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Local discontinuous Galerkin method for distributed-order time-fractional diffusion-wave equation: Application of Laplace transform

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2021年第6期44卷 4923-4937页

作者： Mohammadi-Firouzjaei, Hadi Adibi, Hojatollah Dehghan, Mehdi Amirkabir Univ Technol Dept Appl Math Fac Math & Comp Sci 424 Hafez Ave Tehran 15914 Iran

In this paper, the Laplace transform combined with the local discontinuous Galerkin method is used for distributed-order time-fractional diffusion-wave equation. In this method, at first, we convert the equation to some time-independent problems by Laplace transform. Then, we solve these stationary equations by the local discontinuous Galerkin method to discretize diffusion operators at the same time. Next, by using a numerical inversion of the Laplace transform, we find the solution of the original equation. One of the advantages of this procedure is its capability to be implemented in a parallel environment. It's another advantage is that the number of stationary problems that should be solved is much less than that is needed in time-marching methods. Finally, some numerical experiments have been provided to show the accuracy and efficiency of the method.

关键词： distributed‐ order time‐ fractional diffusion‐ wave equation Laplace transform local discontinuous Galerkin method parallel algorithms

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algorithms for Large Scale Graphs

Algorithms for Large Scale Graphs

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作者： Russell, Katina Georgetown University

学位级别：Ph.D., Doctor of Philosophy

Constructing efficient algorithms for graph problems is a fundamental problem in computer science *** dissertation studies algorithms for large scale graphs and focuses on directed graph *** consider directed graph problems in several models of computation with the goal of improving performance for large scale graphs. The models of computation include the external memory model, the work-span model for parallel algorithms, and the asymmetric RAM *** hypothesis is there exist provably efficient algorithms for directed graphs problems for large scale graphs. The following results are presented. First, an I/O-efficient algorithm for topologically sorting a directed acyclic graph, as well as an algorithm for identifying and topologically sorting the strongly connected components of a directed graph. Both algorithms cost O(E/B log M/B V/B cdot log 4 V) I/Os and are the first I/O-efficient algorithms for these problems for sparse ***, this work shows an algorithm for constructing a (1+ epsilon) -approximate directed hopset of size Tilde O (n) in Tilde O (m) work and n 1/2+o(1) hopbound. Our parallel version of the algorithm can be used to solve parallel approximate single-source shortest paths in Tilde O (m) work and n 1/2+o(1) *** we show a parallel algorithm for distance-limited shortest paths on directed acyclic graphs with 0 and -1 edge weights. The algorithm computes single-source shortest paths for nodes with distance at least -L , and runs in Tilde O (m) work and O(L 1/2 n 1/2 + o(1) ) ***, we give write-efficient algorithms for breadth-first search, depth-first search and strongly connected components. The standard RAM algorithms for these problems write the solution for each node. Instead, we write only a subset of the nodes to save writes, at the expense of more reads to answer a query. Our result is sublinear size data structures that can answer queries for each of the three graph problems.

关键词： Asymmetric memory models Directed graphs External memory model Graph problems parallel algorithms

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A parallel ALGORITHM for LOCAL POINT DENSITY INDEX COMPUTATION of LARGE POINT CLOUDS 16

A PARALLEL ALGORITHM for LOCAL POINT DENSITY INDEX COMPUTATI...

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16th 3D GeoInfo Conference, 3D GeoInfo 2021

作者： Vo, A.V. Lokugam Hewage, C.N. Le Khac, N.A. Bertolotto, M. Laefer, D. School of Computer Science University College Dublin Ireland Center for Urban Science and Progress New York University United States Department of Civil and Urban Engineering New York University United States

Point density is an important property that dictates the usability of a point cloud data set. This paper introduces an efficient, scalable, parallel algorithm for computing the local point density index, a sophisticated point cloud density metric. Computing the local point density index is non-trivial, because this computation involves a neighbour search that is required for each, individual point in the potentially large, input point cloud. Most existing algorithms and software are incapable of computing point density at scale. Therefore, the algorithm introduced in this paper aims to address both the needed computational efficiency and scalability for considering this factor in large, modern point clouds such as those collected in national or regional scans. The proposed algorithm is composed of two stages. In stage 1, a point-level, parallel processing step is performed to partition an unstructured input point cloud into partially overlapping, buffered tiles. A buffer is provided around each tile so that the data partitioning does not introduce spatial discontinuity into the final results. In stage 2, the buffered tiles are distributed to different processors for computing the local point density index in parallel. That tile-level parallel processing step is performed using a conventional algorithm with an R-tree data structure. While straight-forward, the proposed algorithm is efficient and particularly suitable for processing large point clouds. Experiments conducted using a 1.4 billion point data set acquired over part of Dublin, Ireland demonstrated an efficiency factor of up to 14.8/16. More specifically, the computational time was reduced by 14.8 times when the number of processes (i.e. executors) increased by 16 times. Computing the local point density index for the 1.4 billion point data set took just over 5 minutes with 16 executors and 8 cores per executor. The reduction in computational time was nearly 70 times compared to the 6 hours required without

