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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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Author: A. Peano
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Jeff Borggaard
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Category :
Languages : en
Pages :
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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: Sören Bartels
Publisher:
ISBN:
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Languages : en
Pages : 29
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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: Richard A. Shapiro
Publisher: Vieweg+Teubner Verlag
ISBN: 3322878791
Category : Technology & Engineering
Languages : en
Pages : 180
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Book Description
This monograph is the result of my PhD thesis work in Computational Fluid Dynamics at the Massachusettes Institute of Technology under the supervision of Professor Earll Murman. A new finite element al gorithm is presented for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2 to 16, and biquadratic elements are shown to provide potential savings of a factor of 2 to 6. An analysis of the dispersive properties of several discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrat ing some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed.
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:
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Languages : en
Pages :
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In the recent past, the field of scientific computing has become of more and more importance for scientific as well as for industrial research, playing a comparable role as experiment and theory do. This success of computational methods in scientific and engineering research is next to the enormous improvement of computer hardware to a large extend due to contributions from applied mathematicians, who have developed algorithms which make real life applications feasible. Examples are adaptive methods, high order discretization, fast linear and non-linear solvers and multi-level methods. The application of these methods in a large class of problems demands for suitable and robust tools for a flexible and efficient implementation. In order to play a crucial role in scientific and engineering research, besides efficiency in the numerical solution, also efficiency in problem setup and interpretation of simulation results is of utmost importance. As modeling and computing comes closer together, efficient computational methods need to be applied to new sets of equations. The problems to be addressed by simulation methods become more and more complicated, ranging over different scales, interacting on different dimensions and combining different physics. Such problems need to be implemented in a short period of time, solved on complicated domains and visualized with respect to the demand of the user. %Only a modular abstract simulation environment will fulfill these requirements and allow to setup, solve and visualize real-world problems appropriately. In this work, the concepts and the design of the C++ finite element toolbox AMDiS (adaptive multidimensional simulations) are described. It is shown, how abstract data structures and modern software concepts can help to design user-friendly finite element software, which provides large flexibility in problem definition while on the other hand efficiently solves these problems. Also systems of coupled problems can be solved in.
