拟静态电磁边值问题数值解中的流形与度量
Manifold and metric in numerical solution of the quasi-static electromagnetic boundary value problems
摘要：
经典矢量分析是计算电磁学工程师使用的主要形式，尽管流形作为一个理论概念已经存在了一个世纪。本文讨论了流形的好处，在建模的实际问题的传统方法。与结构的方法，它概述了坐标系，度量，本构方程和领域的作用和相互依赖性，并将它们与准静态计算电磁学的实际问题：网格生成，开边界问题，电磁-机械耦合问题，涉及运动和变形。拟议的程序还意味着改进建模软件的灵活性。
英文摘要：
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds over the traditional approach in practical problems of modelling. With a structural approach, it outlines the role and interdependence of coordinate systems, metric, constitutive equations, and fields, and relates them to practical problems of quasi-static computational electromagnetics: mesh generation, open-boundary problems, and electromagnetic-mechanical coupled problems involving motion and deformation. The proposed procedures also imply improvements to the flexibility of the modelling software.
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