结构分析中的GPU并行快速多极边界元法研究

发布时间：2018-01-14 00:29

本文关键词：结构分析中的GPU并行快速多极边界元法研究　出处：《华中科技大学》2013年博士论文　论文类型：学位论文

【摘要】：设计是企业产品创新的源头，是制造业核心竞争力的关键所在。产品创新设计不仅要满足产品结构形状的需求，而且还要满足结构性能要求。当前，大量企业产品设计应用三维CAD软件进行几何建模，采用基于限元法的CAE软件进行结构性能分析，但CAD模型与CAE模型之间的模型转换、模型简化、网格剖分等前处理过程需耗费大量的时间，影响产品设计效率。为此，本文重点对边界元法和快速多极边界元法进行深入研究，提出一种GPU并行的快速多极边界元方法，并应用于产品结构性能分析。该方法能有效简化传统有限元分析前处理过程，提高产品设计效率，同时也为新一代产品设计CAD/CAE软件提供一种可行的集成化方法。论文主要研究工作如下： (1)对三维弹性力学问题的边界元法进行研究，包括边界积分方程建立、单元积分方法、角点问题处理、边界面应力计算及GMRES迭代求解算法等。针对角点处面力不连续问题，提出了一种边界条件相关的混合单元法，并利用三维模型BREP表达中角点拓扑关系实现了混合单元的自动生成。与现有混合单元角点处理算法相比，该方法仅在位移约束角点处采用非连续单元，有效减少非连续单元引起的附加自由度，降低结构分析问题求解规模。 (2)对快速多极边界元法的算法原理进行研究，提出了一种节点单元双重信息自适应结构树的构建方法，实现了高阶边界单元积分的快速计算。基于该方法建立的双重信息快速多极边界元法可将边界元法的时间和空间复杂度由O(N2)降到O(N)，且单元积分计算量仅为采用全局节点法和节点分片法的快速多极边界元法的三分之一。此外，将快速多极边界元法与给定边界条件结合，提出了一种适用于快速多极边界元法的刚体位移特解法，解决了1/r2奇异积分和自由项系数的求解问题。 (3)针对快速多极边界元法中多极展开向局部展开系数传递(M2L)计算过程存在效率低的问题，本文对基于指数展开的新型快速多极边界元法进行探索，研究表明该方法在展开阶次较大时才能达到高的计算精度及显著的加速效果，且需额外增加存储。为此，本文进一步研究子层结点向父层结点越层传递的M2L优化改进方法，实验结果显示，越层传递M2L方法不需增加额外内存，且加速效果与展开阶次无关，有利于结构性能分析的快速计算。 (4)充分利用边界单元及自适应结构树结点的固有并行特征，提出了一种基于CUDA架构的自适应快速多极边界元GPU并行算法，，对快速多极边界元法中多极展开、多极展开系数传递、多极展开向局部展开系数传递、局部展开系数传递以及近场节点单元积分计算进行加速。实验结果表明，该算法不仅具有显著的加速效果，而且对不同形状的三维模型均具有良好的适应性，有效提高产品结构性能分析效率。最后，以上述理论研究为基础，对集成化CAD/CAE产品设计软件技术及系统架构进行研究，结合现有自主知识产权的三维参数化特征建模软件InterSolid，采用Visual C++集成开发环境，研制开发了集成化CAD/CAE设计分析原型系统软件。并以此为基础，针对不同形状、不同复杂程度的典型三维产品实例进行结构分析工程计算验证，实验结果表明，本文所提出的理论及算法具有计算效率高、求解规模大、适应性强等优势，具有良好的工程应用前景。
[Abstract]:The design is the source of enterprise product innovation, is the key to the core competitiveness of manufacturing industry. The product innovation design should not only meet the demand of the product shape, but also to meet the requirement of structural performance. At present, a large number of enterprise product design and application of CAD software for 3D geometric modeling, using the analysis of performance of finite element method based on the CAE software, but conversion between CAD model and CAE model simplification, mesh pretreatment process is time-consuming, affecting the efficiency of product design. Therefore, in-depth study of this paper focuses on the boundary element method and fast multipole boundary element method, proposes a fast multipole boundary element method GPU parallel, and applied to the products the structure performance analysis. This method can effectively simplify the traditional finite element analysis of the pretreatment process, improve the efficiency of product design, but also for the new generation of product design software CAD/CAE Provide a feasible and integrated method. The main research work of this paper is as follows:
(1) to study the boundary element method for 3D elasticity problems, including the establishment of the boundary integral equation, unit integral method, to deal with the problem of corner, boundary stress calculation and GMRES iterative algorithm. Aiming at the corner stress discontinuity problem, put forward a kind of boundary conditions related to mixed element method and, the three-dimensional model of BREP expression in corner topology to realize the automatic generation of mixed units. Compared with the existing hybrid unit corner processing algorithm, this method only in the displacement constraint corner with non continuous unit, effectively reduce the non additional degrees of freedom caused by continuous unit, reduce the solving scale of structure analysis.
(2) study on the algorithm principle of the fast multipole boundary element method, presents a method to construct node dual information adaptive tree, to achieve the rapid calculation of higher-order boundary element integral. The method of establishing the dual information fast multipole boundary element method to boundary element method of time and space complexity by based on O (N2) to O (N), and the unit integral calculation is only using global node method and node partition method of the fast multipole boundary element method 1/3. In addition, combined with the fast multipole boundary element method with given boundary conditions, rigid displacement solution is proposed for fast multipole boundary finite element method, solves the problem of solving 1/r2 singular integral and free term coefficient.
(3) based on the fast multipole boundary element method in multipole expansion to local expansion of transfer coefficient (M2L) calculation process exists the problem of low efficiency, the new fast multipole boundary element method based on the exponential expansion of exploration, the study shows that the method in order to achieve high calculation accuracy and significant acceleration effect and, the need for additional storage. Therefore, this paper further studies the sub layer node to the parent node of the M2L layer transfer layer is optimized and improved method, the experimental results show that the M2L layer transfer method does not need additional memory, and the available fruit and expansion order has nothing to do with the rapid calculation and analysis for structural performance.
(4) make full use of natural boundary element and adaptive tree node parallel feature, proposes a parallel algorithm of adaptive CUDA structure of the fast multipole boundary element GPU based on the fast multipole boundary element method in multipole multipole expansion coefficient, transfer to the Bureau of the Ministry of the multipole expansion coefficients of transfer, local spread coefficient and near transfer a node unit integral calculation speed. The experimental results show that the algorithm not only has acceleration effect significantly, and has good adaptability to different shapes of the 3D model, effectively improve the efficiency analysis of product structure and performance.
Finally, based on above theory research, research of technology and system design of software architecture of integrated CAD/CAE products with independent intellectual property rights of the existing 3D parametric feature modeling software InterSolid, using Visual integrated development environment C++, developed integrated CAD/CAE design analysis software prototype system. And on this basis, according to different shapes a typical example of 3D products, with different degrees of complexity of calculation analysis of engineering structure, the experimental results show that the theory and the proposed algorithm has high computational efficiency, solving the large scale, strong adaptability and other advantages, and has good application prospects.

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH122

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