The Cell Method for Electrical Engineering and Multiphysics Problems - An Introduction
The Cell Method for Electrical Engineering and Multiphysics Problems - An Introduction
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DOI：
10.1007/978-3-642-36101-2
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
P. Alotto;F. Freschi;M. Repetto;C. Rosso
中科院分区：
文献类型：
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作者：
P. Alotto;F. Freschi;M. Repetto;C. Rosso
这本书提出了一个数值计划的解决领域的问题所管辖的偏微分方程：细胞的方法。该技术自然地适用于解决多物理场问题与几个相互作用的现象。细胞的方法，基于一个时空镶嵌，是密切相关的工作，托蒂和他的想法的分类图或，因为他们现在被称为，托蒂图：图形表示的问题的方程可能通过一个适当的选择一个时空框架有关的物理变量彼此。介绍了单元法的主要特点，并将其与其它离散数值方法（有限积分法、时域有限差分法、有限体积法、拟有限差分法等）联系起来。讨论了在概述了该方法的理论基础之后，描述了一组已经用单元法解决的物理问题。这些单物理场和多物理场的问题来源于作者在电磁学、弹性力学、热弹性力学等领域的研究经验。最后，实施的数值技术中描述的所有主要组成部分：时空离散化，问题的制定，解决方案和所产生的物理场的表示。
This book presents a numerical scheme for the solution of field problems governed by partial differential equations: the cell method. The technique lends itself naturally to the solution of multiphysics problems with several interacting phenomena. The Cell Method, based on a space-time tessellation, is intimately related to the work of Tonti and to his ideas of classification diagrams or, as they are nowadays called, Tonti diagrams: a graphical representation of the problem's equations made possible by a suitable selection of a space-time framework relating physical variables to each other. The main features of the cell method are presented and links with many other discrete numerical methods (finite integration techniques, finite difference time domain, finite volumes, mimetic finite differences, etc.) are discussed. After outlining the theoretical basis of the method, a set of physical problems which have been solved with the cell method is described. These single and multiphysics problems stem from the authors' research experience in the fields of electromagnetism, elasticity, thermo-elasticity and others. Finally, the implementation of the numerical technique is described in all its main components: space-time discretization, problem formulation, solution and representation of the resulting physical fields.