Extension of Calculus Operations in Cartesian Tensor Analysis
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/561 |
| _version_ | 1797570908722823168 |
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| author | Yiyu Lu Peng Yue Sibei Wei |
| author_facet | Yiyu Lu Peng Yue Sibei Wei |
| author_sort | Yiyu Lu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T20:32:07Z |
| format | Article |
| id | doaj.art-9e2e6a359f4144abbb2880a808c88aff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:32:07Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9e2e6a359f4144abbb2880a808c88aff2023-11-19T21:19:31ZengMDPI AGMathematics2227-73902020-04-018456110.3390/math8040561Extension of Calculus Operations in Cartesian Tensor AnalysisYiyu Lu0Peng Yue1Sibei Wei2School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, ChinaDepartment of Aircraft Engine Design, National Aerospace University, “KHAI”, 61070 Kharkiv, UkraineIn 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.https://www.mdpi.com/2227-7390/8/4/561vectortensortensor analysisgeneralized differential operationgeneralized integral theorem for tensor analysis |
| spellingShingle | Yiyu Lu Peng Yue Sibei Wei Extension of Calculus Operations in Cartesian Tensor Analysis Mathematics vector tensor tensor analysis generalized differential operation generalized integral theorem for tensor analysis |
| title | Extension of Calculus Operations in Cartesian Tensor Analysis |
| title_full | Extension of Calculus Operations in Cartesian Tensor Analysis |
| title_fullStr | Extension of Calculus Operations in Cartesian Tensor Analysis |
| title_full_unstemmed | Extension of Calculus Operations in Cartesian Tensor Analysis |
| title_short | Extension of Calculus Operations in Cartesian Tensor Analysis |
| title_sort | extension of calculus operations in cartesian tensor analysis |
| topic | vector tensor tensor analysis generalized differential operation generalized integral theorem for tensor analysis |
| url | https://www.mdpi.com/2227-7390/8/4/561 |
| work_keys_str_mv | AT yiyulu extensionofcalculusoperationsincartesiantensoranalysis AT pengyue extensionofcalculusoperationsincartesiantensoranalysis AT sibeiwei extensionofcalculusoperationsincartesiantensoranalysis |