A Finite Element Method for Angular Discretization of the Radiation Transport Equation on Spherical Geodesic Grids

A spherical harmonics—Finite element discretization of the self-adjoint angular flux neutron transport equation

The spherical harmonics (PN) method is widely used in solving the neutron transport equation, but it has some disadvantages. One of them omes from the complexity of the PN equations. Another one comes from the difficulty of dealing with the vacuum boundary condition exactly. In his paper, the PN method is applied to the self-adjoint angular flux (SAAF) neutron transport equation and a set of PN...

Least-Squares Finite Element Discretization of the Neutron Transport Equation in Spherical Geometry

The main focus of this paper is the numerical solution of the Boltzmann transport equation for neutral particles through mixed material media in a spherically symmetric geometry. Standard solution strategies, like the Discrete Ordinates Method (DOM), may lead to nonphysical approximate solutions. In particular, a point source at the center of the sphere yields undesirable ray effects. Posing th...

A spectral element shallow water model on spherical geodesic grids

The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained from the generalized icosahedral grid introduced previously (Giraldo FX. Lagrange– Galerkin methods on spherical geodesic grids: the shallow water equations. Journal of Computa...

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Parallel Performance Analysis of the Finite Element – Spherical Harmonics Radiation Transport Method

To My Parents iv ACKNOWLEDGEMENTS I express my sincere gratitude to HIM for everything. I extend my sincere thanks to my advisor Prof. Cassiano R. E. de Oliveira, working with whom was a very pleasing experience, both personally and intellectually. I appreciate his help in guiding me in learning new subject matters. I would also like to thank Ryosuke, whom I bothered the most while trying to un...