Overview
- Provides a modern overview of scientific computing in direct and iterative methods for linear and nonlinear systems
- Presents important applications in science and engineering, representing the most significant types of mathematical models
- Includes numerous illustrations for ease of understanding
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 41)
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Table of contents (31 chapters)
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Mathematical Modeling, Applications, and Theoretical Foundations
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High Performance and Scientific Computing
Keywords
About this book
Editors and Affiliations
About the editors
David Y Gao is the Alexander Rubinov Chair Professor of Mathematics at the Federation University Australia. He is the author of 14 monograph, handbook, special volumes and more than 200 research papers (> 50% are singleauthored) on applied mathematics, theoretical and computational mechanics, global optimization and operations research etc. His main research contributions include a canonical duality-triality theory, several mathematical models in engineering mechanics and material science, a series of complete solutions to a class of nonconvex/nonsmooth/discrete problems in nonlinear sciences, and some deterministic methods/algorithms for solving certain NPhard problems in global optimization and computational science. One application of this canonical duality theory in large deformation solid mechanics solved a 50-years open problem and leads to a pure complementary energy principle (i.e. the Gao Principle in the literature), which has broad applications in engineering mechanics and physics. One of the large deformed beam models he proposed in 1996 is now recognized as the nonlinear Gao beam which can be used to study postbuckling analysis and plays an important role in real-world applications. In discrete systems, this canonical duality theory shows that the NP-hard 0-1 integer programming problems are identical to a continuous unconstrained Lipschitzian global optimization problem which can be solved deterministically. Professor Gao’s multidisciplinary research has been supported continuously by different programs at US National Science Foundation (NSF) and US Air Force Office for Scientific Research (AFOSR) before he moved to Australia in 2010. He is one of a few researchers in the southern hemisphere who receive research grants every year directly from the AFOSR Washington Office. Recently, Professor Gao’s canonical duality-triality theory has been identified by AFOSR as a breakthrough research and his team has win two prestigious international grant awards with total US$600,000 for 2016-2020.
Andreas Fischer is director of the Institute of Numerical Mathematics at TU Dresden. After his habilitation in 1998, he became an associate professor at the University of Dortmund. Since 2002, he holds the Chair of Numerical Optimization at TU Dresden. His research concentrates on topics around the design and analysis of efficient algorithms in the field of mathematical programming. With his group, he works on theoretical and applied problems in continuous and discrete optimization. For example, this includes generalized Nash equilibria, eigenvalue complementarity problems, beamforming for wireless board-to-board communication, resource allocation, parameter optimization in machine learning, or minimum connectivity inference problems. Currently, he is a principal investigator at the Collaborative Research Center Highly Adaptive Energy-efficient Computing (HAEC) and of further research projects. Andreas Fischer is in the editorial board of several international journals.
Bibliographic Information
Book Title: Advances in Mathematical Methods and High Performance Computing
Editors: Vinai K. Singh, David Gao, Andreas Fischer
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-030-02487-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-02486-4Published: 28 February 2019
eBook ISBN: 978-3-030-02487-1Published: 14 February 2019
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: IX, 503
Number of Illustrations: 70 b/w illustrations, 154 illustrations in colour
Topics: Computational Science and Engineering, Engineering Fluid Dynamics, Numerical Analysis, Math Applications in Computer Science