Kinetic and Related Models (KRM)

Galerkin methods for primary ion transport in inhomogeneous media

Pages: 373 - 394, Volume 3, Issue 3, September 2010      doi:10.3934/krm.2010.3.373

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Mohammad Asadzadeh - Department of Mathematics, Chalmers University of Technology and the University of Gothenburg, SE-412 96, Göteborg, Sweden (email)
Anders Brahme - Medical Radiation Physics, Department of Oncology-Pathology, Karolinska Institute, Stockholm, Sweden (email)
Jiping Xin - Department of Mathematics, University of Karlsruhe (TH), 76128 Karlsruhe, Germany (email)

Abstract: This paper concerns the energy deposition of high-energy (e.g., $\approx 50-500$ MeV) proton and carbon ions and high-energy electrons (of $\approx 50$ MeV), in inhomogeneous media. Our goal is to develop a flexible model incorporated with the analytic theory for ions based on bipartition and Fokker-Planck developments. Both procedures are leading to convection dominated convection diffusion equations. We study convergence for semi-discrete and fully discrete approximations of a such obtained equation, for a broad beam model, using the standard Galerkin and streamline diffusion finite element methods. The analytic broad beam model of the light ion absorbed dose were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT+ and those of Galerkin streamline diffusion approach.

Keywords:  charged particle equations, ion transport, inhomogeneous media, bipartition model, broad beam equation, Galerkin methods, stability, convergence analysis.
Mathematics Subject Classification:  56N15, 65N30, 35L80, 82B40.

Received: May 2009;      Revised: February 2010;      Available Online: July 2010.