GPU accelerated computational homogenization based on a variational approach in a reduced basis framework

Fritzen, Felix; Hodapp, Max; Leuschner, Matthias

doi:10.1016/j.cma.2014.05.006

Cited by 65 publications

(72 citation statements)

References 21 publications

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“…The proposed method has been applied for the design of multiscale elastoviscoplastic structures, where the material law is governed by an underlying representative porous aluminum microstructure Fritzen and Hodapp 2016). In order to provide a computationally efficient, yet accurate homogenized material law for the heterogeneous material, the model reduction approach developed in Fritzen and Leuschner (2013) and Fritzen et al (2014) are adopted. In our previous investigation we considered the optimal design of elasto-viscoplastic structures with consideration of the underlying microstructure.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

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We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106 (6): 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and Liang Xia are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

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Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

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“…Nevertheless, CH is naturally parallelizable (Mosby and Matouš, 2015a) and the method has demonstrated excellent scalability as shown later in this chapter. Alternatively, a growing emphasis is given on its efficiency, whereby use is made of advanced computational techniques and reduced order models (Yvonnet and He, 2007;Fritzen and Leuschner, 2013;Fritzen et al, 2014;Kerfriden et al, 2014).…”

Section: Nonlinear Computational Homogenizationmentioning

confidence: 99%

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

Geers

Kouznetsova

Matouš

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

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“…In [12], a new method for the assembling of the stiffness matrix in case of isogeometric analysis is proposed. Hybrid implementations of multiscale finite element approaches, whereby constitutive material computations at Gauss point level are carried out on the GPU, are discussed in [13] and [14] In most of the above-mentioned applications, results are limited to single-precision arithmetic (e.g. [2,9,14,10]).…”

Section: Introductionmentioning

confidence: 99%

“…Hybrid implementations of multiscale finite element approaches, whereby constitutive material computations at Gauss point level are carried out on the GPU, are discussed in [13] and [14] In most of the above-mentioned applications, results are limited to single-precision arithmetic (e.g. [2,9,14,10]). It is important to recall, as suggested in [8], that, concerning NVIDIA GPUs, in all the implementations before CUDA compute capability 1.3, only single-precision floating point operations are supported directly by the hardware.…”

Section: Introductionmentioning

confidence: 99%

An explicit dynamics GPU structural solver for thin shell finite elements

Bartezzaghi

Cremonesi

Parolini

et al. 2015

Computers & Structures

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With the availability of user oriented software tools, dedicated architectures, such as the parallel computing platform and programming model CUDA (Compute Unified Device Architecture) released by NVIDIA, one of the main producers of graphics cards, and of improved, highly performing GPU (Graphics Processing Unit) boards, GPGPU (General Purpose programming on GPU) is attracting increasing interest in the engineering community, for the development of analysis tools suitable to be used in validation/verification and virtual reality applications. For their inherent explicit and decoupled structure, explicit dynamics finite element formulations appear to be particularly attractive for implementations on hybrid CPU/GPU or pure GPU architectures. The issue of an optimized, double-precision finite element GPU implementation of an explicit dynamics finite element solver for elastic shell problems in small strains and large displacements and rotations, using unstructured meshes, is here addressed. The conceptual difference between a GPU implementation directly adapted from a standard CPU approach and a new optimized formulation, specifically conceived for GPUs, is discussed and comparatively assessed. It is shown that a speedup factor of about 5 can be achieved by an optimized algorithm reformulation and careful memory management. A speedup of more than 40 is achieved with respect of state-of-the art commercial codes running on CPU, obtaining real-time simulations in some cases, on commodity hardware. When a last generation GPU board is used, it is shown that a problem with more than 16 millions degrees of freedom can be solved in just few hours of computing time, opening the way to virtualization approaches for real large scale engineering problems.

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GPU accelerated computational homogenization based on a variational approach in a reduced basis framework

Cited by 65 publications

References 21 publications

Evolutionary topology optimization of elastoplastic structures

Evolutionary topology optimization of elastoplastic structures

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

An explicit dynamics GPU structural solver for thin shell finite elements

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