Solution of the discontinuous P₁ equations in two-dimensional cartesian geometry with two-level preconditioning Academic Article

abstract

• We present a new bilinear discontinuous (Galerkin) finite element discretization of the P1 (spherical harmonics) equations, a first order systems of equations used for describing neutral particle radiation transport or modeling radiative transfer problems. The discrete equations are described for two-dimensional rectangular meshes; we solve the linear system with Krylov iterative methods. We have developed a novel, two-level preconditioner to improve convergence of the Krylov solvers that is based on a linear continuous finite element discretization of the diffusion equation, solved with a conjugate gradient iteration, preceded and followed by one several different smoothing relaxations. A Fourier analysis shows that our approach is very effective over a wide range of problems. Numerical experiments confirm the results of the Fourier analysis. Computations for a realistic problem show that the preconditioner is effective and the solution method is efficient in practice.

authors

• Morel, Jim

published proceedings

• SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

• Warsa, J. S., Wareing, T. A., & Morel, J. E.

citation count

• 10

complete list of authors

• Warsa, JS||Wareing, TA||Morel, JE

publication date

• January 2003

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

keywords

• Diffusion Equation
• Discontinuous Galerkin Methods
• Finite Element Methods
• Krylov Iterative Solvers
• Multilevel Preconditioning
• Neutron Transport
• Radiative Transfer

Digital Object Identifier (DOI)

• 10.1137/S1064827500374583

start page

• 2093

end page

• 2124

volume

• 24

issue

• 6

URL

• http://dx.doi.org/10.1137/s1064827500374583