基于GPU的显式有限元快速计算方法及在车身设计制造中的应用
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摘要
在实际工程中利用有限元理论进行仿真分析时,存在两个主要问题,一个是计算精度,另一个是计算速度。计算精度主要涉及有限元理论的改进,本文对此问题不做深入研究。计算速度问题除了涉及改进有限元理论,还与计算时所采用的计算方式及硬件密切相关。目前在解决实际工程问题时广泛采用的计算方式是串行循环处理,这种计算方式所需时间较长,不能完全满足实际工程问题的需要。计算效率不高也就成了制约有限元进一步推广使用的瓶颈问题。因此,研究如何缩短仿真计算时间、提高计算效率对于解决实际工程问题是有重要的意义。
本文研究内容主要集中在如何将图形处理器(GPU, Graphic Processing Unit)通用计算(GPGPU, General Purpose Graphic Processing Unit)技术应用到有限元仿真计算领域。本文主要工作及创新点如下：
1)提出了利用GPU并行处理的方式来提高薄板冲压成形、薄壁结构耐撞性仿真计算过程中板壳单元计算效率的方法。研究探讨了并行处理方式特点和并行计算速度影响因素,比较了并行、串行处理方式各自的特点,分析了有限元仿真计算并行化处理的可行性,以及有限元仿真计算并行化处理计算过程中必须解决的难题与挑战,包括单元共节点更新问题,单元数据表达,数据格式转换,数据在GPU和CPU之间相互交换等,本文针对这些问题都提出了完整解决方案,并且通过程序证明这些解决办法是切实可行的；
2)提出了在薄板冲压成形、薄壁结构耐撞性仿真计算过程中板壳单元数据在GPU和CPU之间实现交换方法。通过对CPU计算时程序、数据结构特点和GPU并行计算时数据、程序结构特点进行了多方面的比较研究,利用GPU的特点,提出了利用纹理作为数据映射传入GPU时的存储器；根据数组的下标来计算纹理的坐标,完成了对相应的数据的索引任务；并行计算完成后,将计算得到的中间结果再传回到纹理中；
3)提出了在薄板冲压成形、薄壁结构耐撞性仿真计算过程中将串行数组转换成并行数据的方法。本文主要研究并探讨了在GPU并行处理条件下,传统串行编码过程中未曾出现的关于数据结构设计,数据组织,数据访问密度,并行粒度等方面面临的挑战性难题,并且都给出了理想的解决方案。为了解决数据组织的难题,本文分别采用了降低、增加、维持不变数组维度、直接拷贝等手段,达到了既能满足计算要求又能提高计算速度两方面的目的；
4)在薄板冲压成形、薄壁结构耐撞性仿真计算过程中针对变量数量多,而且表达复杂的情况,提出了利用多个片元程序处理同一单元计算任务的方法。针对成形计算过程中涉及到的变量,采用了在并行计算时分别利用全局、局部方式来表达,转换视口大小,改变纹理搜寻方式,成功解决了每次循环变量值都需要更新等挑战性困难,实现了薄板冲压成形、薄壁结构耐撞性仿真计算并行化。
Finite element method (FEM) has been widely used in the practical engineering area. However, there are still some weak points in its application of practical engineering project for simulation analysis. One is computational accuracy, and the other is computational speed. While the former is mainly related to the improvement of the FEM theory, which is not the focus of study in this paper, the latter is closely related not only to the improvement of the theory, but also to the computational methods and the performance of hardware. The computational method of serial loop is commonly used in the existing modern mechanic engineering computation. But it requires so many hours at a time that could not meet the needs of practical engineering projects. Therefore, the inefficiency of computation becomes a bottleneck that restricts the further promotion and appliance of the FEM theory. For this reason, the research on how to shorten the simulation time and improve the efficiency in solving practical engineering problems has important significance.
In this paper, the author made a deep research on how to improve the computational efficiency of FEM simulation and how to reduce the computing time. This paper mainly focus on how to apply the General Purpose Graphic Processing Unit (GPGPU) technology of Graphic Processing Unit (GPU) to the field of FEM simulation, which could be concluded as the following three major different research aspects.
1) The author put forward a new method of using GPU parallel processing to improve computational efficiency in the simulation process of sheet metal forming and thin-walled structures crashworthiness. Through analyzing the parallel architecture and massive-thread working mechanism of modern GPU, this paper sought out the rules of and factors for GPGPU applications to achieve high performance and studied the feasibility of FEM simulation process of parallel computation. Under the FEM theory, this paper analyzed the pros and cons of using GPU parallel process, coordinated the task assignment and data exchange between GPU and CPU and designed a new FEM processing architecture by using the computational resources of GPU.
2) In this paper the author also proposed the methods of data exchange between GPU and CPU in the FEM simulation process. Through making overall comparative studies of CPU and GPU, the author proposed that use texture as memory when data was mapped into GPU. And the author determined the mapping relation between the array subscript and texture coordination and completed the indexical task of the corresponding data. Finally, the intermediate calculated results were brought back to CPU when parallel computation was completed.
3) This paper put forward methods of translating serial data into parallel array. The problems of the data structure design, data organization, data access density, parallel granular and other challenges, which occurred under the condition of the GPU parallel processing and never appeared in the traditional serial encoding process, were studied and discussed in this paper. Through reducing, increasing, remaining the same array dimensions, directly copying, all the computations were carried out in the units. Both the computational accuracy and the calculation speed were all improved.
