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Fast stray field computation on tensor grids.

L Exl1, W Auzinger2, S Bance1

  • 1University of Applied Sciences, Department of Technology, Matthias Corvinus-Straße 15, A-3100 St. Pölten, Austria.

Journal of Computational Physics
|June 10, 2014
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Summary
This summary is machine-generated.

A new algorithm directly computes magnetostatic fields and energy, reducing complex calculations to multilinear algebra. This method offers significant speed improvements for magnetic field computations, especially with canonical tensor formats.

Keywords:
Canonical formatLow-rankMicromagneticsStray fieldTensor gridsTucker tensor

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Area of Science:

  • Computational physics
  • Magnetostatics
  • Numerical methods

Background:

  • Calculating magnetostatic fields and energy is crucial in various physics and engineering applications.
  • Existing methods can be computationally intensive, especially for complex magnetization distributions and non-uniform grids.
  • Efficient algorithms are needed to handle large-scale simulations.

Purpose of the Study:

  • To develop a direct integration algorithm for computing magnetostatic fields and energy.
  • To handle arbitrary magnetization distributions on potentially non-uniform tensor grids.
  • To improve computational efficiency compared to existing methods.

Main Methods:

  • An analytically-based tensor approximation approach is used for function-related tensors.
  • Calculations are reduced to multilinear algebra operations.
  • The algorithm is implemented and tested on numerical examples.

Main Results:

  • The algorithm achieves a computational scaling of N^4/3 with N computational cells.
  • A sublinear scaling of N^2/3 is observed when magnetization is in canonical tensor format.
  • Numerical examples confirm the theoretical predictions for computing times and accuracy.

Conclusions:

  • The developed direct integration algorithm provides an efficient method for magnetostatic field and energy calculations.
  • The tensor approximation approach simplifies complex computations.
  • The algorithm demonstrates significant performance benefits, particularly for canonical tensor formatted magnetization data.