GPU Parallel Solution Of Nonlinear Stokes Equation Based On Finite Element Method

The numerical modeling of glacier and ice sheet evolution is an important part of the numerical simulation for global climate evolution.With the expansion of the simulation scale,the scale of calculation is increasing rapidly.In this dissertation,a nonlinear Stokes equation for glacier model is considered.For its finite element computation format,its parallel solution on GPU is mainly considered.In this dissertation,the GPU parallel process for generation of element stiffness matrix and element load is analyzed.The calculation form for element stiffness matrix and element load in two dimensional and three-dimensional cases is given.According to the calculation characteristics,the structures are given to make the data that needs visited frequently in the structure to improve the efficiency of data accessing and thread communication.The data that need frequent access and is independent with elements is defined as CUDA constant type variable,which improves data access efficiency.In order to get the solution of saddle point problem,this dissertation presents an al-gorithm suitable for parallel on GPU.The structure of GPU acceleration is designed.The multiplication between total stiffness matrix and the vector is given by the multiplication between element stiffness matrix and the vector.Then,with the SOR-like iterative algo-rithmthe,parallel solving of the saddle point problemis is completed.This method makes the storage and computation complexity of matrix vector multiplication be O(N_e)for two-dimensional triangulation case.Finally,some numerical experiments are carried out in this dissertation.