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Author: Alfred Schmidt
Publisher: Springer Science & Business Media
ISBN: 3540271562
Category : Computers
Languages : en
Pages : 329
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Book Description
During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.
Author: Alfred Schmidt
Publisher: Springer Science & Business Media
ISBN: 3540271562
Category : Computers
Languages : en
Pages : 329
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Book Description
During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.
Author: Kunibert G. Siebert
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
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Book Description
Author: Silvia Bertoluzza
Publisher: Springer Science & Business Media
ISBN: 364224078X
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author: Anders Logg
Publisher: Springer Science & Business Media
ISBN: 3642230997
Category : Computers
Languages : en
Pages : 723
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Book Description
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
ISBN: 3662051893
Category : Mathematics
Languages : en
Pages : 354
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Book Description
As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.
Author: Ronald DeVore
Publisher: Springer Science & Business Media
ISBN: 3642034136
Category : Mathematics
Languages : en
Pages : 671
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Book Description
The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.
Author: Richard S. Gallagher
Publisher: CRC Press
ISBN: 1000945324
Category : Computers
Languages : en
Pages : 326
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Book Description
Rapid advances in 3-D scientific visualization have made a major impact on the display of behavior. The use of 3-D has become a key component of both academic research and commercial product development in the field of engineering design. Computer Visualization presents a unified collection of computer graphics techniques for the scientific visualization of behavior. The book combines a basic overview of the fundamentals of computer graphics with a practitioner-oriented review of the latest 3-D graphics display and visualization techniques. Each chapter is written by well-known experts in the field. The first section reviews how computer graphics visualization techniques have evolved to work with digital numerical analysis methods. The fundamentals of computer graphics that apply to the visualization of analysis data are also introduced. The second section presents a detailed discussion of the algorithms and techniques used to visualize behavior in 3-D, as static, interactive, or animated imagery. It discusses the mathematics of engineering data for visualization, as well as providing the current methods used for the display of scalar, vector, and tensor fields. It also examines the more general issues of visualizing a continuum volume field and animating the dimensions of time and motion in a state of behavior. The final section focuses on production visualization capabilities, including the practical computational aspects of visualization such as user interfaces, database architecture, and interaction with a model. The book concludes with an outline of successful practical applications of visualization, and future trends in scientific visualization.
Author: F. R. Sledge
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
An experimental software system for the solution of a class of non-linear, stationary boundary-value problems is currently under development at the University of Pittsburgh. The program NFEARS (Non-linear Finite-Element Adaptive Research Solver) is a further development of the program FEARS which utilized bilinear elements to solve linear elliptic problems. NFEARS retains the functionality of the earlier program, but incorporates a continuation procedure to solve non-linear problems, using biquadratic Hermitian elements. The NFEARS design properties include the following: (1) The system constitutes an applications-independent finite-element solver for a certain class of two-dimensional, non-linear, stationary, boundary-value problems defined by a weak mathematical formulation; (2) Adaptive approaches are employed extensively. A posteriori error indicators are used to control the adaptive processes and to provide a solution with near optimal error within a prescribed cost range; (3) In the system design, advantage was taken of the inherent parallelism and modularity of the finite element method. In particular, a two-level data structure has been employed to take maximum advantage of the parallelism in the continuation process; and (4) The system is highly modular in structure, reflecting not only the natural separation by distinct function, but also the isolation of those processes, particularly error analysis, which are anticipated to be of the greatest experimental interest. In this way, the migration of NFEARS from convenient research vehicle to efficient production tool will be gradual and controlled. Extensive provisions for evaluating the performance are incorporated.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1852
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Book Description
Author: O. C. Zienkiewicz
Publisher: Elsevier
ISBN: 0080531679
Category : Technology & Engineering
Languages : en
Pages : 1863
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Book Description
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics. * This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
