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 53-70Subject Categories
Mathematics
DOI
10.1080/00411450.2012.671206