关键词： parallel algorithms

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Multiwindow discrete Gabor transform using parallel lattice structures

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IET SIGNAL PROCESSING 2020年第7期14卷 420-426页

作者： Li, Rui Tao, Liang Keung Kwan, Hon Anhui Sci & Technol Univ Coll Informat & Network Engn 1501 Huangshan Rd Bengbu 233100 Anhui Peoples R China Anhui Univ Sch Comp Sci & Technol 111 Jiulong Rd Hefei 233100 Anhui Peoples R China Univ Windsor Dept Elect & Comp Engn 401 Sunset Ave Windsor ON N9B 3P4 Canada

The multiwindow discrete Gabor transform (M-DGT) is an effective time-frequency analysis tool to analyse time-varying signals containing components with multiple frequencies. In this study, fast block time-recursive methods for computing the M-DGT coefficients of a signal and the reconstruction of the signal from the transform coefficients are presented with steps as listed, respectively, in algorithms 1 and 2, and their implementations using unified parallel lattice structures are also given. The proposed algorithms consisting of algorithms 1 and 2 for respective forward and inverse transforms are compared to (i) those of the existing serial algorithms in terms of computational complexity and time;and (ii) those of the existing parallel algorithms in terms of hardware complexity. The results indicate that the proposed algorithm is fast in computing M-DGT coefficients of a signal and reconstructing the signal with a reduced hardware complexity.

关键词： discrete transforms parallel algorithms computational complexity signal reconstruction time-frequency analysis transforms signal sampling existing serial algorithms computational complexity existing parallel algorithms M-DGT coefficients multiwindow discrete Gabor effective time-frequency analysis tool time-varying signals time-recursive methods transform coefficients unified parallel lattice structures respective forward transforms inverse transforms

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parallel Algorithm to find Integer k where a given Well-Distributed Graph is k-Metric Dimensional 1

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3rd International Symposium on Signal and Image Processing, ISSIP 2020

作者： Chelladurai, Xavier Kureethara, Joseph Varghese Department of Sciences and Humanities Christ University Bangalore India Department of Mathematics Christ University Bangalore India

ISBN: (数字)9789813369665

ISBN: (纸本)9789813369658

Networks are very important in the world. In signal processing, the towers are modeled as nodes (vertices) and if two towers communicate, then they have an arc (edge) between them or precisely, they are adjacent. The least number of nodes in a network that can uniquely locate every node in the network is known in the network theory as the resolving set of a network. One of the properties that is used in determining the resolving set is the distance between the nodes. Two nodes are at a distance one if there is a single arc can link them whereas the distance between any two random nodes in the network is the least number of distinct arcs that can link them. We propose two algorithms in this paper with the proofs of correctness. The first one is in lines with the BFS that find distance between a designated node to every other node in the network. This algorithm runs in O(log n). The second algorithm is to identify the integer k, such that the given graph is k-metric dimensional. This can be implemented in O(log n) time with O(n2) processors in a CRCW PRAM. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： parallel algorithms

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An Algorithm-Based Fault Tolerance Strategy for the Bitonic Sort parallel Algorithm 10

An Algorithm-Based Fault Tolerance Strategy for the Bitonic ...

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10th Latin-American Symposium on Dependable Computing, LADC 2021

作者： Camargo, Edson T. Duarte, Elias P. Brazil Curitiba Brazil

ISBN: (纸本)9781665478311

High Performance Computing (HPC) systems are employed to solve hard problems and rely on parallel algorithms which present very long execution times-up to several days. These systems are expensive in terms of the computational resources required, including energy consumption. Thus, after failures occur it is highly desirable to loose as little of the work that has already been done as possible. In this work we present an Algorithm-Based Fault Tolerance (ABFT) strategy that can be applied to make a robust version of any hypercube-based parallel algorithm. Note that we do not assume a physical hypercube: After nodes crash, fault-free nodes autonomously adapt themselves according to a logical topology called VCube, preserving several logarithmic properties the proposed strategy guarantees that the algorithm does not halt even after up to (N-1) nodes crash, in a system of N nodes. We use parallel sorting as a case study, describing how to make a fault-Tolerant version of the Bitonic Sort parallel algorithm the algorithm was implemented in MPI using ULMF to handle faults. Experimental results are presented showing the performance and robustness of the proposed solution. © 2021 IEEE.

