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A Linear Streamline Upwind Petrov-Galerkin Angular Stabilization Scheme for the Linear Boltzmann Transport Equation with Magnetic Field

A Swan1*, R Yang2, J St-Aubin3, (1) Tom Baker Cancer Centre, Calgary, AB, CA, (2) Cross Cancer Institute, Edmonton, AB, CA, (3) University of Iowa, Iowa City, IA


(Sunday, 7/12/2020)   [Eastern Time (GMT-4)]

Room: AAPM ePoster Library

Purpose: To implement and test the feasibility of a novel linear Streamline Upwind Petrov-Galerkin (SUPG) scheme for stabilization of the angular advection term in the linear Boltzmann transport equation (LBTE) incorporating magnetic fields.

Methods: The linear SUPG angular method was implemented with a spatial discontinuous Galerkin finite element method (DGFEM) to solve the LBTE with magnetic fields. Simulations were performed in both parallel and perpendicular magnetic field configurations using both homogeneous phantoms and heterogeneous slab geometry phantoms incorporating water, bone, lung and air. Simulation results were compared using gamma analysis against a DGFEM space-angle method which has been validated with Monte Carlo results.

Results: In higher density homogeneous materials such as water or bone, the SUPG method showed both stabilization and excellent accuracy, with a passing rate of 100% for a 2%/2 mm gamma analysis in both magnetic field orientations. Results in the homogeneous lung phantom were 100% (100%) and 88.5% (98.65%) at 2%/2 mm (3%/3 mm) for the parallel and perpendicular magnetic field configurations respectively due to the increased artificial diffusion required for stabilization. Similar results were also seen in the heterogeneous lung slab phantom, but the agreement was reduced to 74% (82%) and 82% (94%) in the heterogeneous air slab phantom for parallel and perpendicular configurations respectively.

Conclusion: A linear SUPG method offers advantages over existing DGFEM methods for angular stabilization of the LBTE with magnetic field in terms of convergence rate and potential for parallelization. However, the accuracy is negatively impacted in low density media due to the large degree of artificial diffusion required. Investigations into a non-linear SUPG method could yield better results in low density media due to the ability to reduce the artificial diffusion in the streamline direction and is the subject of future work.

Funding Support, Disclosures, and Conflict of Interest: This work was funded partially by the Alberta Cancer Foundation.


Not Applicable / None Entered.


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