论文标题
关于分数拉普拉斯的fem刚度基质的对角线优势，并保留分数allen-cahn方程的最大原理
On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for fractional Allen-Cahn equation
论文作者
论文摘要
在本文中，我们研究了刚度矩阵的对角线优势是由一个空间维度下的整体均质dirichlet边界条件下整体分数拉普拉斯的分段线性有限元离散化。我们首先在频率空间中得出该矩阵的确切形式，该形式可扩展到多维矩形元素。然后，当刚度矩阵可以严格地占主导地位时，我们给出了完整的答案。作为一种应用，我们将此概念应用于为分数allen-cahn方程保存最大原理方案的构建，并提供了足够的数值结果来验证我们的发现。
In this paper, we study diagonal dominance of the stiffness matrix resulted from the piecewise linear finite element discretisation of the integral fractional Laplacian under global homogeneous Dirichlet boundary condition in one spatial dimension. We first derive the exact form of this matrix in the frequency space which is extendable to multi-dimensional rectangular elements. Then we give the complete answer when the stiffness matrix can be strictly diagonally dominant. As one application, we apply this notion to the construction of maximum principle preserving schemes for the fractional-in-space Allen-Cahn equation, and provide ample numerical results to verify our findings.
