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A Scalable parallel algorithm for 3-D Magnetotelluric Finite Element Modeling in Anisotropic Media

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2022年 60卷 1页

作者： Zhu, Xiaoxiong Liu, Jie Cui, Yian Gong, Chunye Natl Univ Def Technol Sci & Technol Parallel & Distributed Proc Lab Lab Software Engn Complex Syst Changsha 410073 Peoples R China Cent South Univ Sch Geosci & Info Phys Changsha 410083 Peoples R China

3-D magnetotelluric (MT) forward modeling has always been faced with the problems of high memory requirements and long computing time. In this article, we design a scalable parallel algorithm for 3-D MT finite element modeling in anisotropic media. The parallel algorithm is based on the distributed mesh storage, including multiple parallel granularities, and is implemented through multiple tools. Message-passing interface (MPI) is used to exploit process parallelisms for subdomains, frequencies, and solving equations. Thread parallelisms for merge sorting, element analysis, matrix assembly, and imposing Dirichlet boundary conditions are developed by Open Multi-Processing (OpenMP). We validate the algorithm through several model simulations and study the effects of topography and conductivity anisotropy on apparent resistivities and phase responses. Scalability tests are performed on the Tianhe-2 supercomputer to analyze the parallel performance of different parallel granularities. Three parallel direct solvers Supernodal LU (SUPERLU), MUltifrontal Massively parallel sparse direct Solver (MUMPS), and parallel Sparse matriX package (PASTIX) are compared in solving sparse systems of equations. As a result, reasonable parallel parameters are suggested for practical applications. The developed parallel algorithm is proven to be efficient and scalable.

关键词： Finite element analysis Mathematical model parallel algorithms Memory management Sparse matrices Conductivity Computational modeling Conductivity anisotropy finite element method (FEM) magnetotelluric (MT) parallel algorithm

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A new parallel algorithm for improving the computational efficiency of multi-GNSS precise orbit determination

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GPS SOLUTIONS 2022年第3期26卷 83-83页

作者： Chen, Xinghan Ge, Maorong Hugentobler, Urs Schuh, Harald German Res Ctr Geosci GFZ Telegrafenberg Potsdam Germany Tech Univ Berlin D-10623 Berlin Germany Tech Univ Munchen TUM Arcisstr 21 D-80333 Munich Germany

The computational efficiency is critical with the increasing number of GNSS satellites and ground stations since many unknown parameters must be estimated. Although only active parameters are kept in the normal equation in sequential least square estimation, the computational cost for parameter elimination is still a heavy burden. Therefore, it is necessary to optimize the procedure of parameter elimination to enhance the computational efficiency of GNSS network solutions. An efficient parallel algorithm is developed for accelerating parameter estimation based on modern multi-core processors. In the parallel algorithm, a multi-thread guided scheduling scheme, and cache memory traffic optimizations are implemented in parallelized sub-blocks for normal-equation-level operations. Compared with the traditional serial scheme, the computational time of parameter estimations can be reduced by a factor of three due to the new parallel algorithm using a six-core processor. Our results also confirm that the architecture of computers entirely limits the performance of the parallel algorithm. All the parallel optimizations are also investigated in detail according to the characteristics of CPU architecture. This gives a good reference to architecture-oriented parallel programming in the future development of GNSS software. The performance of the multi-thread parallel algorithm is expected to improve further with the upgrade of new multi-core coprocessors.s

关键词： parallel algorithm GNSS network Parameter elimination OpenMP

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parallel algorithm development and testing using Petri-object simulation

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INTERNATIONAL JOURNAL OF parallel EMERGENT AND DISTRIBUTED SYSTEMS 2021年第6期36卷 549-564页

作者： Stetsenko, Inna V. Pavlov, Alexander A. Dyfuchyna, Oleksandra Igor Sikorsky Kyiv Polytech Inst Dept Informat & Software Engn Kiev Ukraine

parallel algorithms are problematic to develop because of the negative influence of synchronisation, complicated behaviour of threads' capturing computing resources. Experimental results show performance time's strong dependence on algorithm parameters, such as the number of subtasks and the complexity of each task. The optimal value of subtask complexity is revealed for the particular algorithm. It is the same for different complexity of the parallelised task (with the same computing resource). To guarantee algorithm speed-up it is important to have a method for investigating the efficiency of parallel algorithm before its implementation on specified computing resources. Stochastic Petri net potentially could be a high accuracy tool for investigating the efficiency of a parallel algorithm. However, a huge number of elements are needed to compose a model of non-trivial algorithm that limits the application of this tool in practice. Petri-object simulation method allows replication of Petri nets with specified parameters and model creation of a list of linked Petri-objects. Basic templates for the model creation of a multithreaded algorithm are developed. Applying these templates, the model of the parallel discrete event simulation algorithm is developed and investigated. By the model results, the algorithm parameters providing the least performance time can be determined.

