本文關(guān)鍵詞：結(jié)構(gòu)分析中的GPU并行快速多極邊界元法研究　出處：《華中科技大學(xué)》2013年博士論文　論文類型：學(xué)位論文

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【摘要】：設(shè)計是企業(yè)產(chǎn)品創(chuàng)新的源頭，是制造業(yè)核心競爭力的關(guān)鍵所在。產(chǎn)品創(chuàng)新設(shè)計不僅要滿足產(chǎn)品結(jié)構(gòu)形狀的需求，而且還要滿足結(jié)構(gòu)性能要求。當(dāng)前，大量企業(yè)產(chǎn)品設(shè)計應(yīng)用三維CAD軟件進行幾何建模，采用基于限元法的CAE軟件進行結(jié)構(gòu)性能分析，但CAD模型與CAE模型之間的模型轉(zhuǎn)換、模型簡化、網(wǎng)格剖分等前處理過程需耗費大量的時間，影響產(chǎn)品設(shè)計效率。為此，本文重點對邊界元法和快速多極邊界元法進行深入研究，提出一種GPU并行的快速多極邊界元方法，并應(yīng)用于產(chǎn)品結(jié)構(gòu)性能分析。該方法能有效簡化傳統(tǒng)有限元分析前處理過程，提高產(chǎn)品設(shè)計效率，同時也為新一代產(chǎn)品設(shè)計CAD/CAE軟件提供一種可行的集成化方法。論文主要研究工作如下： (1)對三維彈性力學(xué)問題的邊界元法進行研究，包括邊界積分方程建立、單元積分方法、角點問題處理、邊界面應(yīng)力計算及GMRES迭代求解算法等。針對角點處面力不連續(xù)問題，提出了一種邊界條件相關(guān)的混合單元法，并利用三維模型BREP表達中角點拓撲關(guān)系實現(xiàn)了混合單元的自動生成。與現(xiàn)有混合單元角點處理算法相比，該方法僅在位移約束角點處采用非連續(xù)單元，有效減少非連續(xù)單元引起的附加自由度，降低結(jié)構(gòu)分析問題求解規(guī)模。 (2)對快速多極邊界元法的算法原理進行研究，提出了一種節(jié)點單元雙重信息自適應(yīng)結(jié)構(gòu)樹的構(gòu)建方法，實現(xiàn)了高階邊界單元積分的快速計算。基于該方法建立的雙重信息快速多極邊界元法可將邊界元法的時間和空間復(fù)雜度由O(N2)降到O(N)，且單元積分計算量僅為采用全局節(jié)點法和節(jié)點分片法的快速多極邊界元法的三分之一。此外，將快速多極邊界元法與給定邊界條件結(jié)合，提出了一種適用于快速多極邊界元法的剛體位移特解法，解決了1/r2奇異積分和自由項系數(shù)的求解問題。 (3)針對快速多極邊界元法中多極展開向局部展開系數(shù)傳遞(M2L)計算過程存在效率低的問題，本文對基于指數(shù)展開的新型快速多極邊界元法進行探索，研究表明該方法在展開階次較大時才能達到高的計算精度及顯著的加速效果，且需額外增加存儲。為此，本文進一步研究子層結(jié)點向父層結(jié)點越層傳遞的M2L優(yōu)化改進方法，實驗結(jié)果顯示，越層傳遞M2L方法不需增加額外內(nèi)存，且加速效果與展開階次無關(guān)，有利于結(jié)構(gòu)性能分析的快速計算。 (4)充分利用邊界單元及自適應(yīng)結(jié)構(gòu)樹結(jié)點的固有并行特征，提出了一種基于CUDA架構(gòu)的自適應(yīng)快速多極邊界元GPU并行算法，，對快速多極邊界元法中多極展開、多極展開系數(shù)傳遞、多極展開向局部展開系數(shù)傳遞、局部展開系數(shù)傳遞以及近場節(jié)點單元積分計算進行加速。實驗結(jié)果表明，該算法不僅具有顯著的加速效果，而且對不同形狀的三維模型均具有良好的適應(yīng)性，有效提高產(chǎn)品結(jié)構(gòu)性能分析效率。 最后，以上述理論研究為基礎(chǔ)，對集成化CAD/CAE產(chǎn)品設(shè)計軟件技術(shù)及系統(tǒng)架構(gòu)進行研究，結(jié)合現(xiàn)有自主知識產(chǎn)權(quán)的三維參數(shù)化特征建模軟件InterSolid，采用Visual C++集成開發(fā)環(huán)境，研制開發(fā)了集成化CAD/CAE設(shè)計分析原型系統(tǒng)軟件。并以此為基礎(chǔ)，針對不同形狀、不同復(fù)雜程度的典型三維產(chǎn)品實例進行結(jié)構(gòu)分析工程計算驗證，實驗結(jié)果表明，本文所提出的理論及算法具有計算效率高、求解規(guī)模大、適應(yīng)性強等優(yōu)勢，具有良好的工程應(yīng)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.

【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TH122

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