Making full use of a sequential Delaunay-AFT mesher, a parallel method for the generation of large-scale tetrahedral meshes on distributed-memory machines is developed. To generate meshes with the required and the pre...
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Making full use of a sequential Delaunay-AFT mesher, a parallel method for the generation of large-scale tetrahedral meshes on distributed-memory machines is developed. To generate meshes with the required and the preserved properties, a Delaunay-AFT based domain decomposition (DD) technique is employed. Starting from the Delaunay triangulation (DT) covering the problem domain, this technique creates a layer of elements dividing the domain into several zones. The initially coarsely meshed domain is partitioned into DTs of subdomains which can be meshed in parallel. When the size of a subdomain is smaller than a user-specified threshold, it will be meshed with the standard Delaunay-AFT mesher. A two-level DD strategy is designed to improve the parallel efficiency of this algorithm. A dynamic load balancing scheme is also implemented using the Message Passing Interface (MPI). Out-of-core meshing is introduced to accommodate excessive large meshes that cannot be handled by the available memory of the computer (RAM). Numerical tests are performed for various complex geometries with thousands of surface patches. Ultra-large-scale meshes with more than ten billion tetrahedral elements have been created. Moreover, the meshes generated with different numbers of DD operations are nearly identical in quality: showing the consistency and the stability of the automatic decomposition algorithm. (C) 2019 Elsevier Ltd. All rights reserved.
The work of this paper is to solve the Black-Scholes equation under European options based on the time parallel algorithm combined with the kansa method. Firstly, the partial differential equation of the price of deri...
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In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains r...
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In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as forest-of-trees. The framework is grounded on a rich representation of the adaptive mesh suitable for generic finite elements that is built on top of a low-level, light-weight forest-of-trees data structure handled by a specialized, highly parallel adaptive meshing engine, for which we have identified the requirements it must fulfill to be coupled into our framework. Atop this two-layered mesh representation, we build the rest of the data structures required for the numerical integration and assembly of the discrete system of linear equations. We consider algorithms that are suitable for both subassembled and fully assembled distributed data layouts of linear system matrices. The proposed framework has been implemented within the FEMPAR scientific software library, using p4est as a practical forest-of-octrees demonstrator. A strong scaling study of this implementation when applied to Poisson and Maxwell problems reveals remarkable scalability up to 32.2K CPU cores and 482.2M degrees of freedom. Besides, a comparative performance study of FEMPAR and the state-of-the-art deal. II finite element software shows at least comparative performance, and at most a factor of 2-3 improvement in the h-adaptive approximation of a Poisson problem with first- and second-order Lagrangian finite elements, respectively.
The aim of this article is to show that solvers for tridiagonal Toeplitz systems of linear equations can be efficiently implemented for a variety of modern GPU-accelerated and multicore architectures using OpenACC. We...
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A parallel algorithm for solving the 2D shallow water equations coupled with the convection-diffusion equation has been developed, in order to demonstrate the capability and performance of our parallel approach while ...
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In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then em...
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Hash tables are a fundamental data structure for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-...
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Hash tables are a fundamental data structure for effectively storing and accessing sparse data, with widespread usage in domains ranging from computer graphics to machine learning. This study surveys the state-of-the-art research on data-parallel hashing techniques for emerging massively-parallel, many-core GPU architectures. This survey identifies key factors affecting the performance of different techniques and suggests directions for further research.
The stability of a social network has been widely studied as an important indicator for both the network holders and the participants. Existing works on reinforcing networks focus on a local view, e.g., the anchored k...
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One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but ef...
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One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel algorithms have eluded researchers for decades. For sparse high-diameter graphs in particular, there is no known work-efficient parallel algorithm with nontrivial parallelism. This amounts to one of the most fundamental open questions in parallel graph algorithms: Is there a parallel algorithm for digraph reachability with nearly linear work? This article shows that the answer is yes, presenting a randomized parallel algorithm for digraph reachability and related problems with expected work o(m) and span (O) over tilde (n(2/3)), and hence parallelism (O) over tilde (m/n(2/3)) = (Omega) over tilde (n(1/3)), on any graph with n vertices and m arcs. This is the first parallel algorithm having both nearly linear work and strongly sublinear span, i.e., span (O) over tilde (n(1-is an element of)) for any constant is an element of > 0. The algorithm can be extended to produce a directed spanning tree, determine whether the graph is acyclic, topologically sort the strongly connected components of the graph, or produce a directed ear decomposition, all with work (O) over tilde (m) and span (O) over tilde (n(2/3)). The main technical contribution is an efficient Monte Carlo algorithm that, through the addition of a(n) shortcuts, reduces the diameter of the graph to (O) over tilde (n(2/3)) with high probability. While both sequential and parallel algorithms are known with those combinatorial properties, even the sequential algorithms are not efficient, having sequential runtime Omega(mn(Omega(1))). This article presents a surprisingly simple sequential algorithm that achieves the stated diameter reduction and runs in (O) over tilde (m) time. parallelizing that algorithm yields the main result, but doing so involves overcoming several other challen
Edit distance has applications in many domains such as bioinformatics, spell checking, plagiarism checking, query optimization, speech recognition, and data mining. Traditionally, edit distance is computed by dynamic ...
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Edit distance has applications in many domains such as bioinformatics, spell checking, plagiarism checking, query optimization, speech recognition, and data mining. Traditionally, edit distance is computed by dynamic programming based sequential solution which becomes infeasible for large problems. In this paper, we introduce NvPD, a novel algorithm for parallel edit distance computation by resolving dependencies in the conventional dynamic programming based solution. We also establish the correctness of modified dependencies. NvPD exhibits certain characteristics such as balanced workload among processors, less synchronization overhead, maximum utilization of resources and it can exploit spatial locality. It requiresmin(m,n)steps to complete as compared to diagonal based approach that completes inmax(m,n) Experimental evaluation using variety of random and real life data sets over shared memory multi-core systems and graphic processing units (GPUs) show that NvPD outperforms state-of-the-art parallel edit distance algorithms.
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