关键词： Multithreaded programming parallel algorithm parallel simulation discrete event simulation stochastic Petri net Java

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A parallel algorithm for Generalized Multiple-set Split Feasibility with Application to Optimal Control Problems

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TAIWANESE JOURNAL OF MATHEMATICS 2022年第5期26卷 1069-1092页

作者： Nguyen Thi Thu Thuy Nguyen Trung Nghia Hanoi Univ Sci & Technol Sch Appl Math & Informat Hanoi Vietnam

In this paper, we concentrate on the generalized multiple-set split feasibility problems in Hilbert spaces and propose a new iterative method for this problem. One of the most important of this method is using dynamic step-sizes, in which the information of the previous step is the only requirement to compute the next approximation. The strong convergence result of the suggested algorithm is proven theoretically under some feasible assumptions. When considering the main results in some special cases, we also obtain some applications regarding the solution of the multiple-set split feasibility problem, the split feasibility problem with multiple output sets, and the split feasibility problem as well as the linear optimal control problem. Some numerical experiments on infinite-dimensional spaces and applications in optimal control problems are conducted to demonstrate the advantages and computational efficiency of the proposed algorithms over some existing results.

关键词： split feasibility problems multiple-set problems parallel algorithm discrete optimal control problems

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parallel algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors

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algorithmS 2023年第5期16卷 242-242页

作者： Lukyanenko, Dmitry Lomonosov Moscow State Univ Fac Phys Dept Math Moscow 119991 Russia

The paper proposes a parallel algorithm for solving large overdetermined systems of linear algebraic equations with a dense matrix. This algorithm is based on the use of a modification of the conjugate gradient method, which is able to take into account rounding errors accumulated during calculations when making a decision to terminate the iterative process. The parallel algorithm is constructed in such a way that it takes into account the capabilities of the message passing interface (MPI) parallel programming technology, which is used for the software implementation of the proposed algorithm. The programming examples are shown using the Python programming language and the mpi4py package, but all programs are built in such a way that they can be easily rewritten using the C/C++/Fortran programming languages. The advantage of using the modern MPI-4.0 standard is demonstrated.

关键词： parallel algorithm conjugate gradient method rounding error MPI MPI-4

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parallel algorithm for modeling temperature fields using the splines method

Parallel algorithm for modeling temperature fields using the...

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IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS)

作者： Zaynidinov, Hakimjon Mallayev, Oybek Kuchkarov, Muslimjon Tashkent Univ Informat Technol Dept Informat Technol Tech Sci Tashkent 100200 Uzbekistan Tashkent Univ Informat Technol Dept Informat Technol Tashkent 100200 Uzbekistan

ISBN: (纸本)9781665440677

The paper is devoted to the construction of an algorithm for parallelization of temperature field modeling processes based on bicubic spline and the problems that arise in it. It takes a lot of time and memory on a computer to model existing large-scale signals of temperature fields in three-dimensional graphical form. Solving these problems on the basis of the proposed parallel algorithm, the development of parallel algorithms and software tools to qualitatively determine the coordinates of high-temperature hotspots of temperature fields and allow them to be monitored continuously, and to calculate the digital processing of existing large-scale signals of temperature fields. Based on this, the article presents a parallel algorithm for digital processing of signals of temperature fields on the basis of bicubic spline and ways to parallel its computational processes using Open MP technology.

关键词： Vectorization parallelism bicubic spline parallel algorithm Open MP interpolation temperature field coefficient approximation parallel processes

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Efficient parallel algorithm for Minimum Cost Submodular Cover Problem with Lower Adaptive Complexity

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2024年第6期41卷

作者： Nguyen, Hue T. Ha, Dung T. K. Pham, Canh V. Grad Univ Sci & Technol Vietnam Acad Sci & Technol VAST Hanoi Vietnam Hanoi Architecture Univ Fac Informat Technol Hanoi Vietnam Vietnam Natl Univ Univ Engn & Technol Fac Informat Technol 144 Xuan Thuy St Hanoi 10000 Vietnam Phenikaa Univ Yen Nghia Ward Fac Comp Sci ORLab Hanoi 12116 Vietnam

