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Application of a GPU-accelerated hybrid preconditioned conjugate gradient approach for large 3D problems in computational geomechanics

机译:GPU加速的混合预处理共轭梯度方法在计算地球力学中解决大型3D问题的应用

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This paper presents a hybrid preconditioning technique for Conjugate Gradient method and discusses its parallel implementation on Graphic Processing Unit (GPU) for solving large sparse linear systems arising from application of interior point methods to conic optimization problems in the context of nonlinear Finite Element Limit Analysis (FELA) for computational Geomechanics. For large 3D problems, the use of direct solvers in general becomes prohibitively expensive due to exponentially growing memory requirements and computational time. Besides, the so-called saddle-point systems resulting from use of optimization framework is not an exemption. On the other hand, although preconditioned iterative methods have moderate storage requirements and therefore can be applied to much larger problems than direct methods, they usually exhibit high number of iterations to reach convergence. In present paper, we show that this problem can be effectively tackled using the proposed hybrid preconditioner along with an elaborate implementation on GPU. Furthermore, numerical results verify the robustness and efficiency of the proposed technique. Crown Copyright (C) 2015 Published by Elsevier Ltd. All rights reserved.
机译:本文介绍了一种共轭梯度方法的混合预处理技术,并讨论了其在图形处理单元(GPU)上的并行实现,用于解决在非线性有限元极限分析背景下将内点方法应用于圆锥优化问题而产生的大型稀疏线性系统( FELA),用于计算地质力学。对于大型3D问题,由于内存需求和计算时间呈指数级增长,因此直接求解器的使用通常变得过分昂贵。此外,使用优化框架产生的所谓的鞍点系统也不例外。另一方面,尽管预处理的迭代方法具有适度的存储要求,因此可以比直接方法应用于更大的问题,但它们通常会出现大量迭代以达到收敛。在本文中,我们表明,使用建议的混合前置条件器以及在GPU上的精心实现,可以有效解决此问题。此外,数值结果验证了所提出技术的鲁棒性和效率。 Crown版权所有(C)2015,由Elsevier Ltd.发行。保留所有权利。

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