Efficient Parallel Preconditioned Conjugate Gradient Solver on GPU for FE Modeling of Electromagnetic Fields in Highly Dissipative Media

Camargos, Ana Flávia Peixoto de; Silva, Viviane Cristine; Guichon, Jean‐Michel; Munier, Gerard

doi:10.1109/tmag.2013.2285091

Cited by 13 publications

(24 citation statements)

References 11 publications

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“…(6.1). A excitação é em corrente, 6.5. Configurações Utilizadas nos Casos-teste 85 dada na forma de condição de Neumann não homogênea.…”

Section: Configuração 1 -Regime Estacionáriounclassified

“…We performed two test cases. Case 1, solves the problem of 3D underground diffusion of harmonic currents, as presented in [6], [7]. For the sake of completeness, and to evaluate both robustness and applicability of the presented GPU-based tool in other electrical engineering-related systems, we include additional numerical experiments we have performed on systems arising from the application nodal analysis (Kirchhoff to an electric circuit of a power delivery network of a real-world metropolitan area, named Case 2.…”

Section: Principais Dificuldadesmentioning

confidence: 99%

“…The excitation can be in the form of an impressed current, when the total current through a conductor is prescribed, but the current density distribution therein is unknown. This is the case of a skin effect problem with a prescribed current [6], such as in Fig. 2.…”

Section: A Casementioning

confidence: 99%

“…The domain includes a set of grounding electrodes as well as the semi-infinite conducting medium, the soil, which will be truncated with the aid of perfectly matched layers (PML), as described in [6]. The phenomenon is governed by Maxwell equations, namely:…”

Section: A Casementioning

confidence: 99%

“…In all cases the domains were meshed with either 8-or 20-node hexahedral elements. Details about dimensions and physical properties of the tested configuration are given in Table I [6]. We used either none or the UPML technique (uni-axial perfectly-matched layers) to truncate the domain, such as illustrated in Fig.…”

Section: A Tested Configurationmentioning

confidence: 99%

See 4 more Smart Citations

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

Camargos¹

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“…(6.1). A excitação é em corrente, 6.5. Configurações Utilizadas nos Casos-teste 85 dada na forma de condição de Neumann não homogênea.…”

Section: Configuração 1 -Regime Estacionáriounclassified

Section: Principais Dificuldadesmentioning

confidence: 99%

Section: A Casementioning

confidence: 99%

Section: A Casementioning

confidence: 99%

Section: A Tested Configurationmentioning

confidence: 99%

See 3 more Smart Citations

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

Camargos¹

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GPGPU-based parallel computing applied in the FEM using the conjugate gradient algorithm: a review

2018

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Parallelization of the finite-element method (FEM) has been contemplated by the scientific and high-performance computing community for over a decade. Most of the computations in the FEM are related to linear algebra that includes matrix and vector computations. These operations have the single-instruction multiple-data (SIMD) computation pattern, which is beneficial for shared-memory parallel architectures. General-purpose graphics processing units (GPGPUs) have been effectively utilized for the parallelization of FEM computations ever since 2007. The solver step of the FEM is often carried out using conjugate gradient (CG)type iterative methods because of their larger convergence rates and greater opportunities for parallelization. Although the SIMD computation patterns in the FEM are intrinsic for GPU computing, there are some pitfalls, such as the underutilization of threads, uncoalesced memory access, lower arithmetic intensity, limited faster memories on GPUs and synchronizations. Nevertheless, FEM applications have been successfully deployed on GPUs over the last 10 years to achieve a significant performance improvement. This paper presents a comprehensive review of the parallel optimization strategies applied in each step of the FEM. The pitfalls and tradeoffs linked to each step in the FEM are also discussed in this paper. Furthermore, some extraordinary methods that exploit the tremendous amount of computing power of a GPU are also discussed. The proposed review is not limited to a single field of engineering. Rather, it is applicable to all fields of engineering and science in which FEM-based simulations are necessary.

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A novel direct resolution method for coupled systems in finite element analysis

Boutora

Takorabet

2020

COMPEL

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Purpose This paper aims to propose a novel direct method for indefinite algebraic linear systems. It is well adapted for sparse linear systems, such as those of two-dimensional (2-D) finite elements problems, especially for coupled systems. Design/methodology/approach The proposed method is developed on an example of an indefinite symmetric matrix. The algorithm of the method is given next, and a comparison between the numbers of operations required by the method and the Cholesky method is also given. Finally, an application on a magnetostatic problem for classical methods (Gauss and Cholesky) shows the relative efficiency of the proposed method. Findings The proposed method can be used advantageously for 2-D finite elements in stepping methods without using a block decomposition of matrices. Research limitations/implications This method is advantageous for direct linear solving for 2-D problems, but it is not recommended at this time for three-dimensional problems. Originality/value The proposed method is the first direct solver for algebraic linear systems proposed since more than a half century. It is not limited for symmetric positive systems such as many of direct and iterative methods.

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Efficient Parallel Preconditioned Conjugate Gradient Solver on GPU for FE Modeling of Electromagnetic Fields in Highly Dissipative Media

Cited by 13 publications

References 11 publications

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

GPGPU-based parallel computing applied in the FEM using the conjugate gradient algorithm: a review

A novel direct resolution method for coupled systems in finite element analysis

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