Numerical Models For Differential Problems

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Numerical Models For Differential Problems

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-25

Numerical Models For Differential Problems written by Alfio Quarteroni and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-25 with Mathematics categories.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Numerical Models For Differential Problems

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-22

Numerical Models For Differential Problems written by Alfio Quarteroni 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 2010-01-22 with Mathematics categories.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Finite Element Approximation Of Boundary Value Problems

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Author : Franz Chouly
language : en
Publisher: Springer Nature
Release Date : 2024-11-06

Finite Element Approximation Of Boundary Value Problems written by Franz Chouly and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.

This textbook provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience. The author accomplishes this, in part, by including numerous exercises and illustrations. Each chapter begins with a clear outline to help make complex concepts more approachable without sacrificing depth. Structurally, the book begins with the simplest type of finite element method: low order, piecewise continuous, Lagrange finite elements. With this, crucial questions about the stability and approximation errors are answered. Of particular note is the author’s coverage of two specific topics that often go overlooked in introductory material. The first is the numerical treatment of boundary conditions, especially the Nitsche technique. The second is a detailed explanation of the discretization error using specific techniques of a posteriori error estimation. With the book’s compact yet thorough treatment of these areas, readers will have a clear understanding of how mathematical analysis tools can be used in practice. Finite Element Approximation of Boundary Value Problems will be suitable as a supplementary textbook in applied mathematics courses for graduate students, and may also be used for self-study.

Numerical Models For Submerged Breakwaters

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Author : Amir Sharifahmadian
language : en
Publisher: Butterworth-Heinemann
Release Date : 2015-11-24

Numerical Models For Submerged Breakwaters written by Amir Sharifahmadian and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-24 with Technology & Engineering categories.

Numerical Models for Submerged Breakwaters: Coastal Hydrodynamics and Morphodynamics discusses the practice of submerged breakwaters, an increasingly popular tool used as a coastal defense system because of their amenity and aesthetics as compared to common emerged beach protection measures. The book is the perfect guide for experienced professionals who wish to keep abreast of the latest best practices or those who are entering the field and need a reference, explaining new and traditional numerical methodologies for designing submerged breakwaters and measuring their performance. In addition, the book provides case studies, examples, and practical methods for data selection and pre-processing, model setup, calibration, and analysis. - Case studies and worked-out examples illustrate different concepts and methods - Offers practical methods for Data Selection and Pre-Processing - Provides simplified prediction tools for practical applications

Advanced Reduced Order Methods And Applications In Computational Fluid Dynamics

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Author : Gianluigi Rozza
language : en
Publisher: SIAM
Release Date : 2022-11-21

Advanced Reduced Order Methods And Applications In Computational Fluid Dynamics written by Gianluigi Rozza and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-21 with Mathematics categories.

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications. This book will be of interest to researchers and graduate students in the field of reduced order modeling.

Iterative Methods And Preconditioners For Systems Of Linear Equations

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Author : Gabriele Ciaramella
language : en
Publisher: SIAM
Release Date : 2022-02-08

Iterative Methods And Preconditioners For Systems Of Linear Equations written by Gabriele Ciaramella and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Separated Representations And Pgd Based Model Reduction

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Author : Francisco Chinesta
language : en
Publisher: Springer
Release Date : 2014-09-02

Separated Representations And Pgd Based Model Reduction written by Francisco Chinesta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Technology & Engineering categories.

The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,...), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.

Introduction To The Numerical Modeling Of Groundwater And Geothermal Systems

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Author : Jochen Bundschuh
language : en
Publisher: CRC Press
Release Date : 2010-07-05

Introduction To The Numerical Modeling Of Groundwater And Geothermal Systems written by Jochen Bundschuh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-05 with Technology & Engineering categories.

This book provides an introduction to the scientific fundamentals of groundwater and geothermal systems. In a simple and didactic manner the different water and energy problems existing in deformable porous rocks are explained as well as the corresponding theories and the mathematical and numerical tools that lead to modeling and solving them. This

Snapshot Based Methods And Algorithms

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Author : Peter Benner
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-12-16

Snapshot Based Methods And Algorithms written by Peter Benner and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-16 with Mathematics categories.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

Multiscale And Adaptivity Modeling Numerics And Applications

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Author : Silvia Bertoluzza
language : en
