scholarly journals Calculation of heat transfer in nanoscale heterostructures

2019 ◽  
Vol 21 (3) ◽  
pp. 175-181
Author(s):  
K. K. Abgarian ◽  
I. S. Kolbin
Keyword(s):  
Heat Transfer ◽  
Heat Dissipation ◽  
Parallel Implementation ◽  
Numerical Models ◽  
Hybrid Approach ◽  
Mean Free Path ◽  
Algebraic Equations ◽  
Mesh Free ◽  
Linear Algebraic Equations ◽  
Spatial Approximation

Abstract. The article discusses the calculation of the temperature regime in nanoscale AlAs/GaAs binary heterostructures. When modeling heat transfer in nanocomposites, it is important to take into account that heat dissipation in multilayer structures with layer sizes of the order of the mean free path of energy carriers (phonons and electrons) occurs not at the lattice, but at the layer boundaries (interfaces). In this regard, the use of classical numerical models based on the Fourier law is limited, because it gives significant errors. To obtain more accurate results, we used a model in which the heat distribution was assumed to be constant inside the layer, while the temperature was stepwise changed at the interfaces of the layers. A hybrid approach was used for the calculation: a finite−difference method with an implicit scheme for time approximation and a mesh−free model based on a set of radial basis functions for spatial approximation. The calculation of the parameters of the bases was carried out through the solution of the systems of linear algebraic equations. In this case, only weights of neuroelements were selected, and the centers and «widths» were fixed. As an approximator, a set of frequently used basic functions was considered. To increase the speed of calculations, the algorithm was parallelized. Calculation times were measured to estimate the performance gains using the parallel implementation of the method.

Calculation of the Magnetization of Permanent Magnets, Based on the Method for Solving the Inverse Problem Using Parallel Calculations

2021 ◽  
Vol 64 (1) ◽  
pp. 13-21
Author(s):  
Petr Denisov ◽  
◽  
Anna Balaban ◽  
Keyword(s):  
Inverse Problem ◽  
Permanent Magnets ◽  
Parallel Implementation ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Tikhonov Regularization Method ◽  
Field Pattern ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Matrix

The article proposes the modification of a technique for assessing the magnetization of permanent magnets from the known field pattern. The identification method is based on solving an ill-conditioned system of linear algebraic equations by the Tikhonov regularization method. The method of boundary integral equations based on scalar potentials is used to compile the matrix of coefficients. The article presents the algorithm that uses parallel computations when performing the most time-consuming operations to reduce the time for solving the inverse problem. In order to check the proposed method, a program was developed that allows to simulate the measurement process: to calculate the direct problem and find the magnetic induction at the points of the air gap, then introduce the error into the "measurement results" and solve the inverse problem. The results of nu-merical experiments that allow us to evaluate the advantages of parallel implementation using the capabilities of modern multi-core processors are presented.

scholarly journals Numerical simulation of the non-regular mode of cooling a high-temperature metal billet by the flow of a gas-liquid medium

2018 ◽  
Vol 224 ◽  
pp. 04003
Author(s):  
Sergey Makarov ◽  
Vyacheslav Dement’yev ◽  
Tat’yana Makhneva ◽  
Elena Makarova
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
High Temperature ◽  
Liquid Medium ◽  
Liquid Flow ◽  
Control Volume ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Gas Liquid Flow ◽  
Regular Mode

A mathematical model of heat transfer at cooling a high-temperature metal billet from structural steel by the flow of a gas-liquid medium in a vertical circular channel is presented. The model has been built with the use of the continuum mechanics approaches and the theory of heat-mass transfer. The non-regular mode of cooling is considered. The results of the numerical parametric investigations of the heat transfer at cooling a metal billet are obtained for a standard regime of thermomechanical strengthening on the basis of the mathematical model of conjugate heat transfer in a two-dimensional nonstationary formulation accounting for the symmetry of the cooling medium flow relative to the longitudinal axis of a cylinder. The control volume approach is used for solving the system of differential equations. The flow field parameters are computed by an algorithm SIMPLE. For the iterative solution of the systems of linear algebraic equations the Gauss-Seidel method with under-relaxation is used. Taking into account evaporation in the liquid, the intensity of the change of the rate of cooling the material of the metal cylindrical billet by the laminar gas-liquid flow is analyzed depending on the time of cooling and the velocity of the gas-liquid flow.

