A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations
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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.
Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations
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Author : Tarek Mathew
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-25
Domain Decomposition Methods For The Numerical Solution Of Partial Differential Equations written by Tarek Mathew 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 2008-06-25 with Mathematics categories.
Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Optimization With Pde Constraints
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Author : Ronald Hoppe
language : en
Publisher: Springer
Release Date : 2014-09-11
Optimization With Pde Constraints written by Ronald Hoppe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Computers categories.
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).
High Order Nonlinear Numerical Schemes For Evolutionary Pdes
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Author : Rémi Abgrall
language : en
Publisher: Springer
Release Date : 2014-05-19
High Order Nonlinear Numerical Schemes For Evolutionary Pdes written by Rémi Abgrall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Mathematics categories.
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Meshfree Methods For Partial Differential Equations Iv
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-16
Meshfree Methods For Partial Differential Equations Iv written by Michael Griebel 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 2008-10-16 with Mathematics categories.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a active research field both in the mathematics and engineering community. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn.
Recent Trends In Computational Engineering Ce2014
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Author : Miriam Mehl
language : en
Publisher: Springer
Release Date : 2015-10-12
Recent Trends In Computational Engineering Ce2014 written by Miriam Mehl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-12 with Computers categories.
This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer architectures, and novel mathematical approaches. Accordingly, the chapters of the book particularly focus on parallel algorithms and performance optimization, coupled systems, and complex applications and optimization.
Bail 2010 Boundary And Interior Layers Computational And Asymptotic Methods
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Author : Carmelo Clavero
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-11
Bail 2010 Boundary And Interior Layers Computational And Asymptotic Methods written by Carmelo Clavero 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 2011-05-11 with Mathematics categories.
This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.
Computational Methods In Transport Verification And Validation
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Author : Frank Graziani
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-09
Computational Methods In Transport Verification And Validation written by Frank Graziani 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 2008-08-09 with Science categories.
The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.
Sparse Grids And Applications Munich 2012
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Author : Jochen Garcke
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-11
Sparse Grids And Applications Munich 2012 written by Jochen Garcke 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 2014-04-11 with Mathematics categories.
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
Domain Decomposition Methods In Science And Engineering Xxii
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Author : Thomas Dickopf
language : en
Publisher: Springer
Release Date : 2016-03-11
Domain Decomposition Methods In Science And Engineering Xxii written by Thomas Dickopf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-11 with Computers categories.
These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.
