Constant Boundary Elements on graphics hardware: a GPU-CPU complementary implementation

Labaki, Josué; Ferreira, Luiz Otávio; Mesquita, Euclides

doi:10.1590/s1678-58782011000400011

Cited by 8 publications

(4 citation statements)

References 8 publications

(5 reference statements)

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“…Indeks i z równania (2) oznacza punkty źródłowe każdego elementu. Dla każdego węzła (punktu obserwacji) r wykonuje się całkowania wskazane w równaniu (1). Ostatecznie prowadzi to do zapisu macierzowego równania (1) postaci:…”

Section: Schemat Metody Elementów Brzegowychunclassified

Zastosowanie Bibliotek Numerycznych W Obliczeniach Meb

Król

Pańczyk

2014

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środow

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Numerical library usage effectively reduce computation time and facilitate code programming. There are modified versions of popular BLAS and LAPACK libraries, dedicated to multi-core and distributed programming respectively PBLAS and SCALAPACK. Currently, a similar development applies to the GPU programming in two major implementations of GPGPU: NVIDIA CUDA and Kronos / ATI OpenCL. In the same time hybrid CPU-GPU versions of these libraries are intensively developed, a good example of that is MAGMA. This paper will present the effects of some of those libraries implementation used to solve the two-dimensional planar capacitor model by the boundary element method with constant boundary elements.

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Section: Schemat Metody Elementów Brzegowychunclassified

Zastosowanie Bibliotek Numerycznych W Obliczeniach Meb

Król

Pańczyk

2014

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środow

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“…One of the first attempts to speed up the BEM using graphics hardware has been made in 2009 by Takahashi and Hamada [6] when they presented a GPUaccelerated BEM formulation based on the GPU programming platform CUDA to solve the Helmholtz equation in three dimensions. Two years later, Labaki et al [7,8] published a review on three distinct GPU implementations addressing two-dimensional potential and electrostatic problems.…”

Section: Introductionmentioning

confidence: 99%

Simple and efficient GPU parallelization of existing H-Matrix accelerated BEM code

Vater,

Betcke,

Dilba

2017

Preprint

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In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H -Matrices) with ACA (Adaptive Cross Approximation). In particular, we focus on the expensive evaluation of the discrete weak form of boundary operators associated with the Laplace and the Helmholtz equation in three space dimensions. The method is based on offloading the CPU assembly of elements during the ACA assembly onto a GPU device and to use threading strategies across ACA blocks to create sufficient workload for the GPU. The proposed GPU strategy is designed such that it can be implemented in existing code with minimal changes to the surrounding application structure. This is in particular interesting for existing legacy code that is not from the ground-up designed with GPU computing in mind.Our benchmark study gives realistic impressions of the benefits of GPU-accelerated BEM simulations by using state-of-the-art multi-threaded computations on modern high-performance CPUs as a reference, rather than drawing synthetic comparisons with single-threaded codes. Speed-up plots illustrate that performance gains up to a factor of 5.5 could be realized with GPU computing under these conditions. This refers to a boundary element model with about 4 million unknowns, whose H -Matrix weak form associated with a real-valued (Laplace) boundary operator is set up in only 100 minutes harnessing the two GPUs instead of 9 hours when using the 20 CPU cores at disposal only. The benchmark study is followed by a particularly demanding real-life application, where we compute the scattered high-frequency sound field of a submarine to demonstrate the increase in overall application performance from moving to a GPU-based ACA assembly.

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“…Due to the computational power of GPGPUs, there have been attempts to utilize the computational power of GPGPUs to reduce setup times for discretized boundary integral operators [32,24,21,31].…”

Section: Introductionmentioning

confidence: 99%

Approximation of boundary element matrices using GPGPUs and nested cross approximation

Börm¹,

Christophersen²

2015

Preprint

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The efficiency of boundary element methods using a Galerkin discretization depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or H-matrix techniques. The near-field part is typically approximated by special quadrature rules like the Sauter-Schwab technique that can handle the singular integrals appearing in the diagonal and near-diagonal matrix elements.Since computing one element of the matrix requires only a small amount of data but a fairly large number of operations, we propose to use general-purpose graphics processing units (GPGPUs) to handle vectorizable portions of the computation: near-field computations are ideally suited for vectorization and can therefore be handled very well by GPGPUs. Modern far-field compression schemes can be split into a small adaptive portion that exhibits divergent control flows, and should therefore be handled by the CPU, and a vectorizable portion that can again be sent to GPGPUs.We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPGPUs. The method presented in this article is able to reduce the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.

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Constant Boundary Elements on graphics hardware: a GPU-CPU complementary implementation

Cited by 8 publications

References 8 publications

Zastosowanie Bibliotek Numerycznych W Obliczeniach Meb

Zastosowanie Bibliotek Numerycznych W Obliczeniach Meb

Simple and efficient GPU parallelization of existing H-Matrix accelerated BEM code

Approximation of boundary element matrices using GPGPUs and nested cross approximation

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