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Multiscale Nonlinear And Adaptive Approximation
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Book Synopsis Multiscale, Nonlinear and Adaptive Approximation by : Ronald DeVore
Download or read book Multiscale, Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer Science & Business Media. This book was released on 2009-09-16 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.
Book Synopsis Multiscale and Adaptivity: Modeling, Numerics and Applications by : Silvia Bertoluzza
Download or read book Multiscale and Adaptivity: Modeling, Numerics and Applications written by Silvia Bertoluzza and published by Springer. This book was released on 2012-01-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author :Emmanuil H Georgoulis Publisher :Springer Science & Business Media ISBN 13 :3642168760 Total Pages :310 pages Book Rating :4.6/5 (421 download)
Book Synopsis Approximation Algorithms for Complex Systems by : Emmanuil H Georgoulis
Download or read book Approximation Algorithms for Complex Systems written by Emmanuil H Georgoulis and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom.
Book Synopsis A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models by : Tadele Mengesha
Download or read book A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models written by Tadele Mengesha and published by Springer Nature. This book was released on 2023-09-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.
Book Synopsis Numerical Methods for PDEs by : Daniele Antonio Di Pietro
Download or read book Numerical Methods for PDEs written by Daniele Antonio Di Pietro and published by Springer. This book was released on 2018-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.
Book Synopsis Wavelet Based Approximation Schemes for Singular Integral Equations by : Madan Mohan Panja
Download or read book Wavelet Based Approximation Schemes for Singular Integral Equations written by Madan Mohan Panja and published by CRC Press. This book was released on 2020-06-07 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Book Synopsis Finite Element Approximation of Boundary Value Problems by : Franz Chouly
Download or read book Finite Element Approximation of Boundary Value Problems written by Franz Chouly and published by Springer Nature. This book was released on with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uncertainty Quantification for Hyperbolic and Kinetic Equations by : Shi Jin
Download or read book Uncertainty Quantification for Hyperbolic and Kinetic Equations written by Shi Jin and published by Springer. This book was released on 2018-03-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.
Book Synopsis Adaptive wavelet frame methods for nonlinear elliptic problems by : Jens Kappei
Download or read book Adaptive wavelet frame methods for nonlinear elliptic problems written by Jens Kappei and published by Logos Verlag Berlin GmbH. This book was released on 2012-02-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last ten years, adaptive wavelet methods have turned out to be a powerful tool in the numerical treatment of operator equations given on a bounded domain or closed manifold. In this work, we consider semi-nonlinear operator equations, including an elliptic linear operator as well as a nonlinear monotone one. Since the classical approach to construct a wavelet Riesz basis for the solution space is still afflicted with some notable problems, we use the weaker concept of wavelet frames to design an adaptive algorithm for the numerical solution of problems of this type. Choosing an appropriate overlapping decomposition of the given domain, a suitable frame system can be constructed easily. Applying it to the given continuous problem yields a discrete, bi-infinite nonlinear system of equations, which is shown to be solvable by a damped Richardson iteration method. We then successively introduce all building blocks for the numerical implementation of the iteration method. Here, we concentrate on the evaluation of the discrete nonlinearity, where we show that the previously developed auxiliary of tree-structured index sets can be generalized to the wavelet frame setting in a proper way. This allows an effective numerical treatment of the nonlinearity by so-called aggregated trees. Choosing the error tolerances appropriately, we show that our adaptive scheme is asymptotically optimal with respect to aggregated tree-structured index sets, i.e., it realizes the same convergence rate as the sequence of best N-term frame approximations of the solution respecting aggregated trees. Moreover, under the assumption of a sufficiently precise numerical quadrature method, the computational cost of our algorithm stays the same order as the number of wavelets used by it. The theoretical results are widely confirmed by one- and two-dimensional test problems over non-trivial bounded domains.
Book Synopsis Finite Elements II by : Alexandre Ern
Download or read book Finite Elements II written by Alexandre Ern and published by Springer Nature. This book was released on 2021-04-22 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias
Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Book Synopsis Active Flow and Combustion Control 2018 by : Rudibert King
Download or read book Active Flow and Combustion Control 2018 written by Rudibert King and published by Springer. This book was released on 2018-09-03 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reports on the latest theoretical and experimental findings in the field of active flow and combustion control. It covers new developments in actuator technology and sensing, in robust and optimal open- and closed-loop control, as well as in model reduction for control, constant volume combustion and dynamic impingement cooling. The chapters reports oncutting-edge contributions presented during the fourth edition of the Active Flow and Combustion Control conference, held in September 19 to 21, 2018 at the Technische Universität Berlin, in Germany. This conference, as well as the research presented in the book, have been supported by the collaborative research center SFB 1029 on “Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamics”, funded by the DFG (German Research Foundation). It offers a timely guide for researchers and practitioners in the field of aeronautics, turbomachinery, control and combustion.
Book Synopsis Multiscale, Nonlinear and Adaptive Approximation by : Ronald DeVore
Download or read book Multiscale, Nonlinear and Adaptive Approximation written by Ronald DeVore and published by Springer. This book was released on 2010-04-29 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen 's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building t.
Book Synopsis Domain Decomposition Methods in Science and Engineering XX by : Randolph Bank
Download or read book Domain Decomposition Methods in Science and Engineering XX written by Randolph Bank and published by Springer Science & Business Media. This book was released on 2013-07-03 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.
Book Synopsis A Panorama of Mathematics: Pure and Applied by : Carlos M. da Fonseca
Download or read book A Panorama of Mathematics: Pure and Applied written by Carlos M. da Fonseca and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Mathematics and its Applications-2014, held from November 14-17, 2014, at Kuwait University, Safat, Kuwait. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpufThis volume contains the proceedings of the Conference on Mathematics and its Applications–2014, held from November 14–17, 2014, at Kuwait University, Safat, Kuwait. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpuf
Book Synopsis Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory by : Peter Benner
Download or read book Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory written by Peter Benner and published by Springer. This book was released on 2015-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Book Synopsis Geometric Partial Differential Equations - Part I by :
Download or read book Geometric Partial Differential Equations - Part I written by and published by Elsevier. This book was released on 2020-01-14 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs
