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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...
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...
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...
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...
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,...
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.
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.
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...
Two mathematical models of railway track oscillations are compared on the basis of numerical experiments.
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.
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.
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.
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.
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...
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...
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