4) The author designed advanced ways of parallel computation to improve computational speed of GPU as well as the computational accuracy of GPU. There were so many variables and complicated representations in the process of parallel computation that the author put forward to using many fragment programs to deal with the computation of the same unit. And the related challenging difficulties that each loop variable needs to be updated were successfully resolved in the paper. As well, the goal of parallel simulation was achieved in the paper.
本文研究内容主要集中在如何将图形处理器(GPU, Graphic Processing Unit)通用计算(GPGPU, General Purpose Graphic Processing Unit)技术应用到有限元仿真计算领域。本文主要工作及创新点如下：
1)提出了利用GPU并行处理的方式来提高薄板冲压成形、薄壁结构耐撞性仿真计算过程中板壳单元计算效率的方法。研究探讨了并行处理方式特点和并行计算速度影响因素,比较了并行、串行处理方式各自的特点,分析了有限元仿真计算并行化处理的可行性,以及有限元仿真计算并行化处理计算过程中必须解决的难题与挑战,包括单元共节点更新问题,单元数据表达,数据格式转换,数据在GPU和CPU之间相互交换等,本文针对这些问题都提出了完整解决方案,并且通过程序证明这些解决办法是切实可行的；
2)提出了在薄板冲压成形、薄壁结构耐撞性仿真计算过程中板壳单元数据在GPU和CPU之间实现交换方法。通过对CPU计算时程序、数据结构特点和GPU并行计算时数据、程序结构特点进行了多方面的比较研究,利用GPU的特点,提出了利用纹理作为数据映射传入GPU时的存储器；根据数组的下标来计算纹理的坐标,完成了对相应的数据的索引任务；并行计算完成后,将计算得到的中间结果再传回到纹理中；
3)提出了在薄板冲压成形、薄壁结构耐撞性仿真计算过程中将串行数组转换成并行数据的方法。本文主要研究并探讨了在GPU并行处理条件下,传统串行编码过程中未曾出现的关于数据结构设计,数据组织,数据访问密度,并行粒度等方面面临的挑战性难题,并且都给出了理想的解决方案。为了解决数据组织的难题,本文分别采用了降低、增加、维持不变数组维度、直接拷贝等手段,达到了既能满足计算要求又能提高计算速度两方面的目的；
4)在薄板冲压成形、薄壁结构耐撞性仿真计算过程中针对变量数量多,而且表达复杂的情况,提出了利用多个片元程序处理同一单元计算任务的方法。针对成形计算过程中涉及到的变量,采用了在并行计算时分别利用全局、局部方式来表达,转换视口大小,改变纹理搜寻方式,成功解决了每次循环变量值都需要更新等挑战性困难,实现了薄板冲压成形、薄壁结构耐撞性仿真计算并行化。
Finite element method (FEM) has been widely used in the practical engineering area. However, there are still some weak points in its application of practical engineering project for simulation analysis. One is computational accuracy, and the other is computational speed. While the former is mainly related to the improvement of the FEM theory, which is not the focus of study in this paper, the latter is closely related not only to the improvement of the theory, but also to the computational methods and the performance of hardware. The computational method of serial loop is commonly used in the existing modern mechanic engineering computation. But it requires so many hours at a time that could not meet the needs of practical engineering projects. Therefore, the inefficiency of computation becomes a bottleneck that restricts the further promotion and appliance of the FEM theory. For this reason, the research on how to shorten the simulation time and improve the efficiency in solving practical engineering problems has important significance.
In this paper, the author made a deep research on how to improve the computational efficiency of FEM simulation and how to reduce the computing time. This paper mainly focus on how to apply the General Purpose Graphic Processing Unit (GPGPU) technology of Graphic Processing Unit (GPU) to the field of FEM simulation, which could be concluded as the following three major different research aspects.
1) The author put forward a new method of using GPU parallel processing to improve computational efficiency in the simulation process of sheet metal forming and thin-walled structures crashworthiness. Through analyzing the parallel architecture and massive-thread working mechanism of modern GPU, this paper sought out the rules of and factors for GPGPU applications to achieve high performance and studied the feasibility of FEM simulation process of parallel computation. Under the FEM theory, this paper analyzed the pros and cons of using GPU parallel process, coordinated the task assignment and data exchange between GPU and CPU and designed a new FEM processing architecture by using the computational resources of GPU.
2) In this paper the author also proposed the methods of data exchange between GPU and CPU in the FEM simulation process. Through making overall comparative studies of CPU and GPU, the author proposed that use texture as memory when data was mapped into GPU. And the author determined the mapping relation between the array subscript and texture coordination and completed the indexical task of the corresponding data. Finally, the intermediate calculated results were brought back to CPU when parallel computation was completed.
3) This paper put forward methods of translating serial data into parallel array. The problems of the data structure design, data organization, data access density, parallel granular and other challenges, which occurred under the condition of the GPU parallel processing and never appeared in the traditional serial encoding process, were studied and discussed in this paper. Through reducing, increasing, remaining the same array dimensions, directly copying, all the computations were carried out in the units. Both the computational accuracy and the calculation speed were all improved.
4) The author designed advanced ways of parallel computation to improve computational speed of GPU as well as the computational accuracy of GPU. There were so many variables and complicated representations in the process of parallel computation that the author put forward to using many fragment programs to deal with the computation of the same unit. And the related challenging difficulties that each loop variable needs to be updated were successfully resolved in the paper. As well, the goal of parallel simulation was achieved in the paper.
引文
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