Kvadraturní formule pro efektivní numerické řešení transportních rovnic

Abstract

The Boundary Sources Method (BSM) is an integral method introduced in the late 1960s for solving one-dimensional one-velocity neutron transport problems. It is probably the most accurate transport solution method available today for solving piecewise homogenous transport problems. Nevertheless the method is computationally expensive due to the numerical evaluation of a large number of Legendre’s angular moments of the associated Green’s function, which are integrals of product of Chandrasekhar polynomials with a complicated weight function presenting a variety of singularities. The aim of this thesis is to study the integrand and the singularities and to implement selected numerical methods for the numerical quadrature. Result of test cases, in terms of speed and numerical precision, will be presented and discussed.