Generalization Of Mixed Multiscale Finite Element Methods With Applications
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Generalization Of Mixed Multiscale Finite Element Methods With Applications
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Author :
language : en
Publisher:
Release Date : 2016
Generalization Of Mixed Multiscale Finite Element Methods With Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy's flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii.
Multiscale Modeling And Simulation In Science
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Author : Björn Engquist
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Multiscale Modeling And Simulation In Science written by Björn Engquist 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 2009-02-11 with Computers categories.
Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.
Amorphous Semiconductors
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Author : Marc Herbert Brodsky
language : en
Publisher:
Release Date : 1979
Amorphous Semiconductors written by Marc Herbert Brodsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Amorphous semiconductors categories.
Multiscale Model Reduction
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Author : Eric Chung
language : en
Publisher: Springer Nature
Release Date : 2023-06-07
Multiscale Model Reduction written by Eric Chung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-07 with Mathematics categories.
This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.
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.
Multiscale Finite Element Methods
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Author : Marc Herbert Brodsky
language : en
Publisher: Springer
Release Date : 1979
Multiscale Finite Element Methods written by Marc Herbert Brodsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Examines the main concepts and advances in multiscale finite element methods. This title includes chapters that start with a simple introduction and the description of the proposed methods with examples. It is suitable for engineers, applied scientists and those who are interested in multiscale simulations.
A Simple Introduction To The Mixed Finite Element Method
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Author : Gabriel N. Gatica
language : en
Publisher:
Release Date : 2014-01-31
A Simple Introduction To The Mixed Finite Element Method written by Gabriel N. Gatica and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with categories.
Heterogeneous Media
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Author : Konstantin Markov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-02
Heterogeneous Media written by Konstantin Markov 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 2000-02-02 with Technology & Engineering categories.
Most materials used in contemporary life and industry are heterogeneous (composites) and multicomponent, possessing a rich and complex internal structure. This internal structure, or microstructure, plays a key role in understanding and controlling the continuum behavior, or macroscopic, of a wide variety of materials. The modeling process is a critical tool for scientists and engineers studying the analysis and experimentation for the micromechanics and behavior of these materials. "Heterogeneous Media" is a critical, in-depth edited survey of the major topics surrounding the modeling and analysis of problems in micromechanics of multicomponent systems, including conceptual and practical aspects. The goal of this extensive and comprehensive survey is to provide both specialists and nonspecialists with an authoritative and interdisciplinary perspective of current ideas and methods used for modeling heterogeneous materials behavior and their applications. Topics and Features: * all chapters use interdisciplinary modeling perspective for investigating heterogeneous media*Five chapters provide self-contained discussions, with background provided*Focuses only upon most important techniques and models, fully exploring micro-macro interconnections*extensive introductory survey chapter on micromechanics of heterogeneous media*microstructure characterization via statistical correlation functions*micro-scale deformation of pore space*wave fields and effective dynamical properties*modeling of the complex production technologies for composite materials The book is ideal for a general scientific and engineering audience needing an in-depth view and guide to current ideas, methods and
Finite Difference Methods Theory And Applications
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Author : Ivan Dimov
language : en
Publisher: Springer
Release Date : 2019-01-28
Finite Difference Methods Theory And Applications written by Ivan Dimov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-28 with Computers categories.
This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.
Computational Mathematics Algorithms And Data Processing
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Author : Daniele Mortari
language : en
Publisher: MDPI
Release Date : 2020-12-07
Computational Mathematics Algorithms And Data Processing written by Daniele Mortari and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Technology & Engineering categories.
“Computational Mathematics, Algorithms, and Data Processing” of MDPI consists of articles on new mathematical tools and numerical methods for computational problems. Topics covered include: numerical stability, interpolation, approximation, complexity, numerical linear algebra, differential equations (ordinary, partial), optimization, integral equations, systems of nonlinear equations, compression or distillation, and active learning.