Steven Murphy: July 11, 2012
Developing a solver for a high order discontinuous-Galerkin discretisation of the neutron transport equation
Steven MURPHY, CERFACS
Wednesday, July 11, 10:30 a.m. in the CERFACS conference room
Abstract:
In this talk we consider recent developments to a high order discontinuous-Galerkin (DG) finite element method for the discretisation of the mono-energetic steady state neutron transport equation, as well as the solution of the linear systems arising from this method. Unlike the more common discrete ordinates methods, the scheme not only incorporates a higher order discretisation in the spatial variables, but also in the angular variable.
In the case with two spatial dimensions the neutron transport equation is a three dimensional integro-differential equation, with two spatial dimensions and one angular dimension. There will be a discussion of the structure of the linear system resulting from the discretisation, including how the system is affected by properties of the finite element mesh and solution space.
We discuss solving the system using an iteration over the integration term that solves for each element in the angular domain as a separate system. A strategy for the reordering of the spatial elements is then used to transform each matrix into a block triangular structure so that a block substitution procedure may be implemented. The speed and stability of this iterative method will be discussed, as well as performance of the solves on the individual angular elements, including some experiments with LAPACK, MUMPS and MA48.
We then proceed to discuss a generalisation of the method to a pseudo-three dimensional case which incorporates a second dimension in the angular domain and a third, infinitely long, dimension in the spatial domain.
In the case with two spatial dimensions the neutron transport equation is a three dimensional integro-differential equation, with two spatial dimensions and one angular dimension. There will be a discussion of the structure of the linear system resulting from the discretisation, including how the system is affected by properties of the finite element mesh and solution space.
We discuss solving the system using an iteration over the integration term that solves for each element in the angular domain as a separate system. A strategy for the reordering of the spatial elements is then used to transform each matrix into a block triangular structure so that a block substitution procedure may be implemented. The speed and stability of this iterative method will be discussed, as well as performance of the solves on the individual angular elements, including some experiments with LAPACK, MUMPS and MA48.
We then proceed to discuss a generalisation of the method to a pseudo-three dimensional case which incorporates a second dimension in the angular domain and a third, infinitely long, dimension in the spatial domain.
