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Numerical analysis of parallel replica dynamics

Gideon Simpson, Mitchell Luskin (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by...

Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

José R. Fernández (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, the quasistatic thermoviscoelastic thermistor problem is considered. The thermistor model describes the combination of the effects due to the heat, electrical current conduction and Joule's heat generation. The variational formulation leads to a coupled system of nonlinear variational equations for which the existence of a weak solution is recalled. Then, a fully discrete algorithm is introduced based on the finite element method to approximate the spatial variable and an Euler scheme...

Numerical approach to a rate-independent model of decohesion in laminated composites

Zeman, Jan, Gruber, Pavel (2010)

Programs and Algorithms of Numerical Mathematics

In this paper, we present a numerical approach to evolution of decohesion in laminated composites based on incremental variational problems. An energy-based framework is adopted, in which we characterize the system by the stored energy and dissipation functionals quantifying reversible and irreversible processes, respectively. The time-discrete evolution then follows from a solution of incremental minimization problems, which are converted to a fully discrete form by employing the conforming finite...

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke, Tomáš Roubíček (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...

Numerical approaches to the modelling of quasi-brittle crack propagation

Jiří Vala (2023)

Archivum Mathematicum

Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus,...

Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle

Maria I. M. Copetti (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.

Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle

Maria I.M. Copetti (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.

Numerical approximation of flow in a symmetric channel with vibrating walls

Sváček, Petr, Horáček, Jaromír (2010)

Programs and Algorithms of Numerical Mathematics

In this paper the numerical solution of two dimensional fluid-structure interaction problem is addressed. The fluid motion is modelled by the incompressible unsteady Navier-Stokes equations. The spatial discretization by stabilized finite element method is used. The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE) method. The time-space problem is solved with the aid of multigrid method. The method is applied onto a problem of interaction of channel...

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

Numerical model of a pine in a wind

Jan Korbelář, Drahoslava Janovská (1999)

Applications of Mathematics

Steady-state nonlinear differential equations govering the stem curve of a wind-loaded pine are derived and solved numerically. Comparison is made between the results computed and the data from photographs of a pine stem during strong wind. The pine breaking is solved at the end.

Numerical Modelling of Contact Elastic-Plastic Flows

N. M. Bessonov, S. F. Golovashchenko, V. A. Volpert (2009)

Mathematical Modelling of Natural Phenomena

Wilkins' method has been successfully used since early 60s for numerical simulation of high velocity contact elastic-plastic flows. The present work proposes some effective modifications of this method including more sophisticated material model including the Baushinger effect; modification of the algorithm based on correction of the initial configuration of a solid; a contact algorithm based on the idea of a mild contact.

Numerical modelling of semi-coercive beam problem with unilateral elastic subsoil of Winkler's type

Stanislav Sysala (2010)

Applications of Mathematics

A non-linear semi-coercive beam problem is solved in this article. Suitable numerical methods are presented and their uniform convergence properties with respect to the finite element discretization parameter are proved here. The methods are based on the minimization of the total energy functional, where the descent directions of the functional are searched by solving the linear problems with a beam on bilateral elastic ``springs''. The influence of external loads on the convergence properties is...

Numerical simulation of a pulsatile flow through a flexible channel

Cornel Marius Murea (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

An algorithm for approximation of an unsteady fluid-structure interaction problem is proposed. The fluid is governed by the Navier-Stokes equations with boundary conditions on pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary lagrangian Eulerian coordinates and the Finite Element Method for the fluid. In this paper, the continuity of the stresses at the interface was...

Currently displaying 61 – 80 of 98