Double-grid quadrature with interpolation-projection (DoGIP) as a novel discretisation approach: An application to FEM on simplexes
Double-grid quadrature with interpolation-projection (DoGIP) as a novel discretisation approach: An application to FEM on simplexes
复制标题
DOI：
10.1016/j.camwa.2019.05.021
复制
发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
J. Vondrejc
中科院分区：
文献类型：
--
作者：
J. Vondrejc
本文重点研究了双网格插值投影积分法（DoGIP），这是一种新的无矩阵离散化方法，用于傅立叶-伽辽金近似的变分方程的离散化。在这里，它被描述为一个更一般的方法与应用程序的有限元法（FEM）的单形。该方法的基础上处理的试验和测试功能在变分制定在一起，这导致分解成插值和（块）对角矩阵的线性系统。它通常会减少内存需求，特别是高阶基函数，但计算要求更高。这里的数值例子研究两个变分制剂：加权投影和标量椭圆问题建模，例如扩散或稳态传热。本文还为进一步的研究开辟了空间，并在结论中进行了讨论。
This paper is focused on the double-grid integration with interpolation-projection (DoGIP), which is a novel matrix-free discretisation method of variational formulations introduced for Fourier–Galerkin approximation. Here, it is described as a more general approach with an application to the finite element method (FEM) on simplexes. The approach is based on treating the trial and a test function in variational formulation together, which leads to the decomposition of a linear system into interpolation and (block) diagonal matrices. It usually leads to reduced memory demands, especially for higher-order basis functions, but with higher computational requirements. The numerical examples are studied here for two variational formulations: weighted projection and scalar elliptic problem modelling, e.g. diffusion or stationary heat transfer. This paper also opens a room for further investigation, which is discussed in the conclusion.