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Open AccessArticle

Multiobjective Optimization of a Metal Complex Catalytic Reaction Based on a Detailed Kinetic Model with Parallelization of Calculations

by

Sergey Koledin

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Kamila Koledina

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Irek Gubaydullin

Mathematics 2023, 11(9), 2051; https://doi.org/10.3390/math11092051 - 26 Apr 2023

Viewed by 277

Abstract

The solution of the multiobjective optimization problem was performed with the help of the Pareto approximation algorithm. The problem of multiobjective optimization of the reaction process conditions for the olefin hydroalumination catalytic reaction, with the presence of organoaluminum compounds diisobutylaluminiumchloride, diisobutylaluminiumhydrate, and triisobutylaluminum, [...] Read more.

The solution of the multiobjective optimization problem was performed with the help of the Pareto approximation algorithm. The problem of multiobjective optimization of the reaction process conditions for the olefin hydroalumination catalytic reaction, with the presence of organoaluminum compounds diisobutylaluminiumchloride, diisobutylaluminiumhydrate, and triisobutylaluminum, was solved. The optimality criteria are the yield of the reaction resultants. The largest yield of the high-order organoaluminum compound Bu₂AlR was observed for the reactions with diisobutylaluminiumhydrate and triisobutylaluminum. Such results were obtained due to the fact that in the case of diisobutylaluminiumchloride, Bu₂AlR was used for the formation of ClBuAlR. The yield of the Schwartz reagent Cp₂ZrHCl was higher by a third in the reaction in the presence of diisobutylaluminiumchloride. Unlike the experimental isothermal conditions, the temperature optimal control showed the sufficiency of the gradual growth temperature for achieving the same or higher values of optimality criteria. For computational experiments, the algorithm for solving the multi-criteria optimization problem was parallelized using an island model. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

Apex Method: A New Scalable Iterative Method for Linear Programming

by

Leonid B. Sokolinsky

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Irina M. Sokolinskaya

Mathematics 2023, 11(7), 1654; https://doi.org/10.3390/math11071654 - 29 Mar 2023

Viewed by 407

Abstract

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact [...] Read more.

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of a linear programming problem. The optimal path refers to a path of the minimum length according to the Euclidean metric. The apex method is based on the predictor—corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of the linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. AlsoAdditionally, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain

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Mathematics 2023, 11(3), 669; https://doi.org/10.3390/math11030669 - 28 Jan 2023

Viewed by 626

Abstract

The article is devoted to the development of the mathematical model of oxidative regeneration of the cylindrical catalyst grain. The model is constructed using a diffusion approach to modeling catalytic processes. The model is based on the equations of material and thermal balance. [...] Read more.

The article is devoted to the development of the mathematical model of oxidative regeneration of the cylindrical catalyst grain. The model is constructed using a diffusion approach to modeling catalytic processes. The model is based on the equations of material and thermal balance. Mass transfer in the catalyst grain is carried out due to diffusion and the Stefan flow resulting from a decrease in the reaction volume during sorption processes. Chemical transformations of substances are taken into account as a source term in the equation. The thermal balance of the catalyst grain is described by a thermal conductivity equation, with an inhomogeneous term responsible for heating the grain during exothermic chemical reactions. The effective coefficients of heat capacity and thermal conductivity of the catalyst grain, which are determined taking into account the porosity of the grain depending on temperature, were used to calculate the thermal balance of the catalyst grain. The dependencies are approximated using the method of least squares based on experimental data. Different boundary conditions for the developed model allow calculating the main characteristics of the oxidative regeneration process for a whole catalyst grain under different conditions. The mathematical model of oxidative regeneration of a cylindrical catalyst grain is described by a stiff system of differential equations. Splitting by physical processes is applied to avoid computational difficulties. The calculation of flows is carried out sequentially: first, chemical problems are solved using the Radau method, then the diffusion and thermal conductivity equations are solved by the finite volume method. The result of the algorithm implemented in C++ is a picture of the distribution of substances and temperature along the cylindrical grain of the catalyst. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

Energy Efficiency of a New Parallel PIC Code for Numerical Simulation of Plasma Dynamics in Open Trap

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Mathematics 2022, 10(19), 3684; https://doi.org/10.3390/math10193684 - 08 Oct 2022

Viewed by 733

Abstract

The generation of energy-efficient parallel scientific codes became very important in the time of carbon footprint reduction. In this paper, we briefly present our latest particle-in-cell code with the results of a numerical simulation of plasma dynamics in an open trap. This code [...] Read more.

