Numerical Analysis Of Multiscale Problems

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Numerical Analysis Of Multiscale Problems

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Author : Ivan G. Graham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05

Numerical Analysis Of Multiscale Problems written by Ivan G. Graham 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 2012-01-05 with Mathematics categories.

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Numerical Methods And Analysis Of Multiscale Problems

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Author : Alexandre L. Madureira
language : en
Publisher: Springer
Release Date : 2017-02-15

Numerical Methods And Analysis Of Multiscale Problems written by Alexandre L. Madureira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-15 with Mathematics categories.

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

Multiscale Problems Theory Numerical Approximation And Applications

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Author : Alain Damlamian
language : en
Publisher: World Scientific
Release Date : 2011-10-13

Multiscale Problems Theory Numerical Approximation And Applications written by Alain Damlamian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

Analysis Modeling And Simulation Of Multiscale Problems

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Author : Alexander Mielke
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-14

Analysis Modeling And Simulation Of Multiscale Problems written by Alexander Mielke 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 2006-10-14 with Mathematics categories.

This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.

Multiscale Problems

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Author : Alain Damlamian
language : en
Publisher:
Release Date :

Multiscale Problems written by Alain Damlamian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Electronic books categories.

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary NavierStokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) a.

Analysis Modeling And Simulation Of Multiscale Problems

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Author : Alexander Mielke
language : en
Publisher: Springer
Release Date : 2009-09-02

Analysis Modeling And Simulation Of Multiscale Problems written by Alexander Mielke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.

This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.

Multiscale Problems In Science And Technology

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Author : Nenad Antonic
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-06-26

Multiscale Problems In Science And Technology written by Nenad Antonic 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 2002-06-26 with Computers categories.

Proceedings of the Conference on Multiscale Problems in Science and Technology, Dubrovnik, Croatia, 3-9 September 2000

Meshfree Methods For Partial Differential Equations Ix

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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2019-06-19

Meshfree Methods For Partial Differential Equations Ix written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Mathematics categories.

This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.

Modern Solvers For Helmholtz Problems

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Author : Domenico Lahaye
language : en
Publisher: Birkhäuser
Release Date : 2017-03-02

Modern Solvers For Helmholtz Problems written by Domenico Lahaye and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra.

Meshfree Methods For Partial Differential Equations Vii

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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2014-12-02

Meshfree Methods For Partial Differential Equations Vii written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.

Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.