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FEM-BEM coupling for the large-body limit in micromagnetics
M Aurada1, J M Melenk1, D Praetorius1
1Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria.
Journal of Computational and Applied Mathematics
|June 5, 2015
Summary
We developed a new computational method for micromagnetics. This finite element-boundary element method provides a mathematically sound way to analyze magnetic materials.
Area of Science:
- Computational physics
- Materials science
- Applied mathematics
Background:
- Micromagnetics is crucial for understanding magnetic materials.
- Accurate numerical methods are needed for micromagnetic simulations.
- Existing methods may have limitations in certain applications.
Purpose of the Study:
- To introduce a novel coupled finite element-boundary element method (FEM-BEM).
- To analyze the mathematical properties and performance of this new method.
- To provide a robust computational tool for stationary micromagnetics.
Main Methods:
- Utilizing mixed conforming finite elements for the FEM part.
- Developing a coupled FEM-BEM approach for micromagnetic models.
- Performing mathematical analysis for well-posedness and error estimation.
Main Results:
- Demonstrated the well-posedness of the discrete problem in 2D and 3D.
- Provided an a priori error analysis for lowest order elements.
- Established the theoretical foundation for the coupled FEM-BEM method.
Conclusions:
- The presented coupled FEM-BEM method is a theoretically sound approach for stationary micromagnetics.
- The analysis confirms the method's suitability for practical simulations.
- This work contributes to the advancement of computational tools in magnetism research.
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