A distributed memory parallel element-by-element scheme based on Jacobi-conditioned conjugate gradient for 3D finite element analysis

For FEM solution of complex hydraulic structures, a parallel method is usually needed to deal with a large amount of numerical computation. The article introduces an algorithm based on the element-by-element (EBE) scheme of the FEM and Jacobi pre-conditioning conjugate gradient method, including the EBE computation algorithm for boundary conditions and all kinds of loads. Furthermore, based on the concepts of “boundary node” and “local internal node”, a new data exchange technology is developed that realizes the collection and transmission of data and makes it suitable for EBE method to be implemented on distributed memory parallel computers. This algorithm does not generate global stiffness matrix and only stores element stiffness matrices. With this algorithm, a 3D finite element parallel computation program, PFEM, is developed and implemented on a network cluster system to perform 3D finite element computations of an arch dam–foundation system and a large-scale underground tunnel. The results showed that the memory demand of this algorithm is less than that of conventional FEM and the calculation time could be decreased. It works very well for large-scale numerical computation of 3D complex structures like arch dam and underground tunnel.