Extension of Calculus Operations in Cartesian Tensor Analysis

Yiyu Lu, Peng Yue and Sibei Wei
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Yiyu Lu: School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, China
Peng Yue: School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, China
Sibei Wei: Department of Aircraft Engine Design, National Aerospace University, “KHAI”, 61070 Kharkiv, Ukraine

Mathematics, 2020, vol. 8, issue 4, 1-10

Abstract: 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.

Keywords: vector; tensor; tensor analysis; generalized differential operation; generalized integral theorem for tensor analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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