Discrete Variational Problems With Interfaces

Author : Roberto Alicandro,Andrea Braides,Marco Cicalese,Margherita Solci
Publisher : Cambridge University Press
Page : 276 pages
File Size : 51,7 Mb
Release : 2023-12-31
Category : Mathematics
ISBN : 9781009298803

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Discrete Variational Problems with Interfaces by Roberto Alicandro,Andrea Braides,Marco Cicalese,Margherita Solci Pdf

Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

Author : Roberto Alicandro,Andrea Braides,Marco Cicalese,Margherita Solci
Publisher : Cambridge University Press
Page : 275 pages
File Size : 49,6 Mb
Release : 2024-01-31
Category : Mathematics
ISBN : 9781009298780

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Discrete Variational Problems with Interfaces by Roberto Alicandro,Andrea Braides,Marco Cicalese,Margherita Solci Pdf

A systematic presentation of discrete-to-continuum results and methods, offering new perspectives on intrinsically discrete problems.

Author : Roberto Alicandro,Nadia Ansini,Andrea Braides,Andrey Piatnitski,Antonio Tribuzio
Publisher : Springer Nature
Page : 121 pages
File Size : 50,8 Mb
Release : 2023-05-02
Category : Mathematics
ISBN : 9789819906857

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A Variational Theory of Convolution-Type Functionals by Roberto Alicandro,Nadia Ansini,Andrea Braides,Andrey Piatnitski,Antonio Tribuzio Pdf

This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.

Author : Olof B. Widlund,David E. Keyes
Publisher : Springer Science & Business Media
Page : 783 pages
File Size : 44,5 Mb
Release : 2007-01-19
Category : Computers
ISBN : 9783540344681

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Domain Decomposition Methods in Science and Engineering XVI by Olof B. Widlund,David E. Keyes Pdf

Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Author : Katalin Bagi,Maurizio Angelillo
Publisher : Springer Nature
Page : 239 pages
File Size : 52,8 Mb
Release : 2023-09-02
Category : Technology & Engineering
ISBN : 9783031324765

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Discrete Computational Mechanics of Masonry Structures by Katalin Bagi,Maurizio Angelillo Pdf

This book provides an overview to those most important modern and traditional methods of masonry analysis that are able to capture the discrete internal built-up of masonry structures. Such methods are available in a wide variety today – from computational packages based on classical graphical statics techniques through discrete element methods or the most sophisticated no-tension semi-continuum models – , and this book reviews their theoretical foundations, as well as their advantages and preferable fields of application, also calling the attention on their limitations so that the reader could build up a critical view of the choices they have when attacking a masonry mechanics problem. The book gives a basis for the readers to become able to develop their own methods, inspired either by classical graphical statics, or by any modern technique they find promising.

Author : Barbara I. Wohlmuth
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642567674

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Discretization Methods and Iterative Solvers Based on Domain Decomposition by Barbara I. Wohlmuth Pdf

Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Author : Boris N. Khoromskij,Gabriel Wittum
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642187773

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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface by Boris N. Khoromskij,Gabriel Wittum Pdf

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

Author : Zhilin Li,Kazufumi Ito
Publisher : SIAM
Page : 343 pages
File Size : 50,5 Mb
Release : 2006-07-01
Category : Mathematics
ISBN : 9780898716092

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The Immersed Interface Method by Zhilin Li,Kazufumi Ito Pdf

"This book will be a useful resource for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems, particularly problems with fixed and moving interfaces, free boundary problems, and problems on regular domains."--BOOK JACKET.

Author : Tayfun E. Tezduyar
Publisher : Springer Nature
Page : 580 pages
File Size : 42,6 Mb
Release : 2023-11-01
Category : Mathematics
ISBN : 9783031369421

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Frontiers in Computational Fluid-Structure Interaction and Flow Simulation by Tayfun E. Tezduyar Pdf

