Engineering Computational Technology
Chapter 10 E.D. Sotelino and Y. Dere
School of Civil Engineering, Purdue University, West Lafayette, Indiana, United States of America Keywords: parallel processing, distributed computing, finite element analysis, domain decomposition, substructuring, load balancing.
Several sophisticated commercial finite element software packages are available. However, the realistic simulations of structural engineering applications is, in general, computationally intensive and often cannot be achieved using traditional computing facilities. Parallel processing and distributed computing provide possible venues to achieve the needed computational power. Since the late 1980's much research has been carried out to take advantage of this technology in many engineering areas, and, in particular, in structural engineering. The finite element method is the most popular numerical method used to solve structural engineering problems. Various schemes have been proposed to parallelise this method. These attempts date back to the late 1970's, when the Finite Element Machine [1] was developed. In this paper, a number of research topics related to the parallel finite element analysis for structural dynamic applications are discussed. This is an exciting research area and much work is current underway. It should be noted that this work is not intended as a state-of-the-art review of the field. Instead, its goal is to provide some background information in parallel and distributed computing as it applies to the finite element analysis of structures and to discuss some of the research activities that have been carried out in this area. Much research in this area exists and a complete literature review would require a different forum. The next paragraphs give the scope of the topics that are presented in this paper. Many of the existing algorithms for the parallel finite element analysis of structures are based on domain decomposition and substructuring techniques. Both techniques are based on the partition of the physical structure into subdomains or substructures. In Domain Decomposition (DD) or Parallel Substructuring methods, the structure is divided into a number of substructures. The interior degrees-of- freedom (DOF) are condensed out so that the size of the condensed system reduces to the number of interface DOF. The solution for the interior DOF is then recovered from the interface DOF. The condensation procedure can be performed in parallel by each processor independently. For the interface solution, communication is needed since the effective stiffness matrix and the load vector have overlapping coefficients. Reference [2] gives one of the first implementations of this type of approach. Similarly to domain decomposition methods, domain-splitting (DS) methods, divide the physical problem into a number of smaller sub-problems. The main difference between these methods and the previously described ones is that they do not use substructuring in their formulation. Instead, they adopt other approaches to restore the uniqueness of the solution of the interface degrees of freedom. For example, the IGI algorithm [3] uses iterative procedures, while the FETI algorithm [4] uses Lagrange multipliers. Several parallel DD and concurrent DS methods are presented in this paper. The performance of a parallel algorithm based on domain partitioning is highly dependent on how the structure is partitioned. Ideally, a perfect balance of the workload in each processor in a parallel or distributed computer is desired. Thus, many researchers have also studied the partitioning problem. The various approaches that have been used, ranging from automatic domain partitioning algorithms to dynamic load balancing techniques, are also discussed here. Finally, the implementation of the various parallel methods into a single platform poses a great challenge. Research has been carried out on the development of software tools that facilitate and promote the reuse, rapid prototyping and portability of parallel structural engineering software. In particular, one such a tool is the SECSDE (Structural Engineering Concurrent Software Development Environment), which has been developed in the School of Civil Engineering at Purdue University [5]. A brief description of this environment is also provided in this paper.
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