# Multigrid in energy preconditioner for Krylov solvers

@article{Slaybaugh2013MultigridIE, 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.}, year={2013}, volume={242}, pages={405-419} }

## 25 Citations

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

- Computer ScienceArXiv
- 2017

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.

### TWO-LEVEL MULTIGRID PRECONDITIONING OF A NEUTRON NOISE DIFFUSION SOLVER

- Computer Science
- 2019

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.

### The multilevel quasidiffusion method with multigrid in energy for eigenvalue transport problems

- Computer Science
- 2017

### Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems

- Computer ScienceNuclear Science and Engineering
- 2019

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.

### Multigroup diffusion preconditioners for multiplying fixed-source transport problems

- Computer ScienceJ. Comput. Phys.
- 2014

### 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

- Computer ScienceArXiv
- 2019

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

- Computer Science
- 2023

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.

### Solving the Boltzmann transport equation with multigrid and adaptive space/angle discretisations

- Computer Science
- 2015

### 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

- Computer ScienceSIAM J. Sci. Comput.
- 2020

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

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