Numerical simulation of magnetohydrodynamic micropolar fluid flow and heat transfer in a channel with shrinking walls

2014 ◽  
Vol 92 (9) ◽  
pp. 987-996 ◽  
Author(s):  
Kashif Ali ◽  
Muhammad Ashraf ◽  
Nimra Jameel
Keyword(s):  
Heat Transfer ◽  
Micropolar Fluid ◽  
Thermal Control ◽  
Computational Procedure ◽  
Physical Parameters ◽  
Algebraic Equations ◽  
Iteration Parameter ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Linear Algebraic Equations

We numerically study the steady hydromagnetic (magnetohydrodynamic) flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with shrinking walls. Unlike the classical shooting methodology, two distinct numerical techniques are employed to solve the transformed self-similar nonlinear ordinary differential equations (ODEs). One is the combination of a direct and an iterative method (successive over-relaxation with optimal relaxation parameter) for solving the sparse system of linear algebraic equations arising from the finite difference discretization of the linearised ODEs. For the second one, a pseudotransient method is used where time plays the role of an iteration parameter until the steady state is reached. The two approaches may be easily extended to other geometries (for example, sheets, disks, and cylinders) with possible wall conditions like slip, stretching, rotation, suction, and injection. Effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. Detailed description of the computational procedure and the results of the study may be beneficial for the researchers in the flow and thermal control of polymeric processing.

Heatline Based Thermal Behaviour during Cooling of a Hot Moving Steel Plate Using Single Jet

2014 ◽  
Vol 592-594 ◽  
pp. 1622-1626
Author(s):  
Suman Samanta ◽  
Saikat Mukherjee ◽  
Mrinmoy Dhar ◽  
Shambhunath Barman ◽  
Nilkanta Barman ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Steel Plate ◽  
Numerical Code ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Transfer Region ◽  
Linear Algebraic Equations ◽  
Visualization Process ◽  
Single Jet ◽  
Volume Method

The article deals with visualization of heatlines and isotherms during cooling of a hot moving steel plate numerically. The cooling of the plate is assumed using single spray-water jet. The visualization process is carried out by forming and discretizing the governing energy equation based on finite volume method. The linear algebraic equations are solved by tri-diagonal matrix algorithm (TDMA). Accordingly, a numerical code is developed on FORTRAN platform. In the computational domain, a suitable heat transfer region for cooling is identified analyzing the heatline distribution in the domain and depends on the process parameters. Accordingly a parametric study is performed and reveals that effective heat transfer region increases with increasing jet velocity and cooling methods, and decreases with increasing plate velocity.

scholarly journals Simulations of Complex and Microscopic Models of Cardiac Electrophysiology Powered by Multi-GPU Platforms

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Bruno Gouvêa de Barros ◽  
Rafael Sachetto Oliveira ◽  
Wagner Meira ◽  
Marcelo Lobosco ◽  
Rodrigo Weber dos Santos
Keyword(s):  
Graphics Processing Units ◽  
Cardiac Electrophysiology ◽  
Cluster Computing ◽  
Cardiac Tissue ◽  
Parallel Implementation ◽  
Cell Model ◽  
Numerical Models ◽  
Hybrid Approach ◽  
Conduction Block ◽  
General Purpose

Key aspects of cardiac electrophysiology, such as slow conduction, conduction block, and saltatory effects have been the research topic of many studies since they are strongly related to cardiac arrhythmia, reentry, fibrillation, or defibrillation. However, to reproduce these phenomena the numerical models need to use subcellular discretization for the solution of the PDEs and nonuniform, heterogeneous tissue electric conductivity. Due to the high computational costs of simulations that reproduce the fine microstructure of cardiac tissue, previous studies have considered tissue experiments of small or moderate sizes and used simple cardiac cell models. In this paper, we develop a cardiac electrophysiology model that captures the microstructure of cardiac tissue by using a very fine spatial discretization (8 μm) and uses a very modern and complex cell model based on Markov chains for the characterization of ion channel’s structure and dynamics. To cope with the computational challenges, the model was parallelized using a hybrid approach: cluster computing and GPGPUs (general-purpose computing on graphics processing units). Our parallel implementation of this model using a multi-GPU platform was able to reduce the execution times of the simulations from more than 6 days (on a single processor) to 21 minutes (on a small 8-node cluster equipped with 16 GPUs, i.e., 2 GPUs per node).

