Parallel 3-D Finite Element Analysis And Its Application In Hydraulic Engineering

In hydraulic engineering problems, large scale numerical analyses have increased the demand for high-performance computing. To meet the demand, parallel computing is proposed to increase the calculational scale and shorten computing time. This thesis is a study on parallel computing of three-dimensional finite element method(FEM) and its application in hydraulic engineering problems. It is composed of:Techniques about parallel computing and its application in FEM have been discussed and summarized.For the parallel solving of equations set, a parallel solver has been provided based on Jacobi-preconditioned conjugate gradient method in combine with bandwidth reduction technique, which can fully utilize the overlap of computation and data exchange to reduce communication delay. The numerical tests demonstrated that their parallel performance are well done.A detailed derivation for element-by-element(EBE) method has been accomplished. On basis of Jabcobi preconditioned conjugate gradient(JCG) method, a complete parallel algorithm for FEM is presented, including the treatment of different load and boundary conditions. For data exchange, a scheme which only gather and scatter necessary data is advised to make EBE method available for distributed-memory parallel computers. In this way, it could dramatically reduce data exchange and consequently improve efficiency of parallel computing. At the same time, it can be very easy to make load balance for solving three-dimensional FEM. For any complicated three-dimensional structures, the algorithm can be suitable for automatically allocate the task in parallel computing.On the basis of the EBE-JCG method, the author programmed a PFEM(Parallel Finite Element Method) code using MPICH and C/C++ language. Numerical tests on thick walled cylinder and cantilever indicated that they are correct. On the basis of certain criteria and grid refining technology, three-dimensional fracture problem is also implemented in this program. PFEM can be applied to large-scale numerical simulation of arch dam and foundation system successfully. Examples of large-scale numerical computation of two arch dams were demonstrated that the method is efficient and it can effectively solve hydraulic engineering problems with a million degrees of freedom and more.