Applications to analysis of transport problems and numerical algorithms

Abstract

Now we shall try now to demonstrate how the results of chapters 2–4 can be applied to investigate some issues of transport theory (particularity, spectral problems) and to justify numerical algorithms for solving the transport equation with only “generalized regularity.” In this chapter we use properties of reflection operators to formulate a number of domain decomposition algorithms for the transport equation. Moreover, these algorithms will be optimized. Also, in an example of the problem with energy dependence we show that a number of assertions presented in this book for one—velocity transport problems can be extended to boundary value problems for other classes of kinetic equations.