GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A stability analysis of incomplete LU factorizations
Mathematics of Computation
SIAM Journal on Scientific and Statistical Computing
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
Orderings for Factorized Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
On the Incomplete Cholesky Decomposition of a Class of Perturbed Matrices
SIAM Journal on Scientific Computing
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
SIAM Journal on Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Analysis and Comparison of Geometric and Algebraic Multigrid for Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Adaptive preconditioners for nonlinear systems of equations
Journal of Computational and Applied Mathematics
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
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This paper deals with solving sequences of nonsymmetric linear systems with a block structure arising from compressible flow problems. The systems are solved by a preconditioned iterative method. We attempt to improve the overall solution process by sharing a part of the computational effort throughout the sequence. Our approach is fully algebraic and it is based on updating preconditioners by a block triangular update. A particular update is computed in a black-box fashion from the known preconditioner of some of the previous matrices, and from the difference of involved matrices. Results of our test compressible flow problems show, that the strategy speeds up the entire computation. The acceleration is particularly important in phases of instationary behavior where we saved about half of the computational time in the supersonic and moderate Mach number cases. In the low Mach number case the updated decompositions were similarly effective as the frozen preconditioners.