Fast Inversion Algorithms of Toeplitz-plus-Hankel Matrices.
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 a certain Riccati equation through Cauchy-like matrices.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Fast solution of periodic integral equations by GMRES.
Fast Toeplitz Orthogonalization.
Fehlerabschätzung für Eigenwertnäherungen nach der Ersatzkernmethode bei Integralgleichungen.
Fehleranalyse für die Gauß-Elimination zur Berechnung der Lösung minimaler Länge.
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.
Filter factors of truncated TLS regularization with multiple observations
The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of applied to . This paper focuses on the situation...
Finding nonoverlapping substructures of a sparse matrix.
Finite difference operators from moving least squares interpolation
In a foregoing paper [Sonar, ESAIM: M2AN39 (2005) 883–908] we analyzed the Interpolating Moving Least Squares (IMLS) method due to Lancaster and Šalkauskas with respect to its approximation powers and derived finite difference expressions for the derivatives. In this sequel we follow a completely different approach to the IMLS method given by Kunle [Dissertation (2001)]. As a typical problem with IMLS method we address the question of getting admissible results at the boundary by introducing “ghost...
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.
Finite-difference preconditioners for superconsistent pseudospectral approximations
The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented...