| In this dissertation, studies on performing parallel finite element computation in geotechnical engineering on cluster of personal computers (PCs) are carried out. The purpose is to enrich the application of finite element method (FEM) in geotechnical engineering. The parallel strategies of finite element method, the distributed storage of abundant data, the convergence speed of iterative solution of large scale linear equations and the implementation of parallel finite element method are the most important problems. We proposed a system of solutions to these problems. In detail, we have completed the following work,1. Build up a parallel system platform on Window OS based on a cluster of workstations (COW). We connected many PCs by 10~100Mb high speed Ethernet, and on this platform the MPI is used as communication library for parallel finite element software.2. Study on parallel strategies of FEM. The traditional method for parallel FEM is local parallization strategies and it is still used in many softwares. The local parallization is to parallel the large partial calculation of FEM, such as the element assemblage, the solution of equations, etc.. As for distributed parallel system, the efficiency of this scheme is low because of plenty of communication, especially in COW parallel system with low speed of net. So we use domain decomposition method ("divide and conquer"strategy) to achieve the parallization of FEM. In this method, the calculated domain is partitioned into many subdomains which have the same size. Then these subdomains are mapped to many processors and computation are carried out parallelly and independently in each processors. Each process completes all computation of FEM and only common areas need communication to exchange information. Compared with local parallization, domain decomposition method has the advantages of highly parallism, less communication, better scalability, easier transportation and less software maintenance work.3. Study on distributed storage scheme of large FEM data. The main problem for computation of large scale FEM on a single PC is the memory restriction because of large amount of data in FEM. Another consideration for large scale FEM simulation in distributed system should be taken is the reduction of communication among processors. In combination of domain decomposition strategy, we store the data linking with each subdomain in each processor. So the data locality not only can reduce the communication, but also increase the scale of the computation.4. Study on the iterative method for solution of large equations. We adopt preconditioning conjugated gradient (PCG) method to fulfill parallel solution of linear equations because of large requirements of storage and calculation of direct methods. To increase the convergence speed, a preconditioner is created based on subdomain data. So this type of PCG is very suitable for parallel algorithm of large scale linear equations. And it has good convergence and high performance.5. Implementation of parallel FEM. Compared with serial programming, parallel programming is much more difficult. In FEM, the program is very complicate because of quantities of modules and functions. So we utilize object-oriented programming method to develop our parallel FEM software called ParallelGeoFEM. Some abstract class ( such as ParallelFEM, Interface, SubDomain, NewtonRaphson and MeshPartitioner etc.) are used to enclosed the... |
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