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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Updated: Feb 16, 2026

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A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in

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Summary

This study introduces a new method for discretizing angles in transport equations, improving accuracy for magnetic field simulations. Higher-order methods show promise, especially in challenging scenarios like medical physics applications.

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Area of Science:

  • Computational physics
  • Numerical methods
  • Radiation transport

Background:

  • Deterministic solutions to the linear Boltzmann transport equation are sensitive to angular discretization, particularly with magnetic fields.
  • Existing methods struggle with accurate modeling of magnetic field effects on particle transport.

Purpose of the Study:

  • To develop and validate a novel angular finite element method for stabilizing magnetic field terms in transport equations.
  • To improve the accuracy and efficiency of deterministic solutions for radiation transport in the presence of magnetic fields.

Main Methods:

  • A novel stabilization treatment for magnetic field terms using piecewise partitioning of path integrals.
  • Angular finite element discretization on the unit sphere combined with spatial Cartesian voxel elements.
  • Verification using the method of manufactured solutions and validation against GEANT4 Monte Carlo simulations.

Main Results:

  • The new method demonstrates correct order-of-accuracy for various basis functions.
  • Higher-order basis functions reduce errors in strong magnetic fields and low-density media.
  • Simulations in a challenging bone/air scenario with a 1.5 T magnetic field achieved high gamma passing rates (99.96% for 2%/2mm).

Conclusions:

  • The developed angular finite element method effectively stabilizes magnetic field terms, enhancing accuracy in deterministic transport solutions.
  • Quadratic basis functions with 32 angular elements offer a good balance of accuracy and computational efficiency.
  • The method shows robust performance for both parallel and oblique magnetic fields, validated against Monte Carlo methods.