收层的分数阶拉普拉斯方程组的计算方法的推导和分析

本文致力于推导和分析精确有效的完美匹配层（PML）或有效吸收层，以解决初始边界值问题（IBVP）中的分数拉普拉斯方程组。派生出两种主要方法：我们首先提出一种基于傅立叶的伪谱方法，然后提出一种基于有效的带PML的分数拉普拉斯算子的实空间方法。提出了一些数值实验和分析结果来说明所提出的方法。