Computer simulation using particles
Computer simulation using particles
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Asymptotic Mesh Independence of Newton's Method Revisited
SIAM Journal on Numerical Analysis
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
An assumed partition algorithm for determining processor inter-communication
Parallel Computing
A hybrid Godunov method for radiation hydrodynamics
Journal of Computational Physics
Interactive large data exploration over the wide area
Proceedings of the 2011 TeraGrid Conference: Extreme Digital Discovery
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We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologically-expanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the piecewise parabolic method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, including radiation transport, chemical ionization kinetics, and gas energy feedback, form a stiff coupled PDE system, which we solve using a fully-implicit inexact Newton approach, and which forms the crux of this paper. The inner linear Newton systems are solved using a Schur complement formulation, and employ a multigrid-preconditioned conjugate gradient solver for the inner Schur systems. We describe this approach and provide results on a suite of test problems, demonstrating its accuracy, robustness, and scalability to very large problems.