Matrix-free methods for stiff systems of ODE's
SIAM Journal on Numerical Analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Domain decomposition on parallel computers
IMPACT of Computing in Science and Engineering
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Implicit solvers for unstructured meshes
Journal of Computational Physics
Towards polyalgorithmic linear system solvers for nonlinear elliptic problems
SIAM Journal on Scientific Computing
Preconditioned conjugate gradient methods for the Navier-Stokes equations
Journal of Computational Physics
Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
Journal of Computational Physics
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
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Preconditioning techniques for the Newton-Krylov solution of compressible flows
Journal of Computational Physics
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
Achieving high sustained performance in an unstructured mesh CFD application
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Parallel Computer Architecture: A Hardware/Software Approach
Parallel Computer Architecture: A Hardware/Software Approach
KRYLOV METHODS FOR COMPRESSIBLE FLOWS
KRYLOV METHODS FOR COMPRESSIBLE FLOWS
SCHWARZ-BASED ALGORITHMS FOR COMPRESSIBLE FLOWS
SCHWARZ-BASED ALGORITHMS FOR COMPRESSIBLE FLOWS
On Convergence Acceleration Techniques for Unstructured Meshes
On Convergence Acceleration Techniques for Unstructured Meshes
Some domain decomposition algorithms for nonselfadjoint elliptic and parabolic partial differential equations
International Journal of High Performance Computing Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Performance modeling and tuning of an unstructured mesh CFD application
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Generic programming for high performance scientific applications
JGI '02 Proceedings of the 2002 joint ACM-ISCOPE conference on Java Grande
Analyzing the Parallel Scalability of an Implicit Unstructured Mesh CFD Code
HiPC '00 Proceedings of the 7th International Conference on High Performance Computing
Parallel Flood Modeling Systems
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
Parallel Numerical Solution for Flood Modeling Systems
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Concept of a Problem Solving Environment for Flood Forecasting
Proceedings of the 9th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Reducing Power with Performance Constraints for Parallel Sparse Applications
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 11 - Volume 12
An implicit compact scheme solver with application to chemically reacting flows
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows
Journal of Computational Physics
Enhanced TABS-MDS model for simulating large-scale free surface flows
Environmental Modelling & Software
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Sparse triangular solves for ILU revisited: data layout crucial to better performance
International Journal of High Performance Computing Applications
SIAM Journal on Scientific Computing
A parallel adaptive newton-krylov-schwarz method for 3D compressible inviscid flow simulations
Modelling and Simulation in Engineering
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (ΨNKS) algorithmic framework is presented as a widely applicable answer. This article shows that for the classical problem of three-dimensional transonic Euler flow about an M6 wing, ΨNKS can simultaneously deliver globalized, asymptotically rapid convergence through adaptive pseudo-transient continuation and Newton's method; reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of ΨNKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. The authors therefore distill several recommendations from their experience and reading of the literature on various algorithmic components of ΨNKS, and they describe a freely available MPI-based portable parallel software implementation of the solver employed here.