A study of shared-memory parallelism in a multifrontal solver

L’Excellent, Jean-Yves; Sid-Lakhdar, Wissam M.

doi:10.1016/j.parco.2014.02.003

Cited by 14 publications

(2 citation statements)

References 23 publications

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“…L’Excellent and Sid-Lakhdar (2014) adapt a multifrontal distributed-memory solver to hybrid shared- and distributed-memory machines. Instead of relying solely on multithreaded BLAS to take advantage of the shared-memory parallelism, they introduce a layer in the tree under which subtrees are treated by different threads, while all threads collaborate on the treatments above the layer.…”

Section: Multifrontal Methodsmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

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174

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Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.

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Section: Multifrontal Methodsmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

Self Cite

174

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“…erefore, further research work should be focused on decreasing memory resources and computing time of the multifrontal method, for instance, exploring parallel processing or other implementation technique [37][38][39][40][41]. Moreover, the use of new street symbolic models in terms of novel parameters can be researched as future work, parameters such as touristic requirements, evacuation routes, low-risk routes defined in real time, multiple destination positions, and user-defined preference, among others.…”

Section: Nodal Voltages (Volts) Branchmentioning

confidence: 99%

Exploring a Novel Electrical-Modeling-Based Route Planning for Vehicle Guidance

Callejas-Molina

Díaz-Carmona

Vázquez-Leal

et al. 2020

Mathematical Problems in Engineering

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This work describes a novel Electrical-Modeling-Based Route Planner (EMBRP) for vehicle guidance within city street networks (maps), which uses an equivalent linear electrical circuit considering traffic flow direction, length, and other physical attributes of the streets as parameters for the mathematical model of the circuit branch resistances. Thus, modeling a city as an electrical circuit results in a system of linear equations, which are solved using a multifrontal method implemented in the Unsymmetric Multifrontal Pack (UMFPACK) library. In addition, a Modified Local Current Comparison Algorithm (MLCCA) is proposed with the aim to find a suitable route meeting the correct traffic flow direction. The EMBRP has the functionality to accept user-defined symbolic models in terms of street parameters extracted from a public database allowing different route planning applications. For instance, low-risk route planning schemes can be explored also routes with multiple origins and a single destination can be plotted using only a single simulation, among other possibilities. The EMBRP is illustrated through the description of nine real case studies. According to the obtained results, suitable planning routes and small computing times are achieved by this proposal. A performance comparison, in terms of memory consumption and computing time, among EMBRP, the heuristic A∗ algorithm and Hspice numeric engine is presented. The smallest computing time was achieved by the EMBRP. The EMBRP can be useful for engineers and researchers studying route planning techniques and new street models for specific applications.

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