Anderson Acceleration For Numerical Pdes
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Anderson Acceleration For Numerical Pdes
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Author : Sara Pollock
language : en
Publisher: SIAM
Release Date : 2025-07-16
Anderson Acceleration For Numerical Pdes written by Sara Pollock and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-16 with Mathematics categories.
Research on Anderson acceleration (AA) has surged over the last 15 years. This book compiles recent fundamental advancements in AA and its application to nonlinear solvers for partial differential equations (PDEs). These solvers play an important role across mathematics, science, engineering, and economics, serving as a critical technology for determining solutions to predictive models for a wide range of important phenomena. This book covers AA convergence theory for both contractive and noncontractive operators, as well as filtering techniques for AA. It includes examples of how convergence theory can be adapted to various application problems. It also includes AA’s impact on sublinear convergence and integration of AA with Newton’s method. The authors provide detailed proofs of key theorems and results from numerous test examples. Code for the examples is available in an online repository.
Anderson Acceleration For Numerical Pde
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Author : Sara Pollock
language : en
Publisher:
Release Date : 2025-07-31
Anderson Acceleration For Numerical Pde written by Sara Pollock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-31 with categories.
Advances In Numerical Partial Differential Equations And Optimization
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Author : Susana Gomez
language : en
Publisher: SIAM
Release Date : 1990-12-31
Advances In Numerical Partial Differential Equations And Optimization written by Susana Gomez and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-31 with Mathematics categories.
The papers in this volume emphasize the numerical aspects of three main areas: optimization, linear algebra and partial differential equations. Held in January, 1989, in Yucatan, Mexico, the workshop was organized by the Institute for Research in Applied Mathematics of the National University of Mexico in collaboration with the mathematical Sciences Department at Rice University.
Solving Nonlinear Equations With Iterative Methods
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 2022-10-31
Solving Nonlinear Equations With Iterative Methods written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Mathematics categories.
This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.
Property Preserving Numerical Schemes For Conservation Laws
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Author : Dmitri Kuzmin
language : en
Publisher: World Scientific
Release Date : 2023-08-28
Property Preserving Numerical Schemes For Conservation Laws written by Dmitri Kuzmin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful approximations are supposed to satisfy. The finite volume and finite element schemes summarized in this book use limiting techniques to enforce discrete maximum principles and entropy inequalities. Spurious oscillations are prevented using artificial viscosity operators and/or essentially nonoscillatory reconstructions.An introduction to classical nonlinear stabilization approaches is given in the simple context of one-dimensional finite volume discretizations. Subsequent chapters of Part I are focused on recent extensions to continuous and discontinuous Galerkin methods. Many of the algorithms presented in these chapters were developed by the authors and their collaborators. Part II gives a deeper insight into the mathematical theory of property-preserving numerical schemes. It begins with a review of the convergence theory for finite volume methods and ends with analysis of algebraic flux correction schemes for finite elements. In addition to providing ready-to-use algorithms, this text explains the design principles behind such algorithms and shows how to put theory into practice. Although the book is based on lecture notes written for an advanced graduate-level course, it is also aimed at senior researchers who develop and analyze numerical methods for hyperbolic problems.
Finite Element Methods For Computational Fluid Dynamics
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Author : Dmitri Kuzmin
language : en
Publisher: SIAM
Release Date : 2014-12-18
Finite Element Methods For Computational Fluid Dynamics written by Dmitri Kuzmin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-18 with Science categories.
This informal introduction to computational fluid dynamics and practical guide to numerical simulation of transport phenomena covers the derivation of the governing equations, construction of finite element approximations, and qualitative properties of numerical solutions, among other topics. To make the book accessible to readers with diverse interests and backgrounds, the authors begin at a basic level and advance to numerical tools for increasingly difficult flow problems, emphasizing practical implementation rather than mathematical theory.?Finite Element Methods for Computational Fluid Dynamics: A Practical Guide?explains the basics of the finite element method (FEM) in the context of simple model problems, illustrated by numerical examples. It comprehensively reviews stabilization techniques for convection-dominated transport problems, introducing the reader to streamline diffusion methods, Petrov?Galerkin approximations, Taylor?Galerkin schemes, flux-corrected transport algorithms, and other nonlinear high-resolution schemes, and covers Petrov?Galerkin stabilization, classical projection schemes, Schur complement solvers, and the implementation of the k-epsilon turbulence model in its presentation of the FEM for incompressible flow problem. The book also describes the open-source finite element library ELMER, which is recommended as a software development kit for advanced applications in an online component.?
Parallel Numerical Algorithms
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Author : David E. Keyes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Numerical Algorithms written by David E. Keyes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
Density Functional Theory
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Author : Eric Cancès
language : en
Publisher: Springer Nature
Release Date : 2023-07-18
Density Functional Theory written by Eric Cancès and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Mathematics categories.
Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.
Reviews In Numerical Analysis 1980 86
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Author :
language : en
Publisher:
Release Date : 1987
Reviews In Numerical Analysis 1980 86 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Numerical analysis categories.
These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
Computational Fluid Mechanics And Heat Transfer
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Author : Dale Anderson
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Computational Fluid Mechanics And Heat Transfer written by Dale Anderson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Science categories.
Computational Fluid Mechanics and Heat Transfer, Fourth Edition is a fully updated version of the classic text on finite-difference and finite-volume computational methods. Divided into two parts, the text covers essential concepts in the first part, and then moves on to fluids equations in the second. Designed as a valuable resource for practitioners and students, new examples and homework problems have been added to further enhance the student’s understanding of the fundamentals and applications. Provides a thoroughly updated presentation of CFD and computational heat transfer Covers more material than other texts, organized for classroom instruction and self-study Presents a wide range of computation strategies for fluid flow and heat transfer Includes new sections on finite element methods, computational heat transfer, and multiphase flows Features a full Solutions Manual and Figure Slides for classroom projection Written as an introductory text for advanced undergraduates and first-year graduate students, the new edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer.