Galerkin methods for primary ion transport in inhomogeneous media
Artikel i vetenskaplig tidskrift, 2010

This paper concerns the energy deposition of high-energy (e.g., approximate to 50 - 500 MeV) proton and carbon ions and high-energy electrons (of approximate to 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 abroad 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.

convergence analysis

ion transport

inhomogeneous media


bipartition model


Galerkin methods


broad beam equation

charged particle equations


Mohammad Asadzadeh

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

A. Brahme

Karolinska University Hospital

J. P. Xin

Karlsruhe Institute of Technology, Campus South

Kinetic and Related Models

1937-5093 (ISSN) 1937-5077 (eISSN)

Vol. 3 373-394