Dynamics Of Internal Layers And Diffusive Interfaces
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Dynamics Of Internal Layers And Diffusive Interfaces
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Author : Paul C. Fife
language : en
Publisher: SIAM
Release Date : 1988-01-01
Dynamics Of Internal Layers And Diffusive Interfaces written by Paul C. Fife and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Technology & Engineering categories.
Interfacial phenomena are commonplace in physics, chemistry, biology, and in various disciplines bridging these fields. They occur whenever a continuum is present which can exist in at least two different chemical or physical "states," and there is some mechanism which generates or enforces a spatial separation between these states. The separation boundary is then called an interface. In the examples studied here, the separation boundary, and its internal structure, result from the balance between two opposing tendencies: a diffusive effect which attempts to mix and smooth the properties of the material, and a physical or chemical mechanism which works to drive it to one or the other pure state. This volume is unique in that the treatment of flames, as well as internal layer dynamics "including curvature effects," is more detailed and systematic than in publications.
Dynamics Of Internal Layers And Diffusive Interfaces
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Author : Paul C. Fife
language : en
Publisher: SIAM
Release Date : 1988-01-01
Dynamics Of Internal Layers And Diffusive Interfaces written by Paul C. Fife and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Technology & Engineering categories.
A good introduction to interfacial phenomena and is unique in its treatment of flames, as well as internal layer dynamics.
Time Parallel Time Integration
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Author : Martin J. Gander
language : en
Publisher: SIAM
Release Date : 2024-10-15
Time Parallel Time Integration written by Martin J. Gander and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-15 with Mathematics categories.
Predicting the future is a difficult task but, as with the weather, it is possible with good models. But how does one predict the far future before the near future is known? Time parallel time integration, also known as PinT (Parallel-in-Time) methods, aims to predict the near and far future simultaneously. In this self-contained book, the first on the topic, readers will find a comprehensive and up-to-date description of methods and techniques that have been developed to do just this. The authors describe the four main classes of PinT methods: shooting-type methods, waveform relaxation methods, time parallel multigrid methods, and direct time parallel methods. In addition, they provide historical background for each of the method classes, complete convergence analyses for the most representative variants of the methods in each class, and illustrations and runnable MATLAB code. An ideal introduction to this exciting and very active research field, Time Parallel Time Integration can be used for independent study or for a graduate course.
Fast Direct Solvers For Elliptic Pdes
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Author : Per-Gunnar Martinsson
language : en
Publisher: SIAM
Release Date : 2019-12-16
Fast Direct Solvers For Elliptic Pdes written by Per-Gunnar Martinsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.
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.
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
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.
Solving Problems In Multiply Connected Domains
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Author : Darren Crowdy
language : en
Publisher: SIAM
Release Date : 2020-04-20
Solving Problems In Multiply Connected Domains written by Darren Crowdy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-20 with Mathematics categories.
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.
Computational Methods In Optimal Control
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Author : William H. Hager
language : en
Publisher: SIAM
Release Date : 2025-02-13
Computational Methods In Optimal Control written by William H. Hager and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-13 with Mathematics categories.
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions. Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge–Kutta methods. Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer. Computational Methods in Optimal Control: Theory and Practice is intended for numerical analysts and computational scientists. Users of the software package GPOPS may find the book useful since the theoretical basis for the GPOPS algorithm is developed within the book. It is appropriate for courses in variational analysis, numerical optimization, and the calculus of variations.
The Cahn Hilliard Equation Recent Advances And Applications
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Author : Alain Miranville
language : en
Publisher: SIAM
Release Date : 2019-09-09
The Cahn Hilliard Equation Recent Advances And Applications written by Alain Miranville and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This is the first book to present a detailed discussion of both classical and recent results on the popular CahnHilliard equation and some of its variants. The focus is on mathematical analysis of CahnHilliard 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 CahnHilliard 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.
Inverse Scattering Theory And Transmission Eigenvalues
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Author : Fioralba Cakoni
language : en
Publisher: SIAM
Release Date : 2022-12-07
Inverse Scattering Theory And Transmission Eigenvalues written by Fioralba Cakoni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-07 with Mathematics categories.
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.
Geometric Partial Differential Equations Part I
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Author :
language : en
Publisher: Elsevier
Release Date : 2020-01-14
Geometric Partial Differential Equations Part I written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-14 with Mathematics categories.
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