Oldrich Vlach

• VSB - Technical University of Ostrava

Variants of the FETI (finite element tearing and interconnecting) methods introduced by Farhat and Roux [8] belong to the most powerful methods for the massively parallel solution of large discretized elliptic partial differential equations. The basic idea is to decompose the domain into subdomains connected by Lagrange multipliers and then elimina...

We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into m×m×m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{up...

The hybrid FETI-DP method proposed by Klawonn and Rheinbach uses a two-level decomposition of the domain into subdomains and clusters. Here we give bounds on the regular condition number of the clusters obtained by interconnecting the Schur complements of square elastic subdomains by the average rigid body modes of adjacent edges. Using the angles...

The unpreconditioned hybrid domain decomposition method was recently shown to be a competitive solver for linear elliptic PDE problems discretized by structured grids. Here, we plug H-TFETI-DP (hybrid total finite element tearing and interconnecting dual primal) method into the solution of huge boundary elliptic variational inequalities. We decompo...

Augmented Lagrangian method is a well established tool for the solution of optimization problems with equality constraints. If combined with effective algorithms for the solution of bound constrained quadratic programming problems, it can solve efficiently very large problems with bound and linear equality constraints. The point of this paper is to...

Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters ar...

A variationally consistent approximation of contact conditions by means of biorthogonal mortars was introduced by Wohlmuth as a powerful theoretically supported tool for the discretization of contact problems. This approach is especially useful when a potential contact interface is large and curved or when nonmatching grids are applied, but its eff...

Two proportionality based gradient methods for the solution of large convex bound constrained quadratic programming problems, MPRGP (Modified Proportioning with Reduced Gradient Projections) and P2GP (Proportionality-based Two-phase Gradient Projection) are presented and applied to the solution of auxiliary problems in the inner loop of an augmente...

A cheap symmetric stiffness-based preconditioning of the Hessian of the dual problem arising from the application of the finite element tearing and interconnecting domain decomposition to the solution of variational inequalities with varying coefficients is proposed. The preconditioning preserves the structure of the inequality constraints and affe...

Variationally consistent approximation of the non-penetration conditions and friction laws was introduced by Wohlmuth [Acta Numer. 20 (2011) 569–734] as a powerful tool for the effective discretization of contact problems. This approach is especially useful when the potential contact interface is large and curved or when non-matching grids are appl...

We review our results obtained by application of the TFETI domain decomposition method to implement the time step of the Newmark scheme for the solution of transient contact problems without friction. If the ratio of the decomposition and discretization parameters is kept uniformly bounded as well as the ratio of the time and space discretization,...

The FETI based domain decomposition method is adapted to implement the time step of the Newmark scheme for the solution of dynamic contact problems without friction. If the ratio of the decomposition and discretization parameters is kept uniformly bounded, then the cost of the time step is proved to be proportional to the number of nodal variables....

This paper deals with the full discretization of quasistatic 3D Signorini problems with local Coulomb friction and a coefficient of friction which may depend on the solution. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is solved by the T-FETI domain decomposition method use...

The point of this work is to extend our results obtained for elastic contact problems to the con-tact problems with non-matching grids which necessarily emerge, e.g., in the solution of transient contact problems or in contact shape optimization. We want to get good approximation and the constraint matrix B with nearly orthogonal rows. We consider...

Modelling of NO adsorption in fixed bed on activated carbon Adsorption experiments of nitric oxide in nitrogen carrier gas were held on activated carbon in a fixed bed flow system. Breakthrough curves describing the dependence of exit concentrations of nitric oxide on time were matched with theoretical response curves calculated from the linear dri...

Adsorption experiments of nitric oxide in nitrogen carrier gas were held on activated carbon in fixed bed flow system. Breakthrough curves describing the dependence of exit concentrations of nitric oxide on time were matched with theoretical response curves calculated from the linear driving force model (LDF). The model assumes Langmuir adsorption...

The solution of the diffusion equation at the non-stationary boundary represents the so-called Stefan problem which can be solved by means of the thermal potential of a double-layer with the accuracy sufficient for description of diffusion phenomena. The results were methods for determination of the mean values of the interdiffusion coefficients. T...

This contribution illustrates the bifurcation behaviour of solutions to contact problems with local Coulomb friction. The bifurcation character of solutions is well-known for models with a low number of degrees of freedom. Our aim is to show that a similar phenomen occurs when a finite element approximation with a high number of degrees of freedom...

We show how we can exploit our recently proposed algorithms for the solution of contact problem of elasticity to the 2D analysis of the interfacial debonding of samples that consist of several fibres embedded in a homogeneous matrix, aligned in the longitudinal direction. The performance of the algorithm is demonstrated on analysis of deformations...

The paper analyzes discrete contact problems with the Coulomb law of friction which involves a solution-dependent coefficient of friction F. Solutions to these problems are defined as fixed points of an auxiliary mapping. It is shown that there exists at least one solution provided that F is bounded and continuous in R(+)(1). Further, conditions gu...

Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used...

The contact shape optimization problems is one of the computationally most challenging problems. The reason is that not only the cost function is a nonlinear implicit function of the design variables, but that its evaluation requires also a solution of the highly nonlinear variational inequality which describes the equilibrium of a system of elasti...