Fast Multigrid Solvers for Transport with Forward-Peaked Scattering

Tufts University, Medford MA

Investigators

Abstract

The primary goal of this proposal is to develop fast, efficient, and robust multigrid-based solvers for the solution of the linear Boltzmann-transport equation in the regime of highly forward-peaked scattering. Recently, the project team have developed an angular multigrid algorithm for a model problem that captures the essential features of the Boltzmann-transport equation for scattering in a two-dimensional "Flatland" model. The research goals of this project are, thus, to extend this approach to an efficient and effective method for true three-dimensional scattering, in realistic media, with accurate discretizations. Among the challenges of extending the already developed technique to three dimensions are improving the discretization to allow discontinuous coefficients, and local grid refinement needed in regions of interest. Additionally, the project team will investigate theoretical analysis of the convergence of these algorithms, in both two and three spatial dimensions, providing critical insight into the design of these algorithms for realistic scattering kernels. Accurate and efficient models of forward-peaked scattering are of significant interest in both biomedical and nuclear engineering applications. This regime describes the scattering of electron beams, used in radiation therapy for the treatment of certain cancerous tumors, as well as the transport of charged particles in reactor physics and astrophysics. While there is a long history of interest in efficient and accurate algorithms for modeling charged-particle transport, the problem still poses formidable challenges. The approach considered here offers a new direction for research in this area. The proposed work leads directly to simulation tools for biomedical and nuclear engineers and scientists. The active roles of the PI and co-PI in the computational science and mathematical biology communities ensure timely and widespread dissemination of the resulting algorithms. Furthermore, the project directly involves a doctoral student, who is actively mentored by the PI and co-PI, contributing to the training of an early career scientist in an important field of research.