Computational fluid-structure interaction (FSI) and flow simulation are challenging research areas that bring solution and analysis to many classes of problems in science, engineering, and technology. Young investigators under the age of 40 are conducting much of the frontier research in these areas, some of which is highlighted in this volume. The first author of each chapter took the lead role in carrying out the research presented. Some of the topics explored include Direct flow simulation of objects represented by point clouds Computational investigation of leaflet flutter in thinner biological heart valve tissues High-fidelity simulation of hydrokinetic energy applications High-resolution isogeometric analysis of car and tire aerodynamics Computational analysis of air-blast-structure interaction Heart valve computational flow analysis with boundary layer and leaflet contact representation Computational thermal multi-phase flow for metal additive manufacturing This volume will be a valuable resource for early-career researchers and students — not only those interested in computational FSI and flow simulation, but also other fields of engineering and science, including fluid mechanics, solid mechanics, and computational mathematics – as it will provide them with inspiration and guidance for conducting their own successful research. It will also be of interest to senior researchers looking to learn more about successful research led by those under 40 and possibly offer collaboration to these researchers.

Author : Thomas Richter
Publisher : Springer
Page : 436 pages
File Size : 54,9 Mb
Release : 2017-08-26
Category : Mathematics
ISBN : 9783319639703

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Fluid-structure Interactions by Thomas Richter Pdf

This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.

Author : Andreas Dedner,Bernd Flemisch,Robert Klöfkorn
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 40,8 Mb
Release : 2012-04-23
Category : Technology & Engineering
ISBN : 9783642285899

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Advances in DUNE by Andreas Dedner,Bernd Flemisch,Robert Klöfkorn Pdf

DUNE, the Distributed and Unified Numerics Environment, is an open-source modular toolbox for solving partial differential equations with grid-based methods. This book covers recent advances in the development and usage of DUNE. It consists of a collection of 13 articles which mainly evolved from talks given at the First DUNE User Meeting in Stuttgart, Germany, 6.-8.10.2010. The articles nicely illustrate the advanced capabilities and the strong versatility of the DUNE framework. The first part presents extensions of the DUNE core modules, including the construction of local finite element spaces, a discretization toolbox, and two meta-grids, as well as a discussion of performance pitfalls. The second part introduces several external DUNE modules dealing with, e.g., reduced basis methods, unfitted discontinuous Galerkin methods, optimal control problems, and porous media applications. Specific methods and applications are subject of the third part, ranging from two-phase flow in porous media over the implementation of hybrid discontinuous Galerkin and heterogeneous multi-scale methods up to the coupling of DUNE with an existing finite element package.

Author : Anonim
Publisher : ScholarlyEditions
Page : 743 pages
File Size : 49,5 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464965319

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Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition by Anonim Pdf

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Calculus, Mathematical Analysis, and Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Calculus, Mathematical Analysis, and Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Author : Shaoying Lu
Publisher : Unknown
Page : 286 pages
File Size : 49,7 Mb
Release : 2004
Category : Electronic
ISBN : UCSD:31822032468233

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Scalable Parallel Multilevel Algorithms for Solving Partial Differential Equations by Shaoying Lu Pdf

Author : Dieter Bothe,Arnold Reusken
Publisher : Birkhäuser
Page : 679 pages
File Size : 49,6 Mb
Release : 2017-07-13
Category : Mathematics
ISBN : 9783319566023

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Transport Processes at Fluidic Interfaces by Dieter Bothe,Arnold Reusken Pdf

There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”

Author : Paul Concus,Robert Finn
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461246565

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Variational Methods for Free Surface Interfaces by Paul Concus,Robert Finn Pdf

Vallombrosa Center was host during the week September 7-12, 1985 to about 40 mathematicians, physical scientists, and engineers, who share a common interest in free surface phenomena. This volume includes a selection of contributions by participants and also a few papers by interested scientists who were unable to attend in person. Although a proceedings volume cannot recapture entirely the stimulus of personal interaction that ultimately is the best justification for such a gathering, we do offer what we hope is a representative sampling of the contributions, indicating something of the varied and interrelated ways with which these classical but largely unsettled questions are currently being attacked. For the participants, and also for other specialists, the 23 papers that follow should help to establish and to maintain the new ideas and insights that were presented, as active working tools. Much of the material will certainly be of interest also for a broader audience, as it impinges and overlaps with varying directions of scientific development. On behalf of the organizing committee, we thank the speakers for excellent, well-prepared lectures. Additionally, the many lively informal discussions did much to contribute to the success of the conference.