The generation of energy-efficient parallel scientific codes became very important in the time of carbon footprint reduction. In this paper, we briefly present our latest particle-in-cell code with the results of a numerical simulation of plasma dynamics in an open trap. This code can be auto-vectorized by the Fortran compiler for Intel Xeon processors with AVX-512 instructions such as Intel Xeon Phi and the highest series of all generations of Intel Xeon Scalable processors. Efficient use of processor architecture is the main feature of an energy-efficient solution. We present a step-by-step methodology of energy consumption calculation using Intel hardware features and Intel VTune software. We also give an estimated value of carbon footprint with the impact of high-performance water cooled hardware. The Power Usage Effectiveness (PUE) in the case of high-performance water cooled hardware is equal to 1.03–1.05, and is up to 1.3 in the case of air-cooled systems. This means that power consumption of liquid cooled systems is lower than that air-cooled ones by up to 25%. All these factors play an important role in the carbon footprint reduction problem. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

On Solving the Problem of Finding Kinetic Parameters of Catalytic Isomerization of the Pentane-Hexane Fraction Using a Parallel Global Search Algorithm

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Mathematics 2022, 10(19), 3665; https://doi.org/10.3390/math10193665 - 06 Oct 2022

Cited by 2 | Viewed by 636

Abstract

This article is devoted to the problem of developing a kinetic model of a complex chemical reaction using a parallel optimization method. The design of the kinetic model consists of finding the kinetic parameters of the reaction, which cannot be calculated analytically, and [...] Read more.

This article is devoted to the problem of developing a kinetic model of a complex chemical reaction using a parallel optimization method. The design of the kinetic model consists of finding the kinetic parameters of the reaction, which cannot be calculated analytically, and since the chemical reaction involves many stages, the optimization problem is multiextremal. As a chemical reaction, the process of catalytic isomerization of the pentane-hexane fraction is considered, which is now important due to the switch of the oil refining industry to the production of gasoline corresponding to the Euro-5 standard. On the basis of known industrial data on the concentrations of reaction components and the temperature at the outlet of the third reactor, the activation energies and pre-exponential factors of each reaction stage were calculated. To solve the optimization problem, the authors developed a parallel global search algorithm and a program based on Lipschitz optimization. The kinetic parameters found made it possible to develop a mathematical model of the process, which is in good agreement with industrial data. The developed mathematical model in future works will make it possible to study the dynamics of the gas–liquid flow in the reactor unit, taking into account diffusion and heat exchange processes through the catalyst layer. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessFeature PaperArticle

Studying the Efficiency of Parallelization in Optimal Control of Multistage Chemical Reactions

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Mathematics 2022, 10(19), 3589; https://doi.org/10.3390/math10193589 - 01 Oct 2022

Cited by 1 | Viewed by 680

Abstract

In this paper, we investigate the problem of optimal control of complex multistage chemical reactions, which is considered a nonlinear global constrained optimization problem. This class of problems is computationally expensive due to the inclusion of multiple parameters and requires parallel computing systems [...] Read more.

In this paper, we investigate the problem of optimal control of complex multistage chemical reactions, which is considered a nonlinear global constrained optimization problem. This class of problems is computationally expensive due to the inclusion of multiple parameters and requires parallel computing systems and algorithms to obtain a solution within a reasonable time. However, the efficiency of parallel algorithms can differ depending on the architecture of the computing system. One available approach to deal with this is the development of specialized optimization algorithms that consider not only problem-specific features but also peculiarities of a computing system in which the algorithms are launched. In this work, we developed a novel parallel population algorithm based on the mind evolutionary computation method. This algorithm is designed for desktop girds and works in synchronous and asynchronous modes. The algorithm and its software implementation were used to solve the problem of the catalytic reforming of gasoline and to study the parallelization efficiency. Results of the numerical experiments are presented in this paper. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

OMPEGAS: Optimized Relativistic Code for Multicore Architecture

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Mathematics 2022, 10(14), 2546; https://doi.org/10.3390/math10142546 - 21 Jul 2022

Viewed by 871

Abstract

The paper presents a new hydrodynamical code, OMPEGAS, for the 3D simulation of astrophysical flows on shared memory architectures. It provides a numerical method for solving the three-dimensional equations of the gravitational hydrodynamics based on Godunov’s method for solving the Riemann problem and [...] Read more.