关键词： parallel algorithms

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Creating Power System Network Layouts: A Fast parallel Algorithm

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IEEE SYSTEMS JOURNAL 2020年第3期14卷 3687-3694页

作者： Olauson, Jon Marin, Manuel Soder, Lennart KTH Royal Inst Technol Dept Elect Power & Energy Syst S-11428 Stockholm Sweden

When analyzing power systems, it is often desirable to visualize the network of buses and branches. Here, a new algorithm for producing 2-D network layouts is proposed. The method consists of two steps: first, a matrix of desired distances between all bus-pairs is computed based on base voltages and branch reactances and, second, coordinates that minimize the errors between desired and actual distances are found. The parallelization used in the latter step is particularly beneficial for interpreted languages;it is shown that layouts for relatively large systems (a few thousand buses) can be produced within seconds on a standard laptop computer using Python or Matlab. Predefined coordinates for selected buses can optionally be given as input. This can be useful, e.g., when one wants to retain some geographical aspects of the system or wish to compare a full and reduced network model. Although the focus here is on power systems, the algorithm can also be used for other types of networks.

关键词： Layout Power systems Matlab Python Transmission line matrix methods parallel algorithms Computational modeling Gradient methods graph theory layout network topology parallel algorithms power systems visualization

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Flexible selective parallel algorithms for big data optimization

Flexible selective parallel algorithms for big data optimiza...

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Asilomar Conference on Signals, Systems & Computers

作者： Amir Daneshmand Francisco Facchinei Vyacheslav Kungurtsev Gesualdo Scutari Dept. of Electrical Engineering at the State Univ. of New York at Buffalo Buffalo USA Dept. of Computer Control and Management Engneering Univ. of Rome La Sapienza Rome Italy Dept. of Computer Science Czech Technical University Prague

We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a nonsmooth (separable), convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. The main contribution of this work is a novel parallel, hybrid random/deterministic decomposition scheme wherein, at each iteration, a subset of (block) variables is updated at the same time by minimizing local convex approximations of the original nonconvex function. To tackle with huge-scale problems, the (block) variables to be updated are chosen according to a mixed random and deterministic procedure, which captures the advantages of both pure deterministic and random update-based schemes. Almost sure convergence of the proposed scheme is established. Numerical results on huge-scale problems show that the proposed algorithm outperforms current schemes.

关键词： Optimization Approximation methods Convergence Big data parallel algorithms Minimization Linear programming

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Combination of parallel Algorithm and Decomposition Projective Method Based on Orthogonal Complement Space 13

Combination of Parallel Algorithm and Decomposition Projecti...

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13th International Conference on Microwave and Millimeter Wave Technology, ICMMT 2021

作者： Zhang, Zhanshuo Sun, Lianyou Hong, Wei Southeast University State Key Laboratory Of Millimeter Waves Nanjing210096 China

ISBN: (纸本)9781665434379

In order to improve the computational efficiency of DPM(Decomposition Projective Method) based on orthogonal complement space, this paper has reformed the computing process of the above mothed as a parallel algorithm. All the same kind of subdomains, such as the unchanged subdomains or the optimized subdomains, is designed to be computed parallelly. The algorithm efficiency is verified by a numerical example. The results show that the mothed performs very well. © 2021 IEEE.

关键词： parallel algorithms

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parallel algorithm for calculating the dynamics of the electron beam current distribution during pulsed heating of a metal target 4

Parallel algorithm for calculating the dynamics of the elect...

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4th Virtual Workshop on Numerical Modeling in MHD and Plasma Physics: Methods, Tools, and Outcomes, MHD-PP 2021

作者： Lazareva, Galina Korneev, Vladimir Maksimova, Anastasia Arakcheev, Aleksey 6 Miklukho-Maklaya str. Moscow117198 Russia Novosibirsk State University 1 Pirogova str. Novosibirsk630090 Russia Institute of Computational Mathematics and Mathematical Geophysics SB RAS 6 Ac. Lavrentieva Pr. Novosibirsk630090 Russia Budker Institute of Nuclear Physics SB RAS 11 Ac. Lavrentieva Pr. Novosibirsk630090 Russia Novosibirsk State Technical University 20 Prospekt K. Marksa Novosibirsk630073 Russia

Speedup and efficiency of two parallel algorithms for calculating the dynamics of the current distribution when the surface of a tungsten sample is heated by an electron beam pulse are presented. The algorithms are implemented using OpenMP technology. A special case of axial symmetry without taking into account electric driving forces is considered. The temperature in the sample, calculated on the basis of the two-phase Stefan problem, is necessary for solving electrodynamic equations. To implement them, the methods of Jacobi and the successive over-relaxation methods were used. Pipelining is used to parallelize the successive over-relaxation algorithm. The current is considered as a possible source of rotation of the substance, which is observed in the experiment. © 2021 Institute of Physics Publishing. All rights reserved.

关键词： parallel algorithms

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