Abstract
SUMMARYIn a recent article, the author presented several improved multiple‐coarsening/semi‐coarsening schemes for Sn discretizations of the Boltzmann transport equation, improved over the original multiple‐coarsening/semi‐coarsening schemes. These improvements were derived from detailed space‐angle descriptions of the near‐nullspace components of the integral equation operator. In this paper, we use the techniques of this article to derive a description of the near‐nullspace components of the multi‐energetic Boltzmann equation, and use this description to develop a space‐angle‐energy multigrid method for this equation. This multigrid method is a scheme for solving a high‐dimensional equation: for spatial 3‐d, the equation is 6‐d; for spatial 2‐d, the equation is 5‐d. This method is more robust and efficient than both the commonly used block Gauss‐Seidel iteration that requires solving mono‐energetic Boltzmann equations, and the improved multiple‐coarsening/semi‐coarsening schemes simultaneously applied to all the energy groups. Numerical experiments applied to multi‐energetic equations with isotropic scattering cross‐sections that simulate Compton‐like scattering and fission, as well as anisotropic scattering cross‐sections, are performed to demonstrate the effectiveness of the new scheme. Copyright © 2011 John Wiley & Sons, Ltd.
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