An Asymptotic Study of Discretized Transport Equations in the Fokker-Planck Limit

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

“…Despite the high level of maturity of deterministic transport methods, there are some serious drawbacks that prevent its use for the most challenging problems: (i) they can be very expensive in three dimensional geometries requiring fine spatial meshes even for moderate angular expansion orders [8,9] and (ii) the solutions often exhibit a lack of angular resolution, especially when considering charged particle transport with highly forward peaked scattering kernels [10,11] (as encountered in proton or carbon radiotherapy). Even a brute-force increase of the number of directions is no cure for these types of problems.…”

“…Various approaches have been developed to overcome such angular resolution problems and can basically be classified into two types: (i) the use of specially designed quadrature sets that either preserve important properties of the transport equation or are hierarchic [10,[18][19][20][21][22]; (ii) the use of an alternative type of angular discretization, i.e. finite element functions or wavelets [23][24][25][26][27].…”