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Extension of Calculus Operations in Cartesian Tensor Analysis

Author

Listed:
  • Yiyu Lu

    (School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, China
    These authors contributed equally to this work.)

  • Peng Yue

    (School of Aeronautics and Astronautic, University of Electronic Science and Technology of China, Chengdu 611731, China
    These authors contributed equally to this work.
    Current address: Xiyuan Avenue No. 2006, Gaoxin West District, Chengdu 611731, China.)

  • Sibei Wei

    (Department of Aircraft Engine Design, National Aerospace University, “KHAI”, 61070 Kharkiv, Ukraine
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Yiyu Lu & Peng Yue & Sibei Wei, 2020. "Extension of Calculus Operations in Cartesian Tensor Analysis," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:561-:d:344221
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