Author: Douglas N. Arnold
Publisher: Springer Science & Business Media
ISBN: 0387380345
Category : Mathematics
Languages : en
Pages : 247
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Book Description
The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.
Author: Douglas N. Arnold
Publisher: Springer
ISBN: 9780387511535
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.
Author: Arunasalam Rahunanthan
Publisher:
ISBN: 9781109532692
Category : Galerkin methods
Languages : en
Pages : 96
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Book Description
This dissertation consists of two different research efforts. In the first one, a new approach to the treatment of viscous flux in the context of discontinuous Galerkin spatial discretization is addressed. In the second part of the dissertation, an approach to constructing high-order W -methods is discussed. In the first part of the dissertation, a study of boundary and interface conditions for discontinuous Galerkin approximations of fluid flow equations is undertaken. While the interface flux for the inviscid case is usually computed by approximate Riemann solvers, most discretizations of the Navier-Stokes equations use an average of the viscous fluxes from neighboring elements. A methodology for constructing a set of stable boundary/interface conditions that can be thought of as "viscous" Riemann solvers and are compatible with the inviscid limit is presented. In the second part, we turn our attention to temporal discretizations. Implicit methods are the natural choice for solving stiff systems of ODEs. Rosenbrock methods are a class of linear implicit methods for solving such stiff systems of ODEs. In the Rosenbrock methods the exact Jacobian must be evaluated at every step. These evaluations can make the computations costly. By contrast, W -methods use only occasional calculations of the Jacobian matrix. This makes the W-methods popular among the class of linear implicit methods for numerical solution of stiff ODEs. However the price one has to pay is the large amount of work needed to find the coefficients of the W -methods. As the order of the W -methods increases, the number of order conditions of the W-methods increases very fast. This makes the design of high-order W-methods difficult. In the second part, an approach to constructing high-order W -methods is given.
Author: Dario Floreano
Publisher: MIT Press
ISBN: 0262547732
Category : Computers
Languages : en
Pages : 674
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Book Description
A comprehensive introduction to new approaches in artificial intelligence and robotics that are inspired by self-organizing biological processes and structures. New approaches to artificial intelligence spring from the idea that intelligence emerges as much from cells, bodies, and societies as it does from evolution, development, and learning. Traditionally, artificial intelligence has been concerned with reproducing the abilities of human brains; newer approaches take inspiration from a wider range of biological structures that that are capable of autonomous self-organization. Examples of these new approaches include evolutionary computation and evolutionary electronics, artificial neural networks, immune systems, biorobotics, and swarm intelligence—to mention only a few. This book offers a comprehensive introduction to the emerging field of biologically inspired artificial intelligence that can be used as an upper-level text or as a reference for researchers. Each chapter presents computational approaches inspired by a different biological system; each begins with background information about the biological system and then proceeds to develop computational models that make use of biological concepts. The chapters cover evolutionary computation and electronics; cellular systems; neural systems, including neuromorphic engineering; developmental systems; immune systems; behavioral systems—including several approaches to robotics, including behavior-based, bio-mimetic, epigenetic, and evolutionary robots; and collective systems, including swarm robotics as well as cooperative and competitive co-evolving systems. Chapters end with a concluding overview and suggested reading.
Author: Arieh Iserles
Publisher: Cambridge University Press
ISBN: 9780521868150
Category : Mathematics
Languages : en
Pages : 658
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Book Description
A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Author: Marco L. Bittencourt
Publisher: Springer
ISBN: 3319658700
Category : Mathematics
Languages : en
Pages : 681
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Book Description
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Author: Umberto Cugini
Publisher: Springer
ISBN: 0387354956
Category : Computers
Languages : en
Pages : 241
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Book Description
IFIP Working Group 5.2 has organized a series of workshops aimed at presenting and discussing current issues and future perspectives of Geometric Modeling in the CAD environment. From Geometric Modeling to Shape Modeling comprises the proceedings of the seventh GEO workshop, which was sponsored by the International Federation for Information Processing (IFIP) and held in Parma, Italy in October 2000. The workshop looked at new paradigms for CAD including the evolution of geometric-centric CAD systems, modeling of non-rigid materials, shape modeling, geometric modeling and virtual prototyping, and new methods of interaction with geometric models. The seventeen included papers provide an interesting overview of the evolution of geometric centric modeling into shape modeling. Also included is an invited speaker paper, which discusses the foundation of the next generation of CAD systems, where shape and function enhance geometric descriptions. The main topics discussed in the book are: Theoretical foundation for solids and surfaces; Computational basis for geometric modeling; Methods of interaction with geometric models; Industrial and other applications of geometric modeling; New paradigms of geometric modeling for CAD; Shape modeling. From Geometric Modeling to Shape Modeling is essential reading for researchers, graduate and postgraduate students, systems developers of advanced computer-aided design and manufacturing systems, and engineers involved in industrial applications.
Author: Alexandre Ern
Publisher: Springer Nature
ISBN: 3030563413
Category : Mathematics
Languages : en
Pages : 325
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Book Description
This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
Author: Oleg P. Iliev
Publisher: Springer Science & Business Media
ISBN: 1461471729
Category : Mathematics
Languages : en
Pages : 334
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Book Description
One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.
