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On a construction of fast direct solvers

Milan Práger (2003)

Applications of Mathematics

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.

On a devil’s staircase associated to the joint spectral radii of a family of pairs of matrices

Ian D. Morris, Nikita Sidorov (2013)

Journal of the European Mathematical Society

The joint spectral radius of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous work with K. G. Hare and J. Theys we showed that for a certain one-parameter family of pairs of matrices, this maximum possible rate of growth is attained along Sturmian sequences with a certain characteristic ratio which depends continuously upon the parameter. In this note we answer some open questions from that paper...

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 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 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 a b = max { a , b } , a b = a + b . The notation 𝔸 x = 𝕓 represents an interval system of linear equations, where 𝔸 = [ b ¯ , A ¯ ] and 𝕓 = [ b ̲ , b ¯ ] 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...

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