GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A generalized conjugate gradient, least square method
Numerische Mathematik
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Iterative solution methods
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
SIAM Journal on Scientific Computing
Flexible Inner-Outer Krylov Subspace Methods
SIAM Journal on Numerical Analysis
Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators
SIAM Journal on Numerical Analysis
Preconditioning of Boundary Value Problems Using Elementwise Schur Complements
SIAM Journal on Matrix Analysis and Applications
An agglomerate multilevel preconditioner for linear isostasy saddle point problems
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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Extremely large scale problems, modelled by partial differential equations, arise in various applications, and must be solved by properly preconditioned iterative methods. Frequently, the corresponding medium is heterogeneous. Recursively constructed two-by-two block matrix partitioning methods and elementwise constructed preconditioners for the arising pivot block and Schur complement matrices have turned out to be very efficient methods, and are analysed in this paper. Thereby special attention is paid to macroelementwise partitionings, which can be particularly efficient in the modelling of materials with large and narrow variations and can also provide efficient implementations on parallel computers.