Adaptive Parallel Multilevel Methods For Partial Differential Equations
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Adaptive Parallel Multilevel Methods For Partial Differential Equations
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Author : Gerhard Zumbusch
language : en
Publisher:
Release Date : 2001
Adaptive Parallel Multilevel Methods For Partial Differential Equations written by Gerhard Zumbusch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
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 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.
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.
A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations
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Author : Marc Alexander Schweitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations written by Marc Alexander Schweitzer 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.
the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.
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.
Scalable Adaptive Multilevel Solvers For Multiphysics Problems
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Author :
language : en
Publisher:
Release Date : 2014
Scalable Adaptive Multilevel Solvers For Multiphysics Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.
Numerical Solution Of Partial Differential Equations On Parallel Computers
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Author : Are Magnus Bruaset
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-05
Numerical Solution Of Partial Differential Equations On Parallel Computers written by Are Magnus Bruaset 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 2006-03-05 with Mathematics categories.
Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Adaptive Methods For Partial Differential Equations
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Author : Ivo Babushka
language : en
Publisher: SIAM
Release Date : 1989-01-01
Adaptive Methods For Partial Differential Equations written by Ivo Babushka 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.
"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
Scalable Parallel Multilevel Algorithms For Solving Partial Differential Equations
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Author : Shaoying Lu
language : en
Publisher:
Release Date : 2004
Scalable Parallel Multilevel Algorithms For Solving Partial Differential Equations written by Shaoying Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.