For finite element problems involving millions of unknowns, iterative methods setup in a parallel computing platform, are more efficient than direct solver techniques. Considerations that are important in the solution of such problems include the time of computation, the memory required and the type of platform being used to solve the problem. Traditionally shared memory machines were popular. However, distributed memory machines are now gaining wider acceptance due to their relatively low cost and ease of setup. The conventional approach to setup an iterative finite element solver is the Element-by-Element (EBE) method with the preconditioned conjugate gradient (PCG) solver. The EBE method is reported by Horie and Kuramae (1997, Microcomputers in Civil Engineering, 2, 12) to be suitable for shared memory parallel architectures, but has certain conflicts in distributed memory machines. This paper proposes a new algorithm that is developed for the parallelization of the solution algorithm of the finite element setup for a {\em distributed memory\/} environment. The new method, called the Equation-by-Equation (EQBYEQ) method, is based on generating and storing the stiffness matrix on an equation-by-equation basis in contrast to the element-by-element basis. This paper discusses the algorithm and implementation of details. The advantages of the EQBYEQ scheme when compared to the EBE scheme, in distributed environment, is discussed
Ganesh Thiagarajan, Ph.D., P.E. is Assistant Professor of the Department of Civil and Mechanical Engineering at UMKC. He received the Ph.D degree in Civil Engineering and Applied Mechanics from Louisiana State University in 1996 and the MS degree in Structural Engineering and the BS degree in Civil Engineering from Indian Institute of Technology, Madras, India in 1988 and 1985, respectively. His research interests include basic and applied research using continuum mechanics and finite elements, numerical simulation of dynamic and static fracture behavior, application of high performance computing in engineering and dental application areas, multi-scale modeling of material behavior and application of composites in civil engineering. He is a member of the ASCE, ASME and ACI.