Spherical Harmonics and a Semidiscrete Finite Element Approximation for the Transport Equation
Journal article, 2012

This work is the first part in a series of two articles, where the objective is to construct, analyze, and implement realistic particle transport models relevant in applications in radiation cancer therapy. Here we use spherical harmonics and derive an energy-dependent model problem for the transport equation. Then we show stability and derive optimal convergence rates for semidiscrete (discretization in energy) finite element approximations of this model problem. The fully discrete problem that also considers the study of finite element discretizations in radial and spatial domains as well is the subject of a forthcoming article.

transport equation

charged particle beams

finite element method

ion-transport

electron-transport

spherical harmonics

partial-differential-equations

inhomogeneous-media

bipartition model

Author

Mohammad Asadzadeh

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Tobias Gebäck

SuMo Biomaterials

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Transport Theory and Statistical Physics

0041-1450 (ISSN) 1532-2424 (eISSN)

Vol. 41 1-2 53-70

Subject Categories

Mathematics

DOI

10.1080/00411450.2012.671206

More information

Latest update

8/18/2020