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Multiscale Modeling With Meshfree Methods
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Book Synopsis Extended Finite Element and Meshfree Methods by : Timon Rabczuk
Download or read book Extended Finite Element and Meshfree Methods written by Timon Rabczuk and published by Academic Press. This book was released on 2019-11-13 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. - Explains all the important theory behind XFEM and meshfree methods - Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes - Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods - Introduces alternative modeling methods to help readers decide what is most appropriate for their work
Book Synopsis Multiphysics and Multiscale Modeling by : Young W. Kwon
Download or read book Multiphysics and Multiscale Modeling written by Young W. Kwon and published by CRC Press. This book was released on 2015-10-05 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to appeal to a wide field of engineers and scientists who work on multiscale and multiphysics analysis, Multiphysics and Multiscale Modeling: Techniques and Applications is dedicated to the many computational techniques and methods used to develop man-made systems as well as understand living systems that exist in nature. Presenting a body
Book Synopsis Multiscale Models in Mechano and Tumor Biology by : Alf Gerisch
Download or read book Multiscale Models in Mechano and Tumor Biology written by Alf Gerisch and published by Springer. This book was released on 2018-03-16 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.
Book Synopsis Meshfree Methods for Partial Differential Equations IX by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations IX written by Michael Griebel and published by Springer. This book was released on 2019-06-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the 2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.
Book Synopsis Multiresolution Methods in Scattered Data Modelling by : Armin Iske
Download or read book Multiresolution Methods in Scattered Data Modelling written by Armin Iske and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi levelapproximation schemes, and meshfree discretizations for transport equa tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.
Book Synopsis Nonlocal Diffusion and Applications by : Claudia Bucur
Download or read book Nonlocal Diffusion and Applications written by Claudia Bucur and published by Springer. This book was released on 2016-04-08 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
Book Synopsis Multiscale Modeling and Simulation in Science by : Björn Engquist
Download or read book Multiscale Modeling and Simulation in Science written by Björn Engquist and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Meshfree Methods for Partial Differential Equations VII by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations VII written by Michael Griebel and published by Springer. This book was released on 2014-12-02 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Microstructure Investigations to Multiscale Modeling by : Delphine Brancherie
Download or read book From Microstructure Investigations to Multiscale Modeling written by Delphine Brancherie and published by John Wiley & Sons. This book was released on 2018-01-04 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanical behaviors of materials are highly influenced by their architectures and/or microstructures. Hence, progress in material science involves understanding and modeling the link between the microstructure and the material behavior at different scales. This book gathers contributions from eminent researchers in the field of computational and experimental material modeling. It presents advanced experimental techniques to acquire the microstructure features together with dedicated numerical and analytical tools to take into account the randomness of the micro-structure.
Book Synopsis Meshfree Approximation Methods with MATLAB by : Gregory E. Fasshauer
Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
Book Synopsis Meshfree Methods for Partial Differential Equations VIII by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations VIII written by Michael Griebel and published by Springer. This book was released on 2017-04-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer 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 have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.
Book Synopsis Meshfree Methods for Partial Differential Equations V by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations V written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2010-11-04 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.
Book Synopsis Meshfree Methods for Partial Differential Equations VI by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations VI written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2012-12-16 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering.
Book Synopsis Meshfree Methods for Partial Differential Equations II by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations II written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2004-12-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.
Book Synopsis Meshfree Methods for Partial Differential Equations IV by : Michael Griebel
Download or read book Meshfree Methods for Partial Differential Equations IV written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2008-10-10 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. 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. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field.
Book Synopsis Phase-Field Methods in Materials Science and Engineering by : Nikolas Provatas
Download or read book Phase-Field Methods in Materials Science and Engineering written by Nikolas Provatas and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained, one-stop source discusses phase-field methodology in a fundamental way, explaining advanced numerical techniques for solving phase-field and related continuum-field models. It also presents numerical techniques used to simulate various phenomena in a detailed, step-by-step way, such that readers can carry out their own code developments. Features many examples of how the methods explained can be used in materials science and engineering applications.
Book Synopsis Meshless Methods in Solid Mechanics by : Youping Chen
Download or read book Meshless Methods in Solid Mechanics written by Youping Chen and published by Springer Science & Business Media. This book was released on 2006-12-31 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.
