Multigrid In Energy Preconditioner for Krylov Solvers

TL;DR

This paper introduces a multigrid in energy preconditioner for Krylov solvers in radiation transport, improving scalability and reducing iterations in high-performance computing environments.

Contribution

It presents a novel multigrid in energy preconditioner integrated into the Denovo code, enhancing scalability and efficiency of Krylov solvers in energy-dependent transport problems.

Findings

Preconditioner scales well in energy dimension.

Reduces Krylov iteration count significantly.

Enables efficient use with advanced eigenvalue solvers.

Abstract

We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.