Research On Parallel Interpolation Algorithm Adapted To Meshless Method

When the finite element method simulates crack propagation,extra-large deformation,etc.,problems such as grid distortion will occur,and it is necessary to continuously perform mesh re-dissection,which is a waste of time.The meshless method uses a point-based approximation that does not require mesh and avoids the mesh re-segmentation process.However,the development of meshless method is still immature,and the problems of computational efficiency and accuracy need to be solved urgently.In this paper,from the perspective of interpolation shape function,the factors affecting the computational efficiency and calculation accuracy of meshless method were studied.The high-speed parallel computing technology of multi-core CPU and GPU was used to accelerate the meshless interpolation process.This paper analyzed the time-consuming conditions of various interpolation algorithms,determined the acceleration scheme,gave the parallel algorithm calculation flow,and verified the feasibility of the acceleration algorithm through data test.The acceleration effect of the parallel acceleration algorithm was analyzed,and the related influencing factors were discussed.Finally,a parallel interpolation algorithm adapted to the meshless method was developed,and an improved scheme for improving the computational efficiency of the meshless method was proposed.The main research work of this paper is as follows:(1)Serial implementations of the RBF,MLS and Shepard interpolation algorithms were developed considering parallelism and data dependencies on the CPU.And through the use of OpenMP interface to develop parallel implementation of interpolation algorithm on multi-core CPU.The parallel implementation on multi-core CPU was analyzed,the corresponding parallel part code was converted into CUDA kernel function and,The parallel implementation of interpolation algorithm on GPU was developed.Based on the parallel implementation on the GPU,the parallel implementation of the interpolation algorithm on multiple GPUs was developed using the Open-MP interface.(2)This paper tested five sets of data on a workstation equipped with two Quadro M5000 GPUs to evaluate the performance of the proposed parallel interpolation algorithm.For the five different k values of 20,30,40,50 and 60,the running time,corresponding acceleration ratio,and the interpolation accuracy results of each set of data are given.(3)The effects of the selection of basic functions and weight functions,shape parameters,node influence domain size and node distribution characteristics on the calculation accuracy of various interpolation algorithms such as radial basis function interpolation were studied.The calculation error caused by the selection of different parameters was analyzed and compared in detail.In order to further improve the calculation accuracy of the interpolation algorithm,some reference suggestions and improvement schemes were provided,which achieved good results.(4)The calculation process of the interpolation part in the meshless method was analyzed,and the parallel optimization scheme of the interpolation part was proposed.The process of calculating the strain matrix of the integral points in all integral domains was extracted from the assembly overall stiffness process,and this process was optimized and paralleled using the parallel interpolation idea of this paper.The impact of whether to fix the number of field nodes in the support domain on computational efficiency and accuracy was analyzed and discussed.The parallel interpolation idea of this paper was applied to the meshless method of cantilever beam calculation,and the calculation efficiency and calculation accuracy before and after optimization were compared.