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Author:
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ISBN:
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Languages : en
Pages : 20
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Author: Björn Engquist
Publisher: Springer Science & Business Media
ISBN: 3540264442
Category : Technology & Engineering
Languages : en
Pages : 300
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Book Description
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.
Author: Timothy J. Truster
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This work presents an error estimation framework for a mixed displacement-pressure finite element method for nearly incompressible elasticity that is based on variational multiscale concepts. The displacement field is decomposed into coarse scales captured by the finite element mesh and fine scales representing the part of the physics unresolved by the mesh. This solution field decomposition addresses the artificial length scales resulting from discretization of a continuum problem at the variational level to produce a stabilized method equipped with naturally derived error estimators. Two error estimators are proposed. The first employs a representation by bubble functions that arises consistently during the development of the stabilized method and is computed by a simple, direct post-solution evaluation. The second involves solving the fine scale error equation through localization to overlapping patches spread across the domain. The performance of the stabilized method and the error estimators is investigated through numerical convergence tests conducted for two model problems on uniform and distorted meshes. The sharpness and robustness of the estimators is observed to be consistent across the simulations performed.
Author: Sergey I. Repin
Publisher: Walter de Gruyter
ISBN: 3110203049
Category : Mathematics
Languages : en
Pages : 329
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Book Description
This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.
Author: René de Borst
Publisher: Springer Science & Business Media
ISBN: 9048198097
Category : Computers
Languages : en
Pages : 451
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Book Description
This work gives a modern, up-to-date account of recent developments in computational multiscale mechanics. Both upscaling and concurrent computing methodologies will be addressed for a range of application areas in computational solid and fluid mechanics: Scale transitions in materials, turbulence in fluid-structure interaction problems, multiscale/multilevel optimization, multiscale poromechanics. A Dutch-German research group that consists of qualified and well-known researchers in the field has worked for six years on the topic of computational multiscale mechanics. This text provides a unique opportunity to consolidate and disseminate the knowledge gained in this project. The addition of chapters written by experts outside this working group provides a broad and multifaceted view of this rapidly evolving field.
Author: Ivan G. Graham
Publisher: Springer Science & Business Media
ISBN: 3642220614
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Björn Engquist
Publisher: Springer Science & Business Media
ISBN: 3540253351
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.
Author: Volker Schulz
Publisher: Springer
ISBN: 3319904698
Category : Mathematics
Languages : en
Pages : 276
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Book Description
The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers. This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.
Author: Peter Benner
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110671506
Category : Mathematics
Languages : en
Pages : 369
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Book Description
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.
Author: Gunilla Kreiss
Publisher: Springer Science & Business Media
ISBN: 3642117953
Category : Mathematics
Languages : en
Pages : 900
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Book Description
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