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Extension of Calculus Operations in Cartesian Tensor Analysis

by Yiyu Lu 1,†, Peng Yue 1,*,†,‡ and Sibei Wei 2,†
1
School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, China
2
Department of Aircraft Engine Design, National Aerospace University, “KHAI”, 61070 Kharkiv, Ukraine
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Current address: Xiyuan Avenue No. 2006, Gaoxin West District, Chengdu 611731, China.
Mathematics 2020, 8(4), 561; https://doi.org/10.3390/math8040561
Received: 2 February 2020 / Revised: 13 March 2020 / Accepted: 7 April 2020 / Published: 11 April 2020
In this paper, we derive and propose basic differential operations and generalized Green’s integral theorems applicable to multidimensional spaces based on Cartesian tensor analysis to solve some nonlinear problems in smooth spaces in the necessary dimensions. In practical applications, the theorem can be applied to numerical analysis in the conservation law, effectively reducing the dimensions of high-dimensional problems and reducing the computational difficulty, which can be effectively used in the solution of complex dimensional mechanical problems. View Full-Text
Keywords: vector; tensor; tensor analysis; generalized differential operation; generalized integral theorem for tensor analysis vector; tensor; tensor analysis; generalized differential operation; generalized integral theorem for tensor analysis
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Lu, Y.; Yue, P.; Wei, S. Extension of Calculus Operations in Cartesian Tensor Analysis. Mathematics 2020, 8, 561.

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