GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
Krylov subspace methods on supercomputers
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A comparison of preconditioned nonsymmetric Krylov methods on a large-scale MIMD machine
SIAM Journal on Scientific Computing
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Journal of Computational Physics
Efficient parallel computation of unstructured finite element reacting flow solutions
Parallel Computing - Special issue on applications: parallel computing methods in applied fluid mechanics
Multigrid
High-performacne parallel implicit CFD
Parallel Computing - Special issue on parallel computing in aerospace
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Acceleration of the generalized global basis (GGB) method for nonlinear problems
Journal of Computational Physics
PyTrilinos: High-performance distributed-memory solvers for Python
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.48 |
In this paper, we describe an iterative linear system solution methodology used for parallel unstructured finite element simulation of strongly coupled fluid flow, heat transfer, and mass transfer with nonequilibrium chemical reactions. The nonlinear/linear iterative solution strategies are based on a fully coupled Newton solver with preconditioned Krylov subspace methods as the underlying linear iteration. Our discussion considers computational efficiency, robustness and a number of practical implementation issues. The evaluated preconditioners are based on additive Schwarz domain decomposition methods which are applicable for totally unstructured meshes. A number of different aspects of Schwarz schemes are considered including subdomain solves, use of overlap and the introduction of a coarse grid solve (a two-level scheme). As we will show, the proper choice among domain decomposition options is often critical to the efficiency of the overall solution scheme. For this comparison we use a particular spatial discretization of the governing transport/reaction partial differential equations (PDEs) based on a stabilized finite element formulation. Results are presented for a number of standard 2D and 3D computational fluid dynamics (CFD) benchmark problems and some large 3D flow, transport and reacting flow application problems.