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Finite element simulations using symbolic computing

Author

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  • Amberg, Gustav
  • Tönhardt, Robert
  • Winkler, Christian

Abstract

In our work on modelling of phase change, fluid flow and heat transfer in materials processes, it is crucial to have complete control of the mathematical models, and the numerical simulation of the models. We have developed a toolbox in Maple which can be used to generate complete finite element codes in 1, 2 or 3 dimensions, from a symbolic specification of the mathematical problem. It has been used to create codes used in our research on welding, crystal growth, flow of viscoelastic liquids and more. The possibility of defining a complex problem in a compact readable form, without compromising the flexibility and accessibility of the model and the numerical methods, has changed the way we use simulations in research radically.

Suggested Citation

  • Amberg, Gustav & Tönhardt, Robert & Winkler, Christian, 1999. "Finite element simulations using symbolic computing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(4), pages 257-274.
    • Handle: RePEc:eee:matcom:v:49:y:1999:i:4:p:257-274
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    Cited by:

    1. Do-Quang, Minh & Amberg, Gustav, 2010. "Numerical simulation of the coupling problems of a solid sphere impacting on a liquid free surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(8), pages 1664-1673.
    2. Anna Budnikova & Alexei Troshin & Vladimir Sabelnikov, 2023. "A Review of the Computational Studies on the Separated Subsonic Flow in Asymmetric Diffusers Focused on Turbulence Modeling Assessment," Energies, MDPI, vol. 16(13), pages 1-25, June.

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