On a non-stagnation condition for GMRES and application to saddle point matrices.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On a Theorem of Stein-Rosenberg Type in Interval Analysis.
On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems.
On adaptive BDDC for the flow in heterogeneous porous media
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection...
On additive scharz preconditioners for sparse grid discretizations.
On algebraic multilevel methods for non-symmetric systems - convergence results.
On an accelerated procedure of extrapolation.
On an algorithm for testing T4 solvability of max-plus interval systems
In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where , . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm...
On block diagonal and Schur complement preconditioning.
On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices.
On error estimation in the conjugate gradient method and why it works in finite precision computations.
On Fixed Point Linear Equations.
On iterative methods of higher order for systems of linear algebraic equations
The paper is concerned with certain -degree iterative methods for the solution of linear algebraic systems. The successive approximation is determined by means of approximations , , , . In this article to each iterative method of the first degree some -degree iterative method is found in order to accelerate the convergence of the intial method.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning.
On preconditioning Schur complement and Schur complement preconditioning.
On properties of some matrix splittings.