Higher order stray field computation on tensor product domains
- Author(s)
- Lukas Exl, Sebastian Schaffer
- Abstract
We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.
- Organisation(s)
- Research Platform MMM Mathematics-Magnetism-Materials, Department of Mathematics, Department of Geology
- External organisation(s)
- Wolfgang Pauli Institut
- Journal
- Journal of Computational Physics
- Volume
- 550
- ISSN
- 0021-9991
- DOI
- https://doi.org/10.1016/j.jcp.2026.114652
- Publication date
- 04-2026
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101014 Numerical mathematics, 103043 Computational physics, 102019 Machine learning
- Keywords
- ASJC Scopus subject areas
- Numerical Analysis, Modelling and Simulation, Physics and Astronomy (miscellaneous), General Physics and Astronomy, Computer Science Applications, Computational Mathematics, Applied Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/229c959a-b7b5-4b74-91f3-48bc8cd5e655