Nonlocal Modeling Analysis And Computation

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Nonlocal Modeling, Analysis, and Computation

Qiang Du
Nonlocal Modeling Analysis and Computation Book PDF

Author : Qiang Du
Publisher : SIAM
Page : 181 pages
File Size : 44,7 Mb
Release : 2019-03-20
Category : Science
ISBN : 9781611975611

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Nonlocal Modeling, Analysis, and Computation by Qiang Du Pdf

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.

Nonlocal Modeling, Analysis, and Computation

Qiang Du
Nonlocal Modeling Analysis and Computation Book PDF

Author : Qiang Du
Publisher : SIAM
Page : 168 pages
File Size : 43,9 Mb
Release : 2019-03-20
Category : Science
ISBN : 9781611975628

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Nonlocal Modeling, Analysis, and Computation by Qiang Du Pdf

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.

Analysis of Hydrodynamic Models

Peter Constantin
Analysis of Hydrodynamic Models Book PDF

Author : Peter Constantin
Publisher : SIAM
Page : 67 pages
File Size : 50,7 Mb
Release : 2017-04-25
Category : Mathematics
ISBN : 9781611974799

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Analysis of Hydrodynamic Models by Peter Constantin Pdf

Analysis of Hydrodynamic Models presents a concise treatment of a number of partial differential equations of hydrodynamic origin, including the incompressible Euler equations, SQG, Boussinesq, incompressible porous medium, and Oldroyd-B. The author?s approach is based on properties of the particle trajectory maps and on analysis of the back-and-forth passage between the Lagrangian and the Eulerian descriptions. This concise, unified approach brings readers up to date on current open problems. This book is intended for graduate students and junior researchers in mathematics.

A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models

Tadele Mengesha,Abner J. Salgado
A3N2M Approximation Applications and Analysis of Nonlocal Nonlinear Models Book PDF

Author : Tadele Mengesha,Abner J. Salgado
Publisher : Springer Nature
Page : 325 pages
File Size : 44,7 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031340895

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A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models by Tadele Mengesha,Abner J. Salgado Pdf

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.

75 Years of Mathematics of Computation

Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
75 Years of Mathematics of Computation Book PDF

Author : Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 55,8 Mb
Release : 2020-07-29
Category : Education
ISBN : 9781470451639

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75 Years of Mathematics of Computation by Susanne C. Brenner,Igor E. Shparlinski,Chi-Wang Shu,Daniel Szyld Pdf

The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes Book PDF

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 44,7 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Pattern Recognition

Christian Bauckhage,Juergen Gall,Alexander Schwing
Pattern Recognition Book PDF

Author : Christian Bauckhage,Juergen Gall,Alexander Schwing
Publisher : Springer Nature
Page : 734 pages
File Size : 55,9 Mb
Release : 2022-01-13
Category : Computers
ISBN : 9783030926595

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Pattern Recognition by Christian Bauckhage,Juergen Gall,Alexander Schwing Pdf

This book constitutes the refereed proceedings of the 43rd DAGM German Conference on Pattern Recognition, DAGM GCPR 2021, which was held during September 28 – October 1, 2021. The conference was planned to take place in Bonn, Germany, but changed to a virtual event due to the COVID-19 pandemic. The 46 papers presented in this volume were carefully reviewed and selected from 116 submissions. They were organized in topical sections as follows: machine learning and optimization; actions, events, and segmentation; generative models and multimodal data; labeling and self-supervised learning; applications; and 3D modelling and reconstruction.

Mathematical Modeling and Computation of Real-Time Problems

Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy
Mathematical Modeling and Computation of Real Time Problems Book PDF

Author : Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy
Publisher : CRC Press
Page : 172 pages
File Size : 47,9 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9781000288674

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Mathematical Modeling and Computation of Real-Time Problems by Rakhee Kulshrestha,Chandra Shekhar,Madhu Jain,Srinivas R. Chakravarthy Pdf

This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.

