Program Information
A Novel Upwind Stabilized Angular Framework for Magnetic Fields in the First Order Linear Boltzmann Transport Equation
R Yang1*, O Zelyak1 , B Fallone1,2,3 , J St. Aubin1,2 , (1) University of Alberta, Edmonton, AB, (2) Cross Cancer Institute, Edmonton, AB, (3) MagnetTx Oncology Solutions, Edmonton, AB
Presentations
TU-D-205-2 (Tuesday, August 1, 2017) 11:00 AM - 12:15 PM Room: 205
Purpose: To investigate high order finite element (FE) angular discretizations capable of modeling magnetic fields within a deterministic solution to the Linear Boltzmann Transport Equation (LBTE). An upwind stabilization scheme of the magnetic field term is developed for the high order angular FE discretization of the unit sphere.
Methods: The Discontinuous Galerkin Finite Element Method (DGFEM) was applied to the LBTE containing a magnetic field operator, using the multigroup method in energy, Cartesian voxels in space, and triangular elements conformal to the unit sphere in angle. Linear, quadratic, and cubic polynomial angular basis functions were investigated. Upwind stabilization in angle was achieved by a novel piecewise separation of the numerical FE integral for angular edge elements into their upwind and lowind contributions. To simulate magnetic fields directed in oblique orientations, the angular mesh is rotated which preserves the spatial sweep ordering. Central axis dose was compared for a heterogeneous slab phantom under varying angular mesh refinements and polynomial orders.
Results: Higher order finite elements produced greater accuracy for the same angular mesh. Using only 32 angular elements with quadratic basis functions, we achieved an accuracy within 1% of our previously validated deterministic code which used over 16 times more angular elements. However, due to cyclic dependencies along certain edges, the solution required more source iterations to converge. Nevertheless the robustness of this method to different field orientations enables greater flexibility as compared to our previous code.
Conclusion: High order angular FE basis functions, coupled with a Cartesian spatial voxel geometry allows for a significant reduction in the number of angular elements required. Our upwind stabilization technique with elements on the unit sphere was shown to be accurate and flexible to oblique magnetic field orientations. These developments pave the way for fast deterministic dose calculations in magnetic fields.
Funding Support, Disclosures, and Conflict of Interest: Ray Yang and Oleksandr Zelyak are supported by Alberta Innovates Health Solutions. Dr. Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).
Contact Email: