Title:
Combinatorial scientific computing
Author:
Naumann, Uwe, 1969-
ISBN:
9781439827369
Publication Information:
Boca Raton, Fla. : CRC Press, c2012.
Physical Description:
xxiii, 568 p. : ill.
Series:
Chapman & Hall/CRC computational science ; 12
Series Title:
Chapman & Hall/CRC computational science ; 12
Contents:
1. Combinatorial scientific computing : past successes, current opportunities, future challenges / Bruce Hendrickson and Alex Pothen -- 2. Combinatorial problems in solving linear systems / Iain Duff and Bora Uȧr -- 3. Combinatorial preconditioners / Sivan Toledo and Haim Avron -- 4. A scalable hybrid linear solver based on combinatorial algorithms / Madan Sathe ... [et al.] -- 5. Combinatorial problems in algorithmic differentiation / Uwe Naumann and Andrea Walther -- 6. Combinatorial problems in OpenAD / Jean Utke and Uwe Naumann -- 7. Getting started with ADOL-C / Andrea Walther and Andreas Griewank -- 8. Algorithmic differentiation and nonlinear optimization for an inverse medium problem / Johannes Huber ... [et al.] -- 9. Combinatorial aspects/algorithms in computational fluid dynamics / Rainald Lh̲ner -- 10. Unstructured mesh generation / Jonathan Richard Shewchuk -- 11. 3D Delaunay mesh generation / Klaus Gr̃tner ... [et al.] -- 12. Two-dimensional approaches to sparse matrix partitioning / Rob H. Bisseling ... [et al.] -- 13. Parallel partitioning, coloring, and ordering in scientific computing / E.G. Boman ... [et al.] -- 14. Scotch and PT-Scotch graph partitioning software : an overview / Franȯis Pellegrini -- 15. Massively parallel graph partitioning : a case in human bone simulations / C. Bekas ... [et al.] -- 16. Algorithmic and statistical perspectives on large-scale data analysis / Michael W. Mahoney -- 17. Computational challenges in emerging combinatorial scientific computing applications / David A. Bader and Kamesh Madduri -- 18. Spectral graph theory / Daniel Spielman -- 19. Algorithms for visualizing large networks / Yifan Hu.
Abstract:
"Foreword the ongoing era of high-performance computing is filled with enormous potential for scientific simulation, but also with daunting challenges. Architectures for high-performance computing may have thousands of processors and complex memory hierarchies paired with a relatively poor interconnecting network performance. Due to the advances being made in computational science and engineering, the applications that run on these machines involve complex multiscale or multiphase physics, adaptive meshes and/or sophisticated numerical methods. A key challenge for scientific computing is obtaining high performance for these advanced applications on such complicated computers and, thus, to enable scientific simulations on a scale heretofore impossible. A typical model in computational science is expressed using the language of continuous mathematics, such as partial differential equations and linear algebra, but techniques from discrete or combinatorial mathematics also play an important role in solving these models efficiently. Several discrete combinatorial problems and data structures, such as graph and hypergraph partitioning, supernodes and elimination trees, vertex and edge reordering, vertex and edge coloring, and bipartite graph matching, arise in these contexts. As an example, parallel partitioning tools can be used to ease the task of distributing the computational workload across the processors. The computation of such problems can be represented as a composition of graphs and multilevel graph problems that have to be mapped to different microprocessors"-- Provided by publisher.
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