Extrapolated Gauss-Seidel I and SOR Methods for Least-Squares Problems.
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...
Extrapolation of S. O. R. iterations
Factorization Iterative Methods, M-Operators and H-Operators.
Fast iterative methods for solving Toeplitz-plus-Hankel least squares problems.
Fast multigrid solver
In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.
Fast Poisson Solvers on General Two Dimensional Regions for the Dirichlet Problem.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Fast solution of periodic integral equations by GMRES.
FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...
Filter factor analysis of an iterative multilevel regularizing method.
Finite element least-squares methods for a compressible Stokes system.
Finite element methods on non-conforming grids by penalizing the matching constraint
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
Finite element methods on non-conforming grids by penalizing the matching constraint
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
General highly accurate algebraic coarsening.
Generalizations of the Projection Method with Applications to SOR Theory for Hermitian Positive Semidefinite Linear Systems.
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators