On a parallel implementation of the mortar element method
Displaying 321 – 340 of 552
On a Parallel Implementation of the Mortar Element Method
Gassav S. Abdoulaev, Yves Achdou, Yuri A. Kuznetsov, Christophe Prud'homme (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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.
Günter Mayer (1986/1987)
Numerische Mathematik
On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems.
Sogabe, T., Hoshi, T., Zhang, S.-L., Fujiwara, T. (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
On adaptive BDDC for the flow in heterogeneous porous media
Bedřich Sousedík (2019)
Applications of Mathematics
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.
P. Oswald, M. Griebel (1993/1994)
Numerische Mathematik
On algebraic multilevel methods for non-symmetric systems - convergence results.
Mense, Christian, Nabben, Reinhard (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
On an accelerated procedure of extrapolation.
Yeyios, A. (1981)
International Journal of Mathematics and Mathematical Sciences
On an algorithm for testing T4 solvability of max-plus interval systems
Helena Myšková (2012)
Kybernetika
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.
Jan Mandel (1990/1991)
Numerische Mathematik
On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices.
Roland Freund (1990)
Numerische Mathematik
On error estimation in the conjugate gradient method and why it works in finite precision computations.
Strakoš, Zdeněk, Tichý, Petr (2002)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
On Fixed Point Linear Equations.
J.P. Milaszewicz (1982)
Numerische Mathematik
On iterative methods of higher order for systems of linear algebraic equations
Miroslav Šisler (1994)
Applications of Mathematics
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
Xuejun Xu, C. O. Chow, S. H. Lui (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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
Xuejun Xu, C. O. Chow, S. H. Lui (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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.
Castel, Jesús M., Migallón, Violeta, Penadés, José (2001)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
On preconditioning Schur complement and Schur complement preconditioning.
Zhang, Jun (2000)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
On properties of some matrix splittings.
Jedrzejec, Henryk A., Woźnicki, Zbigniew I. (2001)
ELA. The Electronic Journal of Linear Algebra [electronic only]
On selection of interface weights in domain decomposition methods
Čertíková, Marta, Šístek, Jakub, Burda, Pavel (2013)
Programs and Algorithms of Numerical Mathematics
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.