International Journal on Magnetic Particle Imaging IJMPI
Vol. 12 No. 1 Suppl 1 (2026): Int J Mag Part Imag
https://doi.org/10.18416/IJMPI.2026.2603030

Proceedings Articles, ID 951

Efficient solvers for coupled Brown-Néel Fokker-Planck equations II

Main Article Content

Manfred Faldum (Institute for Geometry and Applied Mathematics, RWTH Aachen University), Franziska Schrank (Institute of Imaging and Computer Vision, RWTH Aachen University, Germany), Volkmar Schulz (1) Institute of Imaging and Computer Vision, RWTH Aachen University, Germany 2) Fraunhofer Institute for Digital Medicine MEVIS, Aachen, Germany), Markus Bachmayr (Institute for Geometry and Applied Mathematics, RWTH Aachen University)

Copyright (c) 2026 Manfred Faldum, Franziska Schrank, Volkmar Schulz, Markus Bachmayr

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Solving the inverse problem in magnetic particle imaging (MPI) relies on efficient and accurate solutions to the forward model. In [1] we proposed a numerical method for solving the convection-dominated Fokker-Planck equation arising from coupled Brownian and Néel relaxation mechanisms. Furthermore, this method tackles the parameter dependence coming from the potentially large number of physical parameter combinations. In this work, we present numerical results for the coupled problem using the joint angular-temporal discretization of this partial differential equation (PDE) and a reduced basis (RB) method for the parameter dependence from [1]

Article Details

References

[1] M. Faldum, F. Schrank, V. Schulz, and M. Bachmayr. Efficient solvers for coupled Brown-Néel Fokker-Planck equations, 2025, doi:10.18416/IJMPI.2025.2503011.
[2] J. Weizenecker. The Fokker–Planck equation for coupled Brown–Néel-rotation. Physics in Medicine & Biology, 63(3):035004, 2018, doi:10.1088/1361-6560/aaa186.
[3] H. Egger and J. Schöberl. A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems. IMA Journal of Numerical Analysis, 30(4):1206–1234, 2009, doi:10.1093/imanum/drn083
[4] E. Azizi, S. Mostufa, B. Rezaei, S. Xin, J. Sun, Z. Shi, J. Gómez-Pastora, and K. Wu. Applying stochastic Langevin function with coupled Brownian–Néel relaxations to study the dynamic magnetizations of nanoparticle tracers in magnetic particle imaging. Journal of Physics D: Applied Physics, 58(13):135002, 2025, doi:10.1088/1361-6463/adafbd.

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