S₂SA preconditioning for the S_n equations with strictly nonnegative spatial discretization

abstract

• Preconditioners based upon transport sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D Sn transport equation using a strictly nonnegative nonlinear spatial closure. Linear and nonlinear preconditioners have been derived and analyzed. The effectiveness of various combinations of these preconditioners are compared using the source iteration, matrix-free Picard Krylov, and nonlinear Krylov acceleration methods. In one dimension, preconditioning with a linear S2SA diffusion equation is found to be essentially equivalent to using a nonlinear diffusion equation. The ability to use a linear diffusion equation has important implications for preconditioning the Sn equations with a strictly nonnegative spatial discretization in multiple dimensions. 2014 Elsevier Inc.

authors

• Morel, Jim
• Ragusa, Jean

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Bruss, D. E., Morel, J. E., & Ragusa, J. C.

citation count

• 4

complete list of authors

• Bruss, Don E||Morel, Jim E||Ragusa, Jean C

publication date

• September 2014

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Diffusion Synthetic Acceleration
• Discontinuous Finite Elements
• Discrete Ordinates Method
• Jacobian-free Newton Krylov
• Matrix-free Picard Krylov
• Nonlinear Krylov Acceleration
• Radiation Transport
• Strictly Nonnegative Closure

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2014.05.022

start page

• 706

end page

• 719

volume

• 273

URL

• http://dx.doi.org/10.1016/j.jcp.2014.05.022