The proposed research program concerns mathematical modelling, development, convergence analysis and implementations of numerical methods for radiation particle transport and Vlasov type models. More specifically we use asymptotic expansion theory to derive more accurate forms for the charged particle transport equations. We construct approximate solutions and derive optimal convergence rates in a priori and a posteriori error estimates for, e.g. discontinuous Galerkin, streamline diffusion, Characteristic Galerkin, and spectral type methods. We shall focus on the study of the following classes of problems: I. Linear models for electron and ion transport: bipartition, pencil beam and broad beam models, described by convection-dominated, convection-diffusion equations. II. Nonlinear models for Coulomb particle plasmas: Vlasov type models described by Vlasov-Poisson-Fokker-Planck and Vlasov-Maxwell-Fokker-Planck equations. The results are subject to numerical tests and will be compared with experimental, and also some clinical, data provided by our collaborators from Karolinska Institute.
at Mathematical Sciences, Mathematics
Funding years 2011–2013