Parallel Computation Based On Adaptive Finite Element Of Multi-field Coupling Phase Field Model Simulation

The parallel computing plays an increasingly important role in the field of scientific engineering with the development of computer science and technology.The numerical simulation using computer technology has been adopted by many scholars all over the world.Phase-field method is one of the most effective methods for numerical simulation of microstructure.With the deep application of phase field method development,it is more difficult to solve the phase field model of external influence factors such as coupled solute field and temperature field based on phase field method.It is inevitable that the calculation amount is large,the calculation scale is small,and the calculation efficiency is low.It is a major issue that studying how to use parallel computing technology to solve phase field model,reduce computation time and improve computational efficiency.The essence of the phase field model is a set of partial differential equations.The difficulty in solving the problem lies in how to carry out the dispersion of the solution.The adaptive finite element method can automatically adjust the mesh or solution according to the distribution of numerical solutions or the required numerical solution precision.The method can discretize the differential equations,discretize the continuous solution domain of infinite degrees of freedom into a finite number of degrees of freedom,and automatically adapt the grid or the order of the solution to make the numerical calculation more efficient.This solution is difficult to obtain the exact numerical solution when solving the differential partial differential equation.The mesh quantity and the calculation amount are reduced while ensuring the accuracy of the numerical solution.Therefore,the adaptive finite element method is an advanced numerical simulation method,and it has achieved rapid development in large-scale calculation.In this thesis,based on the adaptive finite element method combined with parallel computing technology to solve the binary alloy phase field model simulation problem.The main work is as follows:(1)The adaptive finite element method is used to solve the pure material phase field model.The effects of physical parameters such as anisotropy and supercooling on dendritic morphology and growth were studied under the condition of large computational domain and thin interfacial layer thickness.By comparing the calculated results with the results of the finite difference method,the degree of freedom at the completion of the calculation is only4.76?10~5,which is an order of magnitude lower than the finite difference method.(2)The simulation of the phase field model of Al-Cu binary alloy is achieved,which is based on adaptive finite element method combined with MPI parallel programming method.The MPI programming method is used to calculate domain partitioning,data communication,task combination and processor mapping based on the discrete phase field model of h-type adaptive finite element method.Exploring and analyzing the parallelism of the phase field model in the adaptive finite element method.The results show that the larger the computational domain,the higher the acceleration ratio obtained.When the computational domain is 6×6 and the number of processes is 12,the highest acceleration ratio of 15.6 is obtained.(3)Optimize the experiment by using MPI+OpenMP hybrid programming,and compare the differences in calculation time,calculation efficiency and acceleration ratio between the two parallel methods.The results show that the MPI+OpenMP hybrid programming method is higher than the MPI under the same conditions.When the calculation domain size is 9×9,the 10.2 times acceleration ratio can be achieved,breaking through the limitations of using pure MPI programming methods,enabling resources to be fully utilized.