N. Sczygiol

Application of Mixed Time Partitioning Methods to Raise the Efficiency of Solidification Modeling

In this paper we focus on the application of a mixed time partitioning methods to raise efficiency of the solidification kernel in the NuscaS system. We are proposing using a fixed time step in the casting and its integer multiple in other parts of mould because the time step size determines the accuracy of the simulation results. By means of numerical experiments we show that our approach allows for up to about three times performance improvement as compared to the standard approach without loosing precision of results. Moreover, this methods will be extended to 3D numerical simulation in a future work. We notice also that our method can be combined with parallel processing to further improve performance of solidification kernels.

Parallel Finite Element Modeling of Solidification Processes

In the paper, parallelization of finite element modeling of solidification is considered. The core of this modeling is solving large sparse linear systems. The Aztec library is used for implementing the model problem on massively parallel computers. Now the complete parallel code is available. The performance results of numerical experiments carried out on the IBM SP2 parallel computer are presented.

Statistics of Critical Avalanches in Vertical Nanopillar Arrays

Nanopillar arrays are encountered in numerous areas of nanotechnology such as bio-medical and chemical sensing, nanoscale electronics, photovoltaics or thermoelectrics. Especially arrays of nanopillars subjected to uniaxial microcompression reveal the potential applicability of nanopillars as components for the fabrication of electro-mechanical sense devices. Thus, it is worth to analyze the failure progress in such systems of pillars. Under the growing load pillars destruction forms an avalanche and when the load exceeds a certain critical value the avalanche becomes self-sustained until the system is completely destroyed. In this work we have explored the distributions of such catastrophic avalanches appearing in overloaded systems. Specifically, we analyze the relations between the size of an avalanche being the numbers of instantaneously crushed pillars and the size of the corresponding array of nanopillars using different load transfer protocols.

Estimate the Impact of Different Heat Capacity Approximation Methods on the Numerical Results During Computer Simulation of Solidification

The article presents the results of numerical modeling of the solidification process. We focused on comparing the results of calculations for various methods of the effective thermal capacity approximation used in the apparent heat capacity formulation of solidification. Apparent heat capacity formulation is one of the enthalpy formulations of solidification, which allows effective simulation of casting solidification with the one domain approach. In particular, we have shown that the choice of one of four tested methods of approximation does not significantly affect the results. Differences in the resulting temperature did not exceed a few degrees. However, it can affect the time needed to execute the numerical simulations. All presented numerical algorithms were implemented in our in-house software. The software is based on very efficient and scalable libraries that ensures applicability to real world engineering problems.

Implementation Aspects of a Recovery-Based Error Estimator in Finite Element Analysis

The paper is devoted to the use of error estimators based on gradient recovery in finite element computations, where the resulting error estimates can be used as the basis for hp-adaptive mesh refinement. Due to high complexity of adaptive numerical software we have decided to take advantage of the object-oriented paradigm of software development. We discuss our implementation of the Zienkiewicz-Zhu error estimator and of selected gradient recovery techniques (averaging and superconvergent patch recovery).

Numerically Stable Computer Simulation of Solidification: Association Between Eigenvalues of Amplification Matrix and Size of Time Step

The constantly increasing demand for efficient and precise computational solvers becomes the crucial factor deciding about usability of a given domain specific simulation software. The main idea of this article is the use of eigenvalues of amplification matrices to determine the size of time step in modeling of solidification. As far as numerical simulations are concerned it is very important to obtain solutions which are stable and physically correct. It is acquired by fulfilling many assumptions and conditions during the construction a numerical model and carrying out computer simulations. One of the conditions is a proper selection of time step. The size of time step has a great impact on the stability of used time integration schemes (e.g. explicit scheme), or on a proper image of physical phenomena occurring during the simulation (e.g. implicit scheme). The eigenvalues of amplification matrix in governing equations influence on the appropriate selection of size of time step in computer simulations. Hence, it allows to better fit the size of time step and time integration scheme for modeled structure.

Distribution of the Distance Between Receptors of Ordered Micropatterned Substrates

We study the statistics of equally spaced pairs of receptors on a family of ordered flat microsubstrates whose adhesive centers form regular tessellations. We establish relationship between the symmetry of substrates and the probability density of the end-to-end polymer separation in terms of the so-called Manhattan distance.

Estimation of Susceptibility to Hot Tearing in Solidifying Casting

Hot tearing, also called hot cracking, is a serious defect that appears during the solidification of an alloy. Due to the low recurrence of the phenomena occurring during alloy solidification, such as the evolution of grained structure or stress redistributions, the casting’s susceptibility to hot tearing can be estimated only in an approximate way. Predicting the appearance of hot tears in alloys is thus an important issue in industrial practice. This work concerns with a new criterion for hot tearing evaluation in castings. An algorithm for the computer simulations of the phenomena accompanying the casting formation is introduced and discussed.

The Use of Scalability of Calculations to Engineering Simulation of Solidification

The paper focuses on the use of scalability of available development tools to engineering simulation of solidification in the mold. An essential aspect of the considerations are the ways parallelization of computations taking into account the contact between the two materials. The implementation uses a TalyFEM and PETSc library. A problem solved with finite element method (FEM) can be parallelized in two ways: the parallelization on the mathematical formulas level and the division of tasks into smaller subtasks—assignment of nodes and elements into specific computational units. Both methods can be used in the TalyFEM library if the input files loading module is modified. We have designed our own parallel input module (finite element mesh) providing a division of loaded nodes and elements into individual computational units. Our solutions enable the full potential of parallel computing available in the TalyFEM library using the MPI protocol. This implemented software can be run on any computer system with distributed memory.

Statistics of End-to-End Distance of a Linear Chain Trapped in a Cubic Lattice of Binding Centers

Two and three dimensional nanostructured substrates are widely employed in a variety of biomedically-oriented nanodevices as well as in functional devices created with the use of DNA scaffolding. In this context spatial arrangements of binding centers influence the efficiency of these substrates. Here, we concentrate on 3D substrates and we compute and analyze the distribution of distances (q) between binding centers in the case where the centers are localized in nodes of a cubic lattice. We find that for this particular lattice the exact node-to-node probability distribution is a fifth-degree polynomial in q. We merge this polynomial-shaped distribution with an end-to-end distance distribution of a linear chain and we find an excellent agreement between it and the corresponding distribution for a self-avoiding walk in 3D.