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Issue Date: Apr-2000
Publisher: Asian Institute of Technology
Abstract: The element-free Galerkin method (EFGM) is a recently developed numerical technique for solving problems in a wide range of application areas including solid and fluid mechanics. The primary benefit of these methods is the elimination of the need for meshing (or remeshing) complex three-dimensional problem domains. With EFGM, the discrete model of the object is completely described by nodes and a description of the problem domain boundary. However, the elimination of meshing difficulties does not come freely since the EFGM is much more computationally expensive than the finite element method (FEM), especially for three-dimensional and non-linear applications. Parallel processing has long been an available technique to improve the performance of scientific computing programs, including the finite element method. With efficient programming, parallel processing can overcome the high computing time that is typically required in analyses employing EFGM or other meshless methods. This work focuses on the application of the concepts in parallel processing to EFGM analyses, particularly in the formulation of the stiffness matrix, the assembly of the system of discrete equations, and the solution for nodal unknowns, so that the time required for EFGM analyses is reduced. Several low-cost personal computers are joined together to form a parallel computer with the potential for raw computing power comparable to that of the fastest serial computers. The processors communicate via a local high-speed network using the Message Passing Interface (MPI), a standard library of functions that enables parallel programs to be executed on and communicate efficiently over a variety of machines. To provide a comparison between the parallelized and the serial versions of the EFGM computer program, several benchmark 3D structural mechanics problems are analyzed to show that the parallelized EFGM program can provide substantially shorter run time than the serial program without loss of solution accuracy.