Multigrid in energy preconditioner for Krylov solvers

  title={Multigrid in energy preconditioner for Krylov solvers},
  author={Rachel N. Slaybaugh and Thomas M. Evans and Gregory G. Davidson and Paul P. H. Wilson},
  journal={J. Comput. Phys.},

Figures and Tables from this paper

Rayleigh Quotient Iteration with a Multigrid in Energy Preconditioner for Massively Parallel Neutron Transport

Using these methods together, RQI converged in fewer iterations and in less time than all PI calculations for a full pressurized water reactor core, and it also scaled reasonably well out to 275,968 cores.


The results show that the two-level scheme improves significantly the performance of GMRES in the solution of two problems and outperforms two general-purpose alternative acceleration methods, i.e. ILU(0) and ILUC.

Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems

Nonlinear multilevel methods with multiple grids in energy for solving the k-eigenvalue problem for multigroup neutron diffusion equations and multigrid-in-energy algorithms based on a nonlinear projection operator and several advanced prolongation operators are presented.

A highly parallel multilevel Newton-Krylov-Schwarz method with subspace-based coarsening and partition-based balancing for the multigroup neutron transport equations on 3D unstructured meshes

A highly parallel multilevel Newton-Krylov-Schwarz method equipped with several novel components that enable the overall simulation strongly scalable in terms of the compute time, numerically showing that the proposed algorithm is scalable with more than 10,000 processor cores for a realistic application with a few billions unknowns on 3D unstructured meshes.

AIR multigrid with GMRES polynomials (AIRG) and additive preconditioners for Boltzmann transport

An iterative method designed for use with scattering which uses the additive combination of two fixed-sparsity preconditioners applied to the angular flux; a single AIRG V-cycle on the streaming / removal operator and a DSA method with a CG FEM.

A Highly Parallel Multilevel Newton-Krylov-Schwarz Method with Subspace-Based Coarsening and Partition-Based Balancing for the Multigroup Neutron Transport Equation on Three-Dimensional Unstructured Meshes

Numerical simulation of the multigroup neutron transport equation is crucial for studying the motion of neutrons and their interaction with materials.



Preconditioned Krylov subspace methods for transport equations

Three-Dimensional Full Core Power Calculations for Pressurized Water Reactors

A new multilevel parallel decomposition in the Denovo discrete ordinates radiation transport code allows concurrency over energy in addition to space-angle and provides enough concurrency to scale to exascale computing and beyond.

Spatial Multigrid for Isotropic Neutron Transport

A spatial multigrid algorithm for isotropic neutron transport is presented in x-y geometry and a small amount of absorption, or "effective absorption” in a time-dependent problem, restores good convergence.

A Novel Multigrid Method for Sn Discretizations of the Mono-Energetic Boltzmann Transport Equation in the Optically Thick and Thin Regimes with Anisotropic Scattering, Part I

  • Barry Lee
  • Computer Science
    SIAM J. Sci. Comput.
  • 2010
A new multigrid method applied to the most common Sn discretizations of the mono-energetic Boltzmann transport equation in the optically thick and thin regimes, and with strong anisotropic scattering is presented.

Fourier Analysis of Inexact Parallel Block-Jacobi Splitting with Transport Synthetic Acceleration

The results for the unaccelerated algorithm show that convergence of IPBJ can degrade, leading in particular to stagnation of the generalized minimum residual method with restart parameter m, GMRES(m), in problems containing optically thin subdomains.


RQI works for some small problems, but the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems, leading to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.

Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE

Denovo is a new, three-dimensional, discrete ordinates (SN) transport code that uses state-of-the-art solution methods to obtain accurate solutions to the Boltzmann transport equation using nonstationary Krylov methods to solve the within-group equations.

A Two-Grid Acceleration Scheme for the Multigroup Sn Equations with Neutron Upscattering

A two-grid acceleration scheme for the multigroup S[sub n] equations with neutron upscattering is developed. Although it has been tested only in one-dimensional slab geometry with

Fast iterative methods for discrete-ordinates particle transport calculations