Eigenvalues of the Anisotropic Transport Equation in a Slab

Numerical results for the transport equation with strongly anisotropic scattering in a slab

“…Finally we note that if we are able to produce C a ; 0 < a < 1 estimates, then the very same techniques as presented by Sauter et al (2012) guarantee error bounds leading to convergence of order h a .…”

“…Following the ideas presented by Azevedo et al (2011Azevedo et al ( , 2013a, Sauter et al (2012) we reformulate the problem (1)-(3) to obtain the solution in terms of an integral equation. First, we use the kernel x 0 (4) and the properties of the Dirac delta function to rewrite Eq.…”

“…This problem can be solved by applying the method of ray tracing, which consists in integrating the transport equation along the ray's direction (see, for instance, Sauter et al, 2012;Modest, 2003). Eq.…”

“…The method consists of transforming the transport problem by an integral representation and projecting the involved operators in finite dimensional spaces. Here, we focus our discussion on the numerical point of view, while observing that the error bounds in the present case can certainly be obtained using the ideas presented by Azevedo et al (2013a) and Sauter et al (2012).…”

Finite Element Method with Spectral Green's Function in Slab Geometry for Neutron Diffusion in Multiplying Media and One Energy Group

“…That is a good approximation when the neutron flux has rough changes in one spatial direction x (axial) and smoother changes in the symmetrical plane y − z. For that reason, many authors use one-dimensional Cartesian geometry models in recent neutron transport works [9,19,20,21].…”