In this paper, we study the Minimum Cost Submodular Cover (MCSC) problem over the ground set of size n, which aims at finding a subset with the minimal cost required so that the utility submodular function exceeds a given threshold. The problem has recently attracted a lot of attention due to its applications in various domains of operations research and artificial intelligence. However, the existing algorithms for this problem may not be effectively parallelized because of their costly adaptive complexity. This paper proposes an efficient parallel algorithm that returns a (1 - lambda, (1 + epsilon)(1 +log 1/lambda))-bicriteria approximation solution within O(log n) adaptive complexity, where lambda, epsilon are fixed parameters. Our algorithm requires O(n(2) log(2) n) query complexity, however, it can reduce to O(n log(3) n) instead while retaining a low adaptive complexity of O(log(2)n). Therefore, our algorithm not only achieves the same approximation guarantees as the state of the art but also significantly improves the best-known low adaptive complexity algorithm for the above problem.

关键词： Submodular cover approximation algorithm parallel algorithm

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parallel algorithm for Minimum Partial Dominating Set in Unit Disk Graph 15th

Parallel Algorithm for Minimum Partial Dominating Set in Uni...

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15th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Hong, Weizhi Zhang, Zhao Ran, Yingli Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Zhejiang Peoples R China

ISBN: (纸本)9783030926816;9783030926809

In this paper, we consider the minimum partial dominating set problem in unit disk graphs (MinPDS-UD). Given a set of points V on the plane with vertical bar V vertical bar = n, two points in V are adjacent in the unit disk graph if their Euclidean distance is no larger than one unit length. A point dominates itself and all its neighboring points. For an integer k <= n, the goal of MinPDS-UD is to find a minimum subset of points D subset of V such that at least k points are dominated by D. We present the first parallel algorithm for MinPDS-UD. It runs in O(log n) rounds on O(n) machines, and achieves a constant approximation ratio.

关键词： Partial dominating set Unit disk graph parallel algorithm Approximation ratio

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A parallel algorithm Based on Regularized Lattice Boltzmann Method for Multi-Layer Grids

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APPLIED SCIENCES-BASEL 2024年第16期14卷 6976页

作者： Liu, Zhixiang Zhao, Yunhao Zhu, Wenhao Wang, Yang Shanghai Ocean Univ Coll Informat Technol Shanghai 201306 Peoples R China Shanghai Univ Sch Comp Engn & Sci Shanghai 200444 Peoples R China

The regularized lattice Boltzmann method (RLBM) is an improvement of the lattice Boltzmann method (LBM). The advantage of RLBM is improved accuracy without increasing computational overheads. The paper introduces the method of multi-layer grids, the multi-layer grids have different resolutions which can accurately solve problems in computational fluid dynamics (CFD) without destroying the parallelism of RLBM. Simulating fluid flow usually requires a large number of grid simulations. Therefore, it is necessary to design a parallel algorithm for RLBM based on multi-layer grids. In this paper, a load-balancing-based grid dividing algorithm and an MPI-based parallel algorithm for RLBM on multi-layer grids are proposed. The load balancing-based grid dividing algorithm ensures that the workload is evenly distributed across processes, minimizing the discrepancies in computational load. The MPI-based parallel algorithm for RLBM on multi-layer grids ensures accurate and efficient numerical simulation. Numerical simulations have verified that the proposed algorithms exhibit excellent performance in both 2D and 3D experiments, maintaining high stability and accuracy. The multi-layer grids method is significantly better than single-layer grids in terms of CPU runtime and number of grids required. Comparative analysis with the OpenMP multi-threading method on the multi-layer grid RLBM shows that the proposed algorithm in this paper achieves superior speedup and efficiency.

关键词： regularized lattice Boltzmann method multi-layer grids parallel algorithm numerical simulation

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A New parallel algorithm for Solving a Class of Variational Inequalities

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ACTA APPLICANDAE MATHEMATICAE 2024年第1期192卷 1-1页

作者： Ha, Nguyen Song Tuyen, Truong Minh Van Huyen, Phan Thi Thainguyen Univ Sci Thainguyen Vietnam Thainguyen Univ Technol Thainguyen Vietnam

In this paper, we study the variational inequality over the solution set of the split common solution problem with multiple output sets for monotone operator equations in real Hilbert spaces. We propose a new approach for solving this problem without depending on the norm of the transfer mappings. Some of its applications for solving the variational inequality over the solution set of the split common fixed point problem with multiple output sets and related problems are also mentioned. Finally, we give numerical examples to illustrate the performance of the proposed algorithm and compare it with several existing previous algorithms.

关键词： Hilbert space Monotone operator Variational inequality parallel algorithm

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