具有对称解的偏微分方程的对称双尺度有限元离散

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED
Pengyu Hou, Fang Liu, Aihui Zhou
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引用次数: 0

摘要

摘要本文给出了一类具有对称解的偏微分方程的对称双尺度有限元方法。利用这些方法,将精细张量积网格上的有限元逼近简化为更粗网格和不变精细网格上的有限元逼近。理论和包括电子结构计算在内的数值都表明,所得到的近似仍然保持渐近最优精度。采用对称双尺度有限元方法,当Ω =(0,1) d \Omega=(0,1)^{d}时,与双尺度有限元方法相比,计算成本可进一步约降低𝑑。因此,对称双尺度有限元方法大大降低了计算成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symmetrized Two-Scale Finite Element Discretizations for Partial Differential Equations with Symmetric Solutions
Abstract In this paper, some symmetrized two-scale finite element methods are proposed for a class of partial differential equations with symmetric solutions. With these methods, the finite element approximation on a fine tensor-product grid is reduced to the finite element approximations on a much coarser grid and a univariant fine grid. It is shown by both theory and numerics including electronic structure calculations that the resulting approximations still maintain an asymptotically optimal accuracy. By symmetrized two-scale finite element methods, the computational cost can be reduced further by a factor of 𝑑 approximately compared with two-scale finite element methods when Ω = ( 0 , 1 ) d \Omega=(0,1)^{d} . Consequently, symmetrized two-scale finite element methods reduce computational cost significantly.
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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