Node-to-Node Realization of Meshless Local Petrov Galerkin (MLPG) Fully in GPU

Amorim, Lucas Pantuza; Mesquita, Renato C.; Goveia, Thiago de Sousa; Correa, Bruno

doi:10.1109/access.2019.2948134

Cited by 3 publications

(5 citation statements)

References 32 publications

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“…GPUs were designed to act as highly parallel coprocessors, initially for graphics processing. With the GPGPU (General Purpose GPU) strengthening, through the use of programming languages (such as OpenCL, OpenMP and CUDA) and libraries (such as CUSPARSE, CUSP and CUBLAS) that allowed the general use programs creation, computational problems cost and potentially parallelizable of diverse areas of science have been rethought for the device [15], [18].…”

Section: Gpus For Scientific Computingmentioning

confidence: 99%

“…C. Solver The linear equation system, 𝐴𝑥 = 𝑏, resulting from the FEM can be solved iteratively by methods that use the Krylov subspaces to find successive approximate solutions, 𝐴 ∈ 𝑅 𝑛×𝑛 and 𝑥, 𝑏 ∈ 𝑅 𝑛 [1], [4][5][6][7], [18]. This choice is due to the following properties:…”

Section: Bmentioning

confidence: 99%

“…The CG method adapted to GPU [1], [10], [12], [18] is used in this work, whose computational cost is smaller and optimized than its EbE-FEM counterpart when the data is processed in the assembled matrix. The solver steps can be decomposed into variables initialization, inner products, vector updates and matrix-vector multiplications, operations with properties that can be exploited under parallel computing environments.…”

Section: Bmentioning

confidence: 99%

“…With the advent of General Purpose Graphics Processing Unit (GP-GPU), several works that harness the massively distributed properties of these devices have been proposed in the literature with the aim of improving computational performance. See for example [1]- [3], [8]- [13], [18]- [19] and references therein.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

GPU Finite Element Method Computation Strategy Without Mesh Coloring

Amorim

Goveia

Mesquita

et al. 2020

J. Microw. Optoelectron. Electromagn. Appl.

Self Cite

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Section: Gpus For Scientific Computingmentioning

confidence: 99%

Section: Bmentioning

confidence: 99%

Section: Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

GPU Finite Element Method Computation Strategy Without Mesh Coloring

Amorim

Goveia

Mesquita

et al. 2020

J. Microw. Optoelectron. Electromagn. Appl.

Self Cite

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“…Zaharovits et al [17] designed a shared memory parallel conjugate gradient method solver for the topology optimization of the finite element method. Amorim et al [18] proposed the Meshless Local Petrov Galerkin Method (MLPG) algorithm to assemble the element stiffness matrix in 2019, and compared the speed difference between the BICG method and related methods of the conjugate gradient method family. Previous research experience shows that if the dimensions of the sparse equations considered are small, using a GPU has no obvious advantage over the CPU.…”

Section: Introductionmentioning

confidence: 99%

Strength Check of Aircraft Parts Based on Multi-GPU Clusters for Fast Calculation of Sparse Linear Equations

Zhang

Hu²

2020

IEEE Access

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In order to improve the cost-effectiveness ratio, the next-generation vehicle needs to meet the requirements of reuse, while adopting a lighter structural weight, so it is necessary to realize the strength calculation and condition monitoring of key components in the digital twin. Most of the current monitoring methods are based on the characteristics of various data acquisition systems, but they need the support of a large number of flight data. The disadvantages of the above strategy can be avoided by reducing the structure of aircraft components to a finite element model and quickly checking the key components in the health management system. In order to solve the problem of fast calculation of the finite element model of the key components of the aircraft, a parallel algorithm and framework of large-scale sparse matrix preprocessing conjugate gradient method based on CUDA(Compute Unified Device Architecture) technology is proposed in the multi GPU(Graphics Processing Unit) workstation cluster environment. Once the sparse matrix is too large to be processed in a single workstation, this paper discusses how to realize the optimized data segmentation in the distributed multi-GPU computing environment. For the problem of iterative solution of matrix preprocessing, two preprocessing strategies of matrix bandwidth reduction parallelization and incomplete Cholesky decomposition are proposed, and asynchronous task concurrency and load balancing strategies are designed on the architecture. The calculation of some examples in the standard sparse matrix database shows that the algorithm and architecture proposed in this paper have the ability to solve large-scale sparse matrix quickly and efficiently, and can complete the fast strength verification of vehicle components.

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Nearest Neighbors Search Using Multi-GPU

Nogueira¹,

Amorim

Baratta³

et al. 2021

Anais Do XXII Simpósio Em Sistemas Computacionais De Alto Desempenho (SSCAD 2021)

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Meshless methods are increasingly gaining space in the study of electromagnetic phenomena as an alternative to traditional mesh-based methods. One of their biggest advantages is the absence of a mesh to describe the simulation domain. Instead, the domain discretization is done by spreading nodes along the domain and its boundaries. Thus, meshless methods are based on the interactions of each node with all its neighbors, and determining the neighborhood of the nodes becomes a fundamental task. The k-nearest neighbors (kNN) is a well-known algorithm used for this purpose, but it becomes a bottleneck for these methods due to its high computational cost. One of the alternatives to reduce the kNN high computational cost is to use spatial partitioning data structures (e.g., planar grid) that allow pruning when performing the k-nearest neighbors search. Furthermore, many of these strategies employed for kNN search have been adapted for graphics processing units (GPUs) and can take advantage of its high potential for parallelism. Thus, this paper proposes a multi-GPU version of the grid method for solving the kNN problem. It was possible to achieve a speedup of up to 1.99x and up to 3.94x using two and four GPUs, respectively, when compared against the single-GPU version of the grid method.

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Node-to-Node Realization of Meshless Local Petrov Galerkin (MLPG) Fully in GPU

Cited by 3 publications

References 32 publications

GPU Finite Element Method Computation Strategy Without Mesh Coloring

GPU Finite Element Method Computation Strategy Without Mesh Coloring

Strength Check of Aircraft Parts Based on Multi-GPU Clusters for Fast Calculation of Sparse Linear Equations

Nearest Neighbors Search Using Multi-GPU

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