Numerical Models for the Sintering of Ceramics in a Multi-Mode Cavity

1994 ◽  
Vol 347 ◽  
Author(s):  
David C. Dibben ◽  
Wai B. Fu ◽  
Ricky A.C. Met Axas
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Models ◽  
Method Of Lines ◽  
Gradient Algorithm ◽  
Microwave Cavity ◽  
Algebraic Equations ◽  
Time Step ◽  
Linear Algebraic Equations ◽  
Multi Mode

ABSTRACTWe present two distinct approaches to the numerical determination of electromagnetic field intensities which must be known before the sintering of ceramics can be modelled in a multi-mode microwave cavity. In the first, a Finite Element Method, we employ edge elements to discretise Maxwell's Equations and apply the conjugate gradient algorithm to solve the resulting system of linear algebraic equations at each time step. The second, which is based on the Method of Lines, is a variant of the Finite Difference Time Domain technique and is used to transform Maxwell's Equations into a set of time-dependent ordinary differential equations. These methods are compared with the help of three examples: a small tray of mashed potatoes placed inside a cavity, a standard waveguide partially filled with a ceramic, and a cavity inhomogeneously loaded with the same material. The good agreements which we have found give us confidence in the soundness of either approach for use in numerical simulation work.

scholarly journals MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1

2021 ◽  
pp. 1-32
Author(s):  
Olga Yurievna Milyukova
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Parallel Implementation ◽  
Sparse Matrix ◽  
Triangular Decomposition ◽  
Algebraic Equations ◽  
First Order ◽  
Partial Inverse ◽  
Linear Algebraic Equations

The paper proposes a new preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix by the method of conjugate gradients – Block Incomplete Inverse Cholesky BIIC preconditioner in combination with a triangular first-order decomposition "by value" - BIIC-IC1. The algorithm based on MPI+OpenMP techniques is proposed for the construction and application of the BIIC preconditioner combined with stabilized triangular decomposition of the second order "by value" (BIIC-IS2S). In this case, the BIIC-IC2S preconditioner uses the number of blocks multiple of the number of processors used and the number of threads used. Two algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the BIIC-IC1 preconditioner. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.

scholarly journals PARALLEL IMPLEMENTATION OF THE YANENKO METHOD FOR SOLVING THE HEAT EQUATION

2021 ◽  
pp. 127-135
Author(s):  
A. N. Semyatova ◽  
E. G. Kenzhebek
Keyword(s):  
Heat Equation ◽  
Parallel Implementation ◽  
Algebraic Equations ◽  
Sweep Method ◽  
Differential Problem ◽  
Computing Systems ◽  
One Dimensional ◽  
Parallel Data ◽  
Linear Algebraic Equations ◽  
Inter Process Communication

In this article, we will consider the parallel implementation of the Yanenko algorithm for the two-dimensional heat equation, and the sweep method was used to numerically solve  the heat equation. The implementation of the sequential  program is carried out simply in two-part steps by the longitudinal-transverse run, however, parallelization of two fractional  steps with an indefinite scheme is difficult due to the creation of inter-process communication of data. In the course of the study, a parallel data distribution with one-dimensional decompositions is shown in the application of the Yanenko method for calculating heat conductivity. The results of parallelization of this task using the 1D decomposition were obtained and acceleration and efficiency images were analyzed in order to evaluate the parallel program. Currently, modeling of processes by numerical solution of differential equations is widely used in every field of Science, the most common methods bring the differential problem to a system of linear algebraic equations, methods that solve such systems include various startup options. The emergence and development of computing systems using Multi-Core processors and graphics accelerators make the problem of startup parallelization relevant; the results of the study are used for teaching in research institutes and universities.

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