High-dimensional space-fractional PDEs are topics of special focus in applied disciplines, but solving them on irregular domains is challenging and deserves particular attention in scientific computing. In response to this issue, we establish a family of differential quadrature (DQ) methods for the space-fractional diffusion equations on 3D irregular domains. The fractional derivatives in space are represented by weighted linear combinations based on the functional values at scattered nodes with their weights determined by using radial basis functions (RBFs) as trial functions. The resulting system of ordinary differential equations (ODEs) are discretized by the weighted average scheme. The presented DQ methods have the virtues which are shared by the classical DQ methods. Several benchmark problems on typical irregular domains are solved to illustrate their advantages in flexibility and accuracy.

中文翻译：

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3D不规则域空间分数扩散方程的一类基于RBFs的DQ方法

高维空间分数 PDE 是应用学科中特别关注的主题，但在不规则域上解决它们具有挑战性，值得科学计算特别关注。针对这个问题，我们为 3D 不规则域上的空间分数扩散方程建立了一系列微分正交 (DQ) 方法。空间中的分数导数由基于分散节点处的函数值的加权线性组合表示，其权重通过使用径向基函数 (RBF) 作为试验函数来确定。所得的常微分方程 (ODE) 系统通过加权平均方案进行离散化。所提出的 DQ 方法具有经典 DQ 方法所共有的优点。