Research And Application Of Finite Element Method Based On Many-core Heterogeneous System Architecture

Calculating numerical solution of partial differential equation takes up a high postion in scienticfic research and industrial design.With the rapid development of computer technology,the scarce computing resource becomes rich and multitudinousness.All kinds of commercial simulation softwares such as Fluent and COMSOL develops very fast and are widely applied.In these methods,finite element method has high accuracy and is easy to couple models,so it becomes pretty popular recently.Although commercial finite element method makes a great success in many design and research scenes,it can not satisfy the simulation demands in some special scenes.For example,finite element method needs coupling with mento carlo method in multi-scale simulation.Besides,only homogenous computing resource is utilized when it runs on a heterogeneous computer.For these problems,this thesis goes into the basic theory of finite element method and its parallelization,designs a program using C++-OOP and design pattern and fulfill a parallel finite element program based on many-core heterogeneous system by MPI and OpenMP.The detail work of this thesis follows as:1.This thesis analyzes the basic theory,procedure and the inf-sup condition when applying FEM to computational fluid dynamic.Different finite element spaces are used to ensure stabilization.And extra term in Petrov-Galerkin method is introduced to reduce the vibration when convection dominates.2.It is analyzed that the main computation focuses on the solving algorithm.This thesis proposes an optimization method of stabilized bi-conjugate gradient algorithm with approximate inverse preconditioner on CPU and Xeon Phi system.OLL,CSR and CSC sparse matrix formats are used.Solving algorithm is realized with MPI and OpenMP.And parallel algorithm and load balancing are optimized.3.The program in this thesis is designed and realized with C++OOP and design pattern and offers rich inerfaces for algorithm coupling and different model.For the problem that the program allocates and copies memories too frequently,this thesis proposes a memory pool method that can be freed quickly for optimization.This thesis completes a finite element method based on parallel heterogeneous system.And the optimation methods above are tested using the data that the program in this thesis produces.It's showed that there exists validity and necessity for memory pool optimation and great effect for parallel realization.Besides,The same example is calculated by the program and COMSOL,verifying the correctness of the program.This thesis simulates the plasma etching process and analyzes the result.