Solution of the discontinuous P-1 equations in two-dimensional cartesian geometry with two-level preconditioning Academic Article uri icon


  • 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.

published proceedings


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