The paper presents a new hydrodynamical code, OMPEGAS, for the 3D simulation of astrophysical flows on shared memory architectures. It provides a numerical method for solving the three-dimensional equations of the gravitational hydrodynamics based on Godunov’s method for solving the Riemann problem and the piecewise parabolic approximation with a local stencil. It obtains a high order of accuracy and low dissipation of the solution. The code is implemented for multicore processors with vector instructions using the OpenMP technology, Intel SDLT library, and compiler auto-vectorization tools. The model problem of simulating a star explosion was used to study the developed code. The experiments show that the presented code reproduces the behavior of the explosion correctly. Experiments for the model problem with a grid size of

128 \times 128 \times 128

were performed on an 16-core Intel Core i9-12900K CPU to study the efficiency and performance of the developed code. By using the autovectorization, we achieved a 3.3-fold increase in speed in comparison with the non-vectorized program on the processor with AVX2 support. By using multithreading with OpenMP, we achieved an increase in speed of 2.6 times on a 16-core processor in comparison with the vectorized single-threaded program. The total increase in speed was up to ninefold. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessArticle

A New Parallel Code Based on a Simple Piecewise Parabolic Method for Numerical Modeling of Colliding Flows in Relativistic Hydrodynamics

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Mathematics 2022, 10(11), 1865; https://doi.org/10.3390/math10111865 - 30 May 2022

Viewed by 950

Abstract

A new parallel code based on models of special relativistic hydrodynamics is presented for describing interacting flows. A new highly accurate numerical method is considered and verified. A parallel implementation of the method by means of Coarray Fortran technology and its efficiency are [...] Read more.

A new parallel code based on models of special relativistic hydrodynamics is presented for describing interacting flows. A new highly accurate numerical method is considered and verified. A parallel implementation of the method by means of Coarray Fortran technology and its efficiency are described in detail. The code scalability is 92% on a cluster with Intel Xeon 6248R NKS-1P with 192 Coarray Fortran images. Different interacting relativistic flows are considered as astrophysical applications. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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Open AccessFeature PaperArticle

Fast Summarization of Long Time Series with Graphics Processor

by

Mikhail Zymbler

and

Andrey Goglachev

Mathematics 2022, 10(10), 1781; https://doi.org/10.3390/math10101781 - 23 May 2022

Cited by 1 | Viewed by 857

Abstract

Summarization of a long time series often occurs in analytical applications related to decision-making, modeling, planning, and so on. Informally, summarization aims at discovering a small-sized set of typical patterns (subsequences) to briefly represent the long time series. Apparent approaches to summarization like [...] Read more.

Summarization of a long time series often occurs in analytical applications related to decision-making, modeling, planning, and so on. Informally, summarization aims at discovering a small-sized set of typical patterns (subsequences) to briefly represent the long time series. Apparent approaches to summarization like motifs, shapelets, cluster centroids, and so on, either require training data or do not provide an analyst with information regarding the fraction of the time series that a typical subsequence found corresponds to. Recently introduced, the time series snippet concept overcomes the above-mentioned limitations. A snippet is a subsequence that is similar to many other subsequences of the time series with respect to a specially defined similarity measure based on the Euclidean distance. However, the original Snippet-Finder algorithm has cubic time complexity concerning the lengths of the time series and the snippet. In this article, we propose the PSF (Parallel Snippet-Finder) algorithm that accelerates the original snippet discovery schema with GPU and ensures acceptable performance over very long time series. As opposed to the original algorithm, PSF splits the calculation of the similarity of all the time series subsequences to a snippet into several steps, each of which is performed in parallel. Experimental evaluation over real-world time series shows that PSF outruns both the original algorithm and a straightforward parallelization. Full article

(This article belongs to the Special Issue Parallel Computing and Applications)

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