Diffuse-interface treatment of the anisotropic mean-curvature flow

summary:We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples

An asynchronous three-field domain decomposition method for first-order evolution problems

summary:We present an asynchronous multi-domain time integration algorithm with a dual domain decomposition method for the initial boundary-value problems for a parabolic equation. For efficient parallel computing, we apply the three-field domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. The implicit method for time discretization and the multi-domain spatial decomposition enable us to use different time steps (subcycling) on different parts of a computational domain, and thus efficiently capture the underlying physics with less computational effort. We illustrate the performance of the proposed multi-domain time integrator by means of a simple numerical example

Direct approach to mean-curvature flow with topological changes

summary:This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves $\Gamma (t) : S \rightarrow \mathbb{R} ^2$, $t \geqq 0$. The curves are driven by the normal velocity $v$ which is the function of curvature $\kappa$ and the position. The evolution law reads as: $v = -\kappa + F$. The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved by tangential redistribution of curve points which allows long time computations and better accuracy. The results of dislocation dynamics simulation are presented (e. g., dislocations in channel or Frank–Read source). We also introduce an algorithm for treatment of topological changes in the evolving curve

HOMOGENIZATION OF TRANSPORT PROCESSES AND HYDRATION PHENOMENA IN FRESH CONCRETE

The problem of hydration and transport processes in fresh concrete is strongly coupled and non- inear, and therefore, very difficult for a numerical modelling. Physically accurate results can be obtained using fine-scale simulations, which are, however, extremely time consuming. Therefore, there is an interest in developing new physically accurate and computationally effective models. In this paper, a new fully coupled two-scale (meso-macro) homogenization framework for modelling of simultaneous heat transfer, moisture flows, and hydration phenomena in fresh concrete is proposed. A modified mesoscalemodelisfirstintroduced. Inthismodel, concreteisassumedasacompositematerialwithtwo periodically distributed mesoscale components, cement paste and aggregates. A homogenized model is then derived by an upscaling method from the mesoscale model. The coefficients for the homogenized model are obtained from the solution of a periodic cell problem. For solving the periodic cell problem, two approaches are used – a standard finite element method and a simplified closed-form approximation taken from literature. The homogenization framework is then implemented in MATLAB environment and finally employed for illustrative numerical experiments, which verify that the homogenized model provides physically accurate results comparable with the results obtained by the mesoscale model. Moreover, it is verified that, using the homogenization framework with a closed-form approach to the periodic cell problem, significant computational cost savings can be achieved