Research Of Parallel PCG Algorithm Based On Multiple GPUs And Its Application In Groundwater Flow Simulation

The parallelization of PCG algorithm has great significance to many research problems,because many numerical simulation problems can be speeded up by improving the efficiency of solving equations with PCG.In order to make scientific use of groundwater resources,it's necessary to analyze and predict the flow rules of groundwater.With the continuous development of research,the groundwater numerical simulation program,MODFLOW,has been unable to simulate and analyze large-scale experimental problems.In order to improve the simulation efficiency of MODFLOW,this paper mainly studies the parallelization of PCG algorithm in multiple GPUs environment,and applies the parallel PCG to MODFLOW to realize the parallelization simulation of MODFLOW.In this paper,the linear algebra computing in PCG algorithm is implemented as CUDA kernel functions,and the DIA format of sparse matrix is mainly studied and a highly efficient SpMV kernel function is realized.In order to parallelize PCG in a single-node and multi-GPU environment,the computing are equally divided into multiple GPUs and solved separately.The data communication between multiple GPUs is a performance bottleneck.Therefore,this paper reduces data communication overhead by reducing unnecessary data transfer and overlapping the SpMV calculation with data transfer,which improves the PCG speedup.In the environment with 6 GPUs in a single-node,the speedup of PCG increases significantly with the increase of GPU's number and data size,getting a maximum speedup of 36.3.In the multi-node environment,multiple processes are created using MPI to solve the equations with multiple GPUs.This paper unifies the differences of data communication between intra-node and inter-node by using a data communication model,making it portable and efficient.In the environment using 2 nodes and 4 GPUs,the maximum speedup of the experiment is 17.3,which is less than that of the single-node environment.In order to parallelize MODFLOW,this paper analyzes its modular structure and designs the parallel simulation flow based on OpenMP + CUDA in a single-node environment.The modules of constructing equations and solving equations are redesigned to realize the division of computing and using PCG solvers by multiple threads to simulate.The experimental results in the single-node using 6 GPUs environment show that the maximum speedup of MODFLOW is 11,which is less than that of the parallel PCG.The reason is that the proportion of the parallelizable part in MODFLOW decreases,which leads to the speedup reduces.The results also show that the speedup of steady-state simulation is larger,because the additional overhead is less.In order to study the scalability of MODFLOW,a parallel simulation flow based on MPI + CUDA is designed in the multi-node environment.The experimental results show that in the environment of using 2 nodes and 4 GPUs,the maximum speedup of parallel MODFLOW is 8.5,indicating that it has a bit of scalability.In the multi-node environment,the low bandwidth of data communication between nodes is a performance bottleneck,which leads to the speedup is less than that in the single-node environment in the same experimental conditions.