论文标题
在非均匀网格上的积分分数拉普拉斯的明确形式
On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes
论文作者
论文摘要
我们在一个维度上为积分分数拉普拉斯运算符的一般非均匀网格上的分段线性有限元刚度矩阵提供精确形式，在一个维度上，在傅立叶变换空间中实现了派生。有了这样的精确配方，我们能够在某些常用的非均匀网格（例如，渐变的网格）上（例如，渐变的网格）上研究分数刚度矩阵的某些内在特性，以检查它们无缝过渡到通常的Laplacian。
We derive exact form of the piecewise-linear finite element stiffness matrix on general non-uniform meshes for the integral fractional Laplacian operator in one dimension, where the derivation is accomplished in the Fourier transformed space. With such an exact formulation at our disposal, we are able to numerically study some intrinsic properties of the fractional stiffness matrix on some commonly used non-uniform meshes (e.g., the graded mesh), in particular, to examine their seamless transition to those of the usual Laplacian.
