Toward GPU accelerated topology optimization on unstructured meshes

Zegard, Tomás; Paulino, Gláucio H.

doi:10.1007/s00158-013-0920-y

Cited by 51 publications

(28 citation statements)

References 30 publications

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“…This is also done for solving anisotropic elliptic PDEs for the pressure correction in numerical weather forecast [32]. Recently, the GPU implementation of matrix-free methods is used to accelerate topology optimization algorithms for large-scale finite element models using whether voxelization [39] or structured meshes [14].…”

Section: Previous Workmentioning

confidence: 99%

“…The Jacobi preconditioner is adopted in this work because the data needed to calculate it can be obtained from elemental stiffness matrices. Its implementation consists of two inner loops (line [6][7][8][9][10][11][12][13][14]. The first loop applies to the DoFs u A U whereas the second loop operates on the elements eA E ðuÞ containing the unknown u.…”

Section: Vector Arithmeticmentioning

confidence: 99%

“…The use of these graphic cards in non-graphics HPC applications is becoming very popular due to their high computing capacity. GPU computing has been successfully applied in a wide spectrum of scientific, engineering and enterprise applications, such as electromagnetic simulations [9], fluid-structure interaction [10], numerical simulation in neuroscience [11], N-body simulations [12], seismic computations [13], structural topology optimization [14], and medical image processing [15], to name but a few. The reader is referred to [16][17][18] for comprehensive reviews of this research field.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Martínez-Frutos

Herrero-Pérez

2015

Finite Elements in Analysis and Design

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Section: Previous Workmentioning

confidence: 99%

Section: Vector Arithmeticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Martínez-Frutos

Herrero-Pérez

2015

Finite Elements in Analysis and Design

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“…This leads to performance improvements of 292 GB/s versus 268 GB/s. Low register counts (28)(29)(30)(31)(32) and single-precision data types also resulted in achieving a higher occupancy on the GPU compared to Airfoil. This, we believe explains why performance appears to be independent of the block size as shown in the Figure 11.…”

Section: Volnamentioning

confidence: 99%

Locality optimized unstructured mesh algorithms on GPUs

Sulyok

Balogh

Reguly

et al. 2019

Journal of Parallel and Distributed Computing

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Unstructured-mesh based numerical algorithms such as finite volume and finite element algorithms form an important class of applications for many scientific and engineering domains. The key difficulty in achieving higher performance from these applications is the indirect accesses that lead to data-races when parallelized. Current methods for handling such data-races lead to reduced parallelism and suboptimal performance. Particularly on modern many-core architectures, such as GPUs, that has increasing core/thread counts, reducing data movement and exploiting memory locality is vital for gaining good performance.In this work we present novel locality-exploiting optimizations for the efficient execution of unstructured-mesh algorithms on GPUs. Building on a two-layered coloring strategy for handling data races, we introduce novel reordering and partitioning techniques to further improve efficient execution. The new optimizations are then applied to several well established unstructuredmesh applications, investigating their performance on NVIDIA's latest P100 and V100 GPUs. We demonstrate significant speedups (1.1-1.75×) compared to the state-of-the-art. A range of performance metrics are benchmarked including runtime, memory transactions, achieved bandwidth performance, GPU occupancy and data reuse factors and are used to understand and explain the key factors impacting performance. The optimized algorithms are implemented as an open-source software library and we illustrate its use for improving performance of existing or new unstructured-mesh applications.

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“…Finally, the methodology proposed in this paper is fully based on (typically vectorizable and/or parallelizable) iterative schemes. It could thus be of benefit to the (re-)emerging methods of distributed optimization [7] and optimization on vector processors, namely GPU [23,28], not only in the context of topology optimization.…”

mentioning

confidence: 99%

Primal-Dual Interior Point Multigrid Method for Topology Optimization

Kočvara¹,

Mohammed²

2016

SIAM J. Sci. Comput.

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Abstract. An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared with the so-called optimality condition method, an established technique in topology optimization. This method is also equipped with the multigrid preconditioned conjugate gradient algorithm. We conclude that, for large scale problems, the interior point method with an inexact iterative linear solver is superior to any other variant studied in the paper.Keywords:. topology optimization, multigrid methods, interior point methods, preconditioners for iterative methods MSC2010:. 65N55, 35Q93, 90C51, 65F081. Introduction. The discipline of topology optimization offers challenging problems to researchers working in large scale numerical optimization. The results are essentially colors of pixels in a 2d or 3d "pictures". Hence, in order to obtain highquality results, i.e., fine pictures capturing all details, a very large number of variables is essential. In this article we only consider the discretized, finite dimensional topology optimization problem. For its derivation and for general introduction to topology optimization, see, e.g., [5].We will consider the basic problem of topology optimization: minimization of compliance under equilibrium equation constraints and the most basic linear constraints on the design variables:

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Toward GPU accelerated topology optimization on unstructured meshes

Cited by 51 publications

References 30 publications

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Locality optimized unstructured mesh algorithms on GPUs

Primal-Dual Interior Point Multigrid Method for Topology Optimization

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