Finite Element Methods: : Parallel-Sparse Statics and Eigen-Solutions

FEM, and the associated computer software are widely recognized as some of the most effective tools for solutions of large-scale engineering applications. Efficient equation and eigen-solvers play critical roles in solving these problems. Sparse matrix technologies have evolved and are now mature enough that all popular and commercialized FEM codes have inserted sparse solvers into their software. So far, however, few books include detailed discussion and explanation of sparse equation-solvers and Lanczos domain decomposition (DD) or finite element formulation for parallel computing purposes. The material in **Finite Element Methods: Parallel-Sparse Statics and Eigen-Solutions** has evolved over the past several years from the author's research work and his graduate courses. This book is ideal for graduate students, practicing engineers and researchers, as well as mathematicians and computer scientists. Dr. Duc T. Nguyen is the founding Director of the Institute for Multidisciplinary Parallel-Vector Computation and Professor of Civil and Environmental Engineering at Old Dominion University. Dr. Nguyen has been listed as an ISI Highly Cited ResearcherTM in the field of engineering. Finite element methods (FEM), and its associated computer software have been widely accepted as one of the most effective general tools for solving large-scale, practical engineering and science applications. For implicit finite element codes, it is a well-known fact that efficient equation and eigen-solvers play critical roles in solving large-scale, practical engineering/science problems. Sparse matrix technologies have been evolved and become mature enough that all popular, commercialized FEM codes have already inserted sparse solvers into their software. However, a few FEM books have detailed discussions about Lanczos eigen-solvers, or explain domain decomposition (DD) finite element formulation (including detailed hand-calculator numerical examples) for parallel computing purposes. The materials from this book have been evolved over the past several years through the author's research work, and graduate courses. This textbook should be useful for graduate students, practicing engineers, and researchers who wish to thoroughly understand the detailed step-by-step algorithms, used during the finite element (truly sparse) assembly, the "direct" and "iterative" sparse equation * eigen-solvers and incorporating the DD formulation for efficient parallel computation.