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About this paper
Abele Simona, Luca Bonaventura, Carlo de Falco, Sebastian Schöps
A numerical method for electromagnetic problems in axisymmetric domains is developed, combining spectral Fourier approximation in the azimuthal direction with IsoGeometric Analysis (IGA) in the radial and axial directions. This approach achieves high-order convergence rates (up to 2p for eigenvalues) and successfully avoids spurious modes, providing a robust and efficient framework for various electromagnetic simulations.
Key insights
- Mapping functions between cylindrical and Cartesian weighted Hilbert spaces enables the construction of discrete de Rham sequences using standard 2D Cartesian IGA spaces.
- The orthogonality of the Fourier basis effectively decouples the original 3D problem into mode-dependent 2D problems, which can be solved in parallel for increased computational efficiency.
- Preserving the de Rham exactness at the discrete level is crucial for achieving high-order accuracy, ensuring numerical stability, and preventing the generation of spurious modes, particularly important for eigenvalue problems.
Summary by alphaXiv.
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