Discrete Variational Problems with Interfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Variational Problems with Interfaces write by Roberto Alicandro. This book was released on 2023-12-31. Discrete Variational Problems with Interfaces available in PDF, EPUB and Kindle. 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.
A Variational Theory of Convolution-Type Functionals
A Variational Theory of Convolution-Type Functionals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Variational Theory of Convolution-Type Functionals write by Roberto Alicandro. This book was released on 2023-05-02. A Variational Theory of Convolution-Type Functionals available in PDF, EPUB and Kindle. 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.
Domain Decomposition Methods in Science and Engineering XVI
Domain Decomposition Methods in Science and Engineering XVI - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Domain Decomposition Methods in Science and Engineering XVI write by Olof B. Widlund. This book was released on 2007-01-19. Domain Decomposition Methods in Science and Engineering XVI available in PDF, EPUB and Kindle. 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.
Discrete Computational Mechanics of Masonry Structures
Discrete Computational Mechanics of Masonry Structures - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Computational Mechanics of Masonry Structures write by Katalin Bagi. This book was released on 2023-09-02. Discrete Computational Mechanics of Masonry Structures available in PDF, EPUB and Kindle. 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.
Discretization Methods and Iterative Solvers Based on Domain Decomposition
Discretization Methods and Iterative Solvers Based on Domain Decomposition - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discretization Methods and Iterative Solvers Based on Domain Decomposition write by Barbara I. Wohlmuth. This book was released on 2012-12-06. Discretization Methods and Iterative Solvers Based on Domain Decomposition available in PDF, EPUB and Kindle. 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.