Geometric Partial Differential Equations - Part I

Anonim
Geometric Partial Differential Equations Part I Book PDF

Author : Anonim
Publisher : Elsevier
Page : 710 pages
File Size : 42,5 Mb
Release : 2020-01-14
Category : Mathematics
ISBN : 9780444640048

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Geometric Partial Differential Equations - Part I by Anonim Pdf

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

Solving Problems in Multiply Connected Domains

Darren Crowdy
Solving Problems in Multiply Connected Domains Book PDF

Author : Darren Crowdy
Publisher : SIAM
Page : 456 pages
File Size : 43,6 Mb
Release : 2020-04-20
Category : Mathematics
ISBN : 9781611976151

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Solving Problems in Multiply Connected Domains by Darren Crowdy Pdf

Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.

Inverse Scattering Theory and Transmission Eigenvalues

Fioralba Cakoni,David Colton,Houssem Haddar
Inverse Scattering Theory and Transmission Eigenvalues Book PDF

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 259 pages
File Size : 52,9 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9781611977424

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Inverse Scattering Theory and Transmission Eigenvalues by Fioralba Cakoni,David Colton,Houssem Haddar Pdf

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

Fast Direct Solvers for Elliptic PDEs

Per-Gunnar Martinsson
Fast Direct Solvers for Elliptic PDEs Book PDF

Author : Per-Gunnar Martinsson
Publisher : SIAM
Page : 332 pages
File Size : 42,6 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9781611976045

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Fast Direct Solvers for Elliptic PDEs by Per-Gunnar Martinsson Pdf

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

The Cahn–Hilliard Equation: Recent Advances and Applications

Alain Miranville
The Cahn Hilliard Equation Recent Advances and Applications Book PDF

Author : Alain Miranville
Publisher : SIAM
Page : 216 pages
File Size : 45,5 Mb
Release : 2019-09-09
Category : Mathematics
ISBN : 9781611975925

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The Cahn–Hilliard Equation: Recent Advances and Applications by Alain Miranville Pdf

This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Handbook of Peridynamic Modeling

Florin Bobaru,John T. Foster,Philippe H Geubelle,Stewart A. Silling
Handbook of Peridynamic Modeling Book PDF

Author : Florin Bobaru,John T. Foster,Philippe H Geubelle,Stewart A. Silling
Publisher : CRC Press
Page : 540 pages
File Size : 46,8 Mb
Release : 2016-11-03
Category : Mathematics
ISBN : 9781315355948

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Handbook of Peridynamic Modeling by Florin Bobaru,John T. Foster,Philippe H Geubelle,Stewart A. Silling Pdf

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.

Perspectives in Civil Engineering

Jeffrey S. Russell
Perspectives in Civil Engineering Book PDF

Author : Jeffrey S. Russell
Publisher : ASCE Publications
Page : 422 pages
File Size : 41,6 Mb
Release : 2003-01-01
Category : Technology & Engineering
ISBN : 0784475385

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Perspectives in Civil Engineering by Jeffrey S. Russell Pdf

This report contains 27 papers that serve as a testament to the state-of-the-art of civil engineering at the outset of the 21st century, as well as to commemorate the ASCE's Sesquicentennial. Written by the leading practitioners, educators, and researchers of civil engineering, each of these peer-reviewed papers explores a particular aspect of civil engineering knowledge and practice. Each paper explores the development of a particular civil engineering specialty, including milestones and future barriers, constraints, and opportunities. The papers celebrate the history, heritage, and accomplishments of the profession in all facets of practice, including construction facilities, special structures, engineering mechanics, surveying and mapping, irrigation and water quality, forensics, computing, materials, geotechnical engineering, hydraulic engineering, and transportation engineering. While each paper is unique, collectively they provide a snapshot of the profession while offering thoughtful predictions of likely developments in the years to come. Together the papers illuminate the mounting complexity facing civil engineering stemming from rapid growth in scientific knowledge, technological development, and human populations, especially in the last 50 years. An overarching theme is the need for systems-level approaches and consideration from undergraduate education through advanced engineering materials, processes, technologies, and design methods and tools. These papers speak to the need for civil engineers of all specialties to recognize and embrace the growing interconnectedness of the global infrastructure, economy, society, and the need to work for more sustainable, life-cycle-oriented solutions. While embracing the past and the present, the papers collected here clearly have an eye on the future needs of ASCE and the civil engineering profession.