数值分析中的收敛几何

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2019-09-20 DOI:10.3934/jcd.2021003

G. Patrick

引用次数: 0

摘要

网格函数的域是连续自变量底层空间的严格子集。拓扑空间之间的部分映射空间允许不依赖于任何度量的拓扑。这种拓扑从几何上推广了通常的收敛性数值分析定义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The geometry of convergence in numerical analysis

The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies geometrically generalize the usual numerical analysis definitions of convergence.

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.