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Abstract The solution of a sparse and dense symmetric system of linear equations is essential to finite element simulation in geotechnical engineering. However，the traditional direct method will cost too much memory and calculation time. The paper tries to adopt the successive over relaxation(SSOR)-preconditioned conjugate gradient(PCG) method to solve linear systems and provide a new way to realize the SSOR-PCG method，which can remarkably save the memory and calculation time. In this scheme，the global stiffness is stored in a vector so that the cost of memory is the least. In the same time，the form of preconditioned matrix is changed，which makes it possible store the global stiffness and the preconditioned matrix in the same block of memory on the premise of increasing little extra calculation time. A new method to realize multiplying the global stiffness by a vector is also introduced，and it is found that the time of the iterative operation in any time is reduced greatly. Moreover，the definition of double data structure forms is presented，where the information of global stiffness is stored and this is essential to solve the special problem in rather complex geologic environment. To avoid drastic transformation of the global stiffness caused by the boundary conditions and initial information，an additional information matrix is allocated，and the global stiffness and the global load vector are also changed in accordance with a special rule. By this way，a large account of calculation is avoided on the premise of not influencing the final result. It has been proven by numerical examples that the linear equation solver based on the above improvements shows robust. The solver is able to solve the linear system of 3D structural problems with about 300 000 nodes within 50 minutes on a personal computer with Pentium 2.8 GHz CPU and 1.0 GB memory.
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Received: 23 March 2006
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