GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Implementation of the GMRES method using householder transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Journal of Computational Physics
Java Threads
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Development of a 2-D algorithm to simulate convection and phase transition efficiently
Journal of Computational Physics
A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows
Journal of Computational Physics
Nested parallelism for multi-core HPC systems using Java
Journal of Parallel and Distributed Computing
On physics-based preconditioning of the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm
Journal of Computational Physics
Journal of Computational Physics
F-MPJ: scalable Java message-passing communications on parallel systems
The Journal of Supercomputing
Device level communication libraries for high-performance computing in Java
Concurrency and Computation: Practice & Experience
Java in the High Performance Computing arena: Research, practice and experience
Science of Computer Programming
Journal of Computational Physics
A parallel Jacobian-free Newton-Krylov solver for a coupled sea ice-ocean model
Journal of Computational Physics
Hi-index | 31.46 |
The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing-emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram-Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.