PhiFEM Project - Docs
Project
GitHub
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Internship
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GitHub Repository Weekly tracking (PDF) Internship report (PDF)
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Phi-FEM Project

    • PhiFEM project
      • Introduction
        • Scientific Context
        • Presentation of the team
        • Objectives
        • Deliverables
      • Finite Element Methods (FEMs)
        • Standard FEM
          • Some notions of functional analysis.
          • General principle of the method
          • Some details on FEM
          • Application to the Poisson problem
        • \(\phi\)-FEM
          • Fictitious domain methods
          • General presentation of the \(\phi\)-FEM method
          • Description of the \(\phi\)-FEM direct method
          • Description of the \(\phi\)-FEM dual method
          • Some details on the stabilization terms
      • Fourier Neural Operator (FNO)
        • Architecture of the FNO
        • Fourier Layer structure
        • Some details on the convolution sub-layer
        • Application
      • Correction
        • Presentation of different problems considered
          • First domain : the Circle.
          • Second domain : the Square.
        • Presentation of the different correction methods considered
          • Correction by adding
          • Correction by multiplying
          • Correction by multiplying on an elevated problem
        • Theoretical results
          • Error estimation of the correction on the elevated problem
          • Interest of elevating the problem
          • Comparison of correction methods
        • Numerical results
          • Correction on exact solution
          • Correction on disturbed solution
          • Correction on \(\phi\)-FEM solution
          • Correction on a FNO prediction
          • Correction with other networks
      • Conclusion
Phi-FEM Project 1.0.3
  • Phi-FEM Project
    • 1.0.3
  • Phi-FEM Project
  • PhiFEM project
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Phi-FEM Project

The features include

  • Introduction

  • Finite Element Methods (FEMs)

  • Fourier Neural Operator (FNO)

  • Correction

  • Conclusion

You can find the internship report in PDF just HERE as well as a weekly tracking of the internship HERE (in french).