三维非平面断层破裂数值模拟的GPU实现

Accelerating three-dimensional curved grid finite-difference modelling for non-planar rupture dynamics using GPU graphics card

李孟阳

11749033

硕士

物理学

张振国

2019-05-23

2019-05-31

哈尔滨工业大学

深圳

在地震动力学研究中，实际发生地震的断层往往不仅具有复杂的表面地形环境，断层本身的形状分布也非常复杂，没有有效的分析解法，一直以数值分析模拟地方式进行研究。三维非平面断层破裂模拟采用曲线有限差分方法，能够模拟复杂地形表面，倾斜、具有不规则几何形状的断层破裂过程，拓宽了有限差分方法所能适用的模型。但在继承了有限差分方法精度高、直观的优点的同时，也同时有有限差分方法计算密集，对计算资源要求较高的缺点。随着摩尔定律的失效，CPU(Central Process Unit)性能提升缓慢，而图像处理单元GPU(Graphics Process Unit)在单机游戏图像处理的市场需求下迅速发展，渲染像素的图像处理过程需要大规模并行计算，为满足这一需要，GPU在硬件设计即为大规模并行运算架构。近年英伟达公司发展的的CUDA编程模型，为将通用计算程序移植到GPU设备上提供了方便。使用GPU并行处理加速计算任务、缩短运算时间，迅速在学界和业界得到大规模应用，并成为新的超算基准。本文从介绍GPU异构编程和CUDA并行编程模型谈起，介绍了三维曲线有限差分方法在描述地震波波场传播和滑动弱化准则下断层自发破裂过程的理论基础。并结合两者利用CUDA并行编程模型进行程序设计，完整实现了三维非平面断层破裂模拟的曲线有限差分程序，即曲线坐标下地震波波场传播过程，地震断层自发破裂作为波场内边界条件与波场的耦合，牵引力镜像法实现地表自由表面的模拟，和CPML吸收边界条件。最后对比了本研究编写的GPU程序和三维非平面断层破裂数值模拟的CPU端多核心MPI程序在全空间均匀介质平面断层和带自由表面的倾向断层的模拟结果，在精度范围内两者具有很好的一致性。并应本用GPU程序带自由表面的粗糙断层的模拟上验证其对复杂断层模拟的普适性。在保证精确性和普适性的基础上，对比了GPU相对CPU在使用单精度浮点数模拟的加速效果，相比于1/4/12/24处理器最高分别获得413.6/181.7/76.6/30.7倍的加速效果。截至目前，本研究为使用GPU加速三维非平面断层破裂数值模拟的首次实现。

In the study of seismic dynamics, the faults of actual earthquakes often have not only complex surface topographical environments, but also the shape distribution of the faults. There is no effective analytical solution, so most researchs have been carried out in numerical simulation. The three-dimensional non-planar fault rupture simulation adopts the curve finite difference method, which can simulate the complex terrain-surface, the slope and the fault rupture process with irregular geometry, and broaden the model that the finite difference method can be applied. However, while inheriting the advantages of high precision and intuition of the finite difference method, it also has the disadvantage that the finite difference method is computationally intensive and requires high computational resources.With the failure of Moore's Law, the performance of CPU (Central Process Unit) updates is slowing down, at the same time, the GPU (Graphics Process Unit) is rapidly developing driving by the game market. Image processing requires massive parallel computing to meet this need, so GPU is designed as a massively parallel computing architecture in hardware design. In recent years, the CUDA programming model developed by NVIDIA has facilitated the porting of general-purpose computing programs to GPU devices. Using GPU parallel processing to speed up computing tasks, shorten computing time, and quickly achieve large-scale application in the academic and industry.This paper introduces the GPU heterogeneous programming and CUDA parallel programming model, and introduces the theoretical basis of the three-dimensional curve finite difference method in describing the spontaneous rupture process of faults, under seismic wave field propagation and sliding weakening criteria. Combined with the CUDA parallel programming model for programming, implemented the finite difference program of the three-dimensional non-planar fault rupture simulation, that is, the seismic wave field propagation under the curve coordinates, the spontaneous fault of the seismic fault is used as the boundary condition and wave field in the wave field. The coupling, traction image method achieves surface free surface simulation, and CPML boundary conditions.Finally, the simulation results of the multi-core MPI program of the GPU program and the three-dimensional non-planar fault rupture numerical simulation in the whole space uniform medium plane fault and the free surface tending fault are compared, and both of them have good accuracy within the precision range. Consistency. The generality of the complex fault simulation should be verified by simulating the rough fault of the free surface with the GPU program. On the basis of ensuring accuracy and universality, the acceleration effect of GPU versus CPU using single-precision floating-point simulation is compared, which is around 413.6/181.7/76.6/30.7 speedup respectively compared with 1/4/12/24 processor(s). As of now, this study is the first implementation of numerical simulation using GPU to accelerate 3D non-planar fault rupture.

GPU 数值模拟 有限差分 非平面断层 断层破裂动力学 计算地震学

GPU Numerical approximations and analysis FDM Non-planar fault Rupture dynamics Computational seismology

中文

联合培养

南方科技大学

李孟阳. 三维非平面断层破裂数值模拟的GPU实现[D]. 深圳. 哈尔滨工业大学,2019.