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A topology optimization algorithm for magnetic structures based on a hybrid FEM-BEM method utilizing the adjoint

Gregor Wautischer1, Claas Abert2,3, Florian Bruckner2

  • 1Faculty of Physics, University of Vienna, Vienna, Austria. gregor.wautischer@univie.ac.at.

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|January 22, 2022
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Summary

This study presents an efficient topology optimization method for magnetic structures. The approach optimizes both hard and soft magnetic materials, achieving accurate results verified by analytical solutions.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Engineering

Background:

  • Topology optimization is crucial for designing magnetic structures.
  • Efficient computation of stray fields and gradients is a key challenge.
  • Existing methods may lack efficiency or broad applicability to different magnetic materials.

Purpose of the Study:

  • To develop and implement an efficient topology optimization method for magnetic structures.
  • To apply the method to both hard and soft magnetic materials.
  • To validate the method's accuracy and efficiency.

Main Methods:

  • Utilized the density approach for topology optimization.
  • Employed a hybrid finite element-boundary element method for stray field computation.
  • Applied the adjoint approach for efficient gradient calculation using a "first optimize then discretize" scheme.

Main Results:

  • Successfully optimized the topology of hard and soft magnetic thin film structures.
  • Demonstrated efficient calculation of necessary gradients via the adjoint method.
  • The stray field operator's self-adjoint property simplified adjoint equation solving.

Conclusions:

  • The developed method provides an efficient and accurate means for magnetic structure topology optimization.
  • The approach is versatile, applicable to both hard and soft magnetic materials.
  • The validation against analytical solutions confirms the method's reliability.