The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings. The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.

The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.

Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful . ​

"Interactive display and visualization of large geometric and textured models is becoming a fundamental capability. There are numerous application areas, including games, movies, CAD, virtual prototyping, and scientific visualization. One of observations about geometric models used in interactive applications is that their model complexity continues to increase because of fundamental advances in 3D modeling, simulation, and data capture technologies." "As computing power increases, users take advantage of the algorithmic advances and generate even more complex models and data sets. Therefore, there are many cases where we are required to visualize massive models that consist of hundreds of millions of triangles and, even, billions of triangles. However, interactive visualization and handling of such massive models still remains a challenge in computer graphics and visualization. In this monograph we discuss various techniques that enable interactive visualization of massive models." "These techniques include visibility computation, simplification, levels-of-detail, and cache-coherent data management. We believe that the combinations of these techniques can make it possible to interactively visualize massive models in commodity hardware."--BOOK JACKET.

The Encyclopedia of GIS provides a comprehensive and authoritative guide, contributed by experts and peer-reviewed for accuracy, and alphabetically arranged for convenient access. The entries explain key software and processes used by geographers and computational scientists. Major overviews are provided for nearly 200 topics: Geoinformatics, Spatial Cognition, and Location-Based Services and more. Shorter entries define specific terms and concepts. The reference will be published as a print volume with abundant black and white art, and simultaneously as an XML online reference with hyperlinked citations, cross-references, four-color art, links to web-based maps, and other interactive features.

The Third International Frontiers of Algorithmics Workshop (FAW 2009), held during June 20–23,2009 at Hefei University of Technology, Hefei, Anhui, China, continued to provide a focused forum on current trends in research on algori- mics,includingdiscretestructures,andtheirapplications.We aimatstimulating the various ?elds for which algorithmics can become a crucial enabler, and to strengthenthe ties between the Easternand Westernalgorithmicsresearchc- munities as well as theory and practice of algorithmics. We had three distinguished invited speakers: Guoliang Chen, Andrew Chi- Chih Yao and Frances Foong Yao, speaking on parallel computing, communication complexity and applications, and computer and network power management. The ?nal program also included 33 peer-reviewed papers selected out of 87 contributed submissions, covering topics including approximation and online - gorithms; computational geometry; graph theory and graph algorithms; games and applications; heuristics; large-scale data mining; machine learning; pattern recognition algorithms; and parameterized algorithms. April 2009 Xiaotie Deng John Hopcroft Jinyun Xue Organization FAW 2009 was organized by Hefei University of Technology, China.

This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.

The Collaborative Research Center SFB 401: Flow Modulation and Fluid-Structure Interaction at Airplane Wings investigates numerically and experimentally fundamental problems of very high capacity aircraft having large elastic wings. This issue summarizes the findings of the 12-year research program at RWTH Aachen University which was funded by the Deutsche Forschungsgemeinschaft (DFG) from 1997 through 2008. The research program covered the following three main topics of large transport aircraft: (i) Model flow, wakes, and vortices of airplanes in high-lift-configuration, (ii) Numerical tools for large scale adaptive flow simulation based on multiscale analysis and a parametric mapping concept for grid generation, and (iii) Validated computational design tools based on direct aeroelastic simulation with reduced structural models.

The aim of this book is to provide the latest research findings, innovative research results, methods and development techniques from both theoretical and practical perspectives related to intelligent social networks and collaborative systems, intelligent networking systems, mobile collaborative systems, secure intelligent cloud systems, etc., and to reveal synergies among various paradigms in the multi-disciplinary field of intelligent collaborative systems. It presents the Proceedings of the 9th International Conference on Intelligent Networking and Collaborative Systems (INCoS-2017), held on August 24–26, 2017 in Toronto, Canada. With the rapid evolution of the Internet, we are currently experiencing a shift from the traditional sharing of information and applications as the main purpose of the Web to an emergent paradigm that puts people at the very centre of networks and exploits the value of people’s connections, relations and collaborations. Social networks are also pla ying a major role in the dynamics and structure of intelligent Web-based networking and collaborative systems. Virtual campuses, virtual communities and organizations effectively leverage intelligent networking and collaborative systems by tapping into a broad range of formal and informal electronic relations, such as business-to-business, peer-to-peer and many types of online collaborative learning interactions, including the emerging e-learning systems. This has resulted in entangled systems that need to be managed efficiently and autonomously. In addition, the latest and powerful technologies based on Grid and wireless infrastructure as well as Cloud computing are now greatly enhancing collaborative and networking applications, but are also facing new issues and challenges. The principal objective of the research and development community is to stimulate research that leads to the creation of responsive environments for networking and, in the longer-term, the developmen t of adaptive, secure, mobile, and intuitive intelligent systems for collaborative work and learning.