Spherical Harmonics and a Semidiscrete Finite Element Approximation for the Transport Equation
Artikel i vetenskaplig tidskrift, 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.

electron-transport

inhomogeneous-media

charged particle beams

spherical harmonics

partial-differential-equations

finite element method

bipartition model

ion-transport

transport equation

Författare

Mohammad Asadzadeh

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Tobias Gebäck

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

SuMo Biomaterials

Transport Theory and Statistical Physics

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

Vol. 41 1-2 53-70

Ämneskategorier

Matematik

DOI

10.1080/00411450.2012.671206

Mer information

Skapat

2017-10-07