The analysis of parallel OpenFOAM solver for the heat transfer in electrical power cables

Proceedings of the First PhD Symposium on Sustainable Ultrascale Computing Systems (NESUS PhD 2016) Timisoara, Romania. February 8-11, 2016.Here we present the part of results obtained in PhD thesis “The investigation of efficiency of physical phenomena modelling using differential equations on distributed systems” by Andrej Bugajev. This work is dedicated to development of mathematical modelling software. While applying a numerical method it is important to take into account the limited computer resources, the architecture of these resources and how do methods affect software robustness. Three main aspects of this investigation are that software implementation must be efficient, robust and be able to utilize specific hardware resources. The hardware specificity in this work is related to distributed computations. The investigation is done for FVM method usage to implement efficient calculations of a very specific heat transferring problem. That lets to create technological components that make a software implementation robust and efficient. OpenFOAM open source software is selected as a basis for implementation of calculations and a few algorithms to solve efficiency issues are proposed. The FVM parallel solver is implemented and analyzed, it is adapted to heterogeneous cluster Vilkas.European Cooperation in Science and Technology. COSTThe paper was supported by NESUS project Winter School & PhD Symposium 2016

On Efficiency of the OpenFOAM-based Parallel Solver for the Heat Transfer in Electrical Power Cables

Proceedings of: First International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2014). Porto (Portugal), August 27-28, 2014.In this work, we study the efficiency of the OpenFOAM-based parallel solver for the heat conduction in electrical power cables. The 2D benchmark problem with three cables is used for our numerical tests. We study and compare the efficiency of conjugate gradient solver with diagonal incomplete Cholesky (DIC) preconditioner and generalized geometric algebraic multigrid solver (GAMG), which is available in Open- FOAM. The convergence and parallel scalability of the solvers are presented and analyzed. Parallel numerical tests are performed on the cluster of multicore computers.The work of authors was supported by Eureka project E!6799 POWEROPT "Mathematical modelling and optimization of electrical power cables for an improvement of their design rules". The work presented in this paper has been partially supported by EU under the COST programme Action IC1305, ’Network for Sustainable Ultrascale Computing (NESUS)’

Distributed Parallel Computing for Visual Cryptography Algorithms

Proceedings of: Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015). Krakow (Poland), September 10-11, 2015.The recent activities to construct exascale and ultrascale distributed computational systems are opening a possibility to apply parallel and distributed computing techniques for applied problems which previously were considered as not solvable with the standard computational resources. In this paper we consider one global optimization problem where a set of feasible solutions is discrete and very large. There is no possibility to apply some apriori estimation techniques to exclude an essential part of these elements from the computational analysis, e.g. applying branch and bound type methods. Thus a full search is required in order to solve such global optimization problems. The considered problem describes visual cryptography algorithms. The main goal is to find optimal perfect gratings, which can guarantee high quality and security of the visual cryptography method. The full search parallel algorithm is based on master-slave paradigm. We present a library of C++ templates that allow the developer to implement parallel master-slave algorithms for his application without any parallel programming and knowledge of parallel programming API. These templates automatically give parallel solvers tailored for clusters of computers using MPI API and distributed computing applications using BOINC API. Results of some computational experiments are presented.The work presented in this paper has been partially supported by EU under the COST programme Action IC1305, ’Network for Sustainable Ultrascale Computing (NESUS)’

The mathematical simulation of the liquid transport in a multilayered nonwoven

In this report we treat an optimization task, which should make the choice of nonwoven for making diapers faster. A mathematical model for the liquid transport in nonwoven is developed. The main attention is focussed on the handling of fully and partially saturated zones, which leads to a parabolic-elliptic problem. Finite-difference schemes are proposed for numerical solving of the differential problem. Paralle algorithms are considered and results of numerical experiments are given

The Mathematical Simulation Of The Liquid Transport In A Multilayered Nonwoven

In this report we treat an optimization task, which should make the choice of nonwovens for making diapers faster. A mathematical model for the liquid transport in nonwoven is developed. Finite-difference schemes are proposed for numerical solving of the differential problem. Parallel algorithms are considered and results of numerical experiments are given. 1. INTRODUCTION It is shown in Alt and Luckhaus [1] that mathematical models of the liquid transport in multilayered nonwovens leads to an elliptic-parabolic equation since this problem becomes elliptic in the region of saturation. In the parabolic region equation is of nonlinear degenerate parabolic type and it can lead to a nonlinear convection-dominated diffusion equation, at least in some parts of the domain. In our model the convection is due to the gravity. Effects of multilayered liquid transport are also included into our mathematical model. This paper deals with numerical methods for solving problems described above. Finit..

Stability analysis of some odd-even schemes for two-dimensional diffusion and Schrödinger problems

A stability analysis is given for two classes of odd-even finite-difference schemes, which approximate the two dimensional variable coefficient heat conduction and the Schrödinger problems. Sufficient and necessary stability conditions are derived for the von Neumann stability for the case of constant coefficient problems. The case of variable coefficients is investigated by the discrete energy method