论文标题
一种系统的方法来减少GLT
A systematic approach to reduced GLT
论文作者
论文摘要
本文涉及对矩阵序列的光谱分析，这些分析是通过偏微分方程（PDE）的离散化和数值近似产生的，如果域是可测量的普通Peano-Jordan。可以观察到，这种矩阵序列通常具有光谱符号，这是描述特征值渐近行为的可测量函数。当该域是超立方体时，可以使用广义局部toeplitz（GLT）序列进行分析，但是在通用域的情况下，必须形式化一种新型的矩阵序列和理论。因此，我们介绍了减少的GLT序列和符号，完整地详细地开发了其理论，并提出了一些应用，以实现有限的差异和有限元素，以使对流扩散 - 扩散反应微分方程离散化。
This paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations (PDEs), in case the domain is a generic Peano-Jordan measurable set. It is observed that such matrix-sequences often present a spectral symbol, that is a measurable function describing the asymptotic behaviour of the eigenvalues. When the domain is a hypercube, the analysis can be conducted using the theory of generalized locally Toeplitz (GLT) sequences, but in case of generic domain, a new kind of matrix-sequences and theory has to be formalized. We thus introduce the Reduced GLT sequences and symbols, developing in full detail its theory, and presenting some application to finite differences and finite elements discretization for convection-diffusion-reaction differential equations.
