Mathematical And Computational Techniques For Multilevel Adaptive Methods
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Mathematical And Computational Techniques For Multilevel Adaptive Methods
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Author : Ulrich Ruede
language : en
Publisher: SIAM
Release Date : 1993-01-01
Mathematical And Computational Techniques For Multilevel Adaptive Methods written by Ulrich Ruede and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures.
Mathematical And Computational Techniques For Multilevel Adaptive Methods
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Author : Ulrich Ruede
language : en
Publisher: SIAM
Release Date : 1993-01-01
Mathematical And Computational Techniques For Multilevel Adaptive Methods written by Ulrich Ruede and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures. Rüde introduces a well-founded mathematical theory that leads to intelligent, adaptive algorithms, and suggests advanced software techniques. This new kind of multigrid theory supports the so-called "BPX" and "multilevel Schwarz" methods, and leads to the discovery of faster more robust algorithms. These techniques are deeply rooted in the theory of function spaces. Mathematical and Computational Techniques for Multilevel Adaptive Methods examines this development together with its implications for relevant algorithms for adaptive PDE methods. The author shows how abstract data types and object-oriented programming can be used for improved implementation.
Computational Techniques For Multilevel Adaptive Methods
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Author : Ulrich Rüde
language : en
Publisher:
Release Date : 1993
Computational Techniques For Multilevel Adaptive Methods written by Ulrich Rüde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Multilevel Adaptive Methods For Partial Differential Equations
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Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1989-01-01
Multilevel Adaptive Methods For Partial Differential Equations written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques. It also contains new material, which is included to fill in certain gaps and to expose new avenues of research. Also, because adaptive refinement seems to demand a lot of attention to philosophical issues, personal perspectives are often brought freely into the discussion.
Mathematical And Computational Techniques For Multilevel Adaptative Methods
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Author : Ulrich Rüde
language : en
Publisher:
Release Date : 1993
Mathematical And Computational Techniques For Multilevel Adaptative Methods written by Ulrich Rüde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Computational Techniques And Applications Ctac 97 Proceedings Of The Eight Biennial Conference
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Author : John Noye
language : en
Publisher: World Scientific
Release Date : 1998-08-08
Computational Techniques And Applications Ctac 97 Proceedings Of The Eight Biennial Conference written by John Noye and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-08 with categories.
This proceedings volume contains three invited papers and 93 contributed papers. The topics covered range from studies of theoretical aspects of computational methods to simulation of industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will have much interest in this volume.
Parallel Multilevel Methods
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Author : Gerhard Zumbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Multilevel Methods written by Gerhard Zumbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Multilevel Projection Methods For Partial Differential Equations
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Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1992-01-01
Multilevel Projection Methods For Partial Differential Equations written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick.
Adaptive Methods Algorithms Theory And Applications
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Author : W. Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Adaptive Methods Algorithms Theory And Applications written by W. Hackbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Computers categories.
The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.
Design Of Adaptive Finite Element Software
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Author : Alfred Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Design Of Adaptive Finite Element Software written by Alfred Schmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Computers categories.
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.