3D finite element numerical integration on GPUs

Macioł, Paweł; Płaszewski, Przemysław; Banaś, Krzysztof

doi:10.1016/j.procs.2010.04.121

Cited by 25 publications

(18 citation statements)

References 3 publications

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“…Another GPU implementation of the numerical integration has been presented in [20]. In this paper, prismatic elements and shape functions being products of 2D shape functions for triangles and 1D shape functions in the vertical direction were considered.…”

Section: Numerical Integrationmentioning

confidence: 99%

“…The outer one is over M tetrahedra, while the inner loop involves Q iterations where Q is the number of points in the Gauss quadrature (in our case Q = 81). In [19,20] a single thread block (work-group) is responsible for processing a single finite element, which means that the outer loop is parallelized . In our implementation we also parallelize the outer loop.…”

Section: Numerical Integrationmentioning

confidence: 99%

“…This Fermi architecture feature provides a twofold parallelization -not only threads inside kernels work in parallel, but also kernels are executed independently. What is worth mentioning, a concurrent kernel execution has not been utilized in any previous papers [19][20][21][22].…”

Section: Numerical Integrationmentioning

confidence: 99%

“…An obvious way to accelerate the finite element matrix generation process (matgen) is to parallelize numerical computations. Surprisingly, only few papers have been published on parallelization of steps ((ii)-(iii)) that occur in the finite element method on a CPU and a GPU [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Matrix Generation on a Gpu

Dziekonski¹,

Sypek²,

Lamęcki³

et al. 2012

PIER

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Abstract-This paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core Opterons), indicate that the GPU implementation of the matrix generation allows one to achieve speedups by a factor of 81 and 19 over the optimized singleand multi-threaded CPU-only implementations, respectively.

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Section: Numerical Integrationmentioning

confidence: 99%

Section: Numerical Integrationmentioning

confidence: 99%

Section: Numerical Integrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Element Matrix Generation on a Gpu

Dziekonski¹,

Sypek²,

Lamęcki³

et al. 2012

PIER

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“…In [52] we presented numerical integration on GPUs for 2D linear elasticity, CUDA environment and older generations of GPUs. This work was extended to OpenCL programming model in [34] and to 3D Laplace operators in [53]. We investigate separately numerical integration procedures for CBE processors in [52] and [54].…”

Section: Current Contributionmentioning

confidence: 99%

Numerical integration on GPUs for higher order finite elements

Banaś

Płaszewski

Macioł

2014

Computers & Mathematics with Applications

Self Cite

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The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose integration procedures, as well as particular example applications. The most important characteristic of the problem investigated is the large variation of required processor and memory resources associated with different degrees of approximating polynomials. The questions that we try to answer are whether it is possible to design a single integration kernel for different GPUs and different orders of approximation and what performance can be expected in such a case.

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Finite element assembly strategies on multi‐core and many‐core architectures

Markall

Slemmer

Ham

et al. 2012

Numerical Methods in Fluids

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SUMMARY We demonstrate that radically differing implementations of finite element methods (FEMs) are needed on multi‐core (CPU) and many‐core (GPU) architectures, if their respective performance potential is to be realised. Our numerical investigations using a finite element advection–diffusion solver show that increased performance on each architecture can only be achieved by committing to specific and diverse algorithmic choices that cut across the high‐level structure of the implementation. Making these commitments to achieve high performance for a single architecture leads to a loss of performance portability. Data structures that include redundant data but enable coalesced memory accesses are faster on many‐core architectures, whereas redundancy‐free data structures that are accessed indirectly are faster on multi‐core architectures. The Addto algorithm for global assembly is optimal on multi‐core architectures, whereas the Local Matrix Approach is optimal on many‐core architectures despite requiring more computation than the Addto algorithm. These results demonstrate the value in making the correct choice of algorithm and data structure when implementing FEMs, spectral element methods and low‐order discontinuous Galerkin methods on modern high‐performance architectures. Copyright © 2012 John Wiley & Sons, Ltd.

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3D finite element numerical integration on GPUs

Cited by 25 publications

References 3 publications

Finite Element Matrix Generation on a Gpu

Finite Element Matrix Generation on a Gpu

Numerical integration on GPUs for higher order finite elements

Finite element assembly strategies on multi‐core and many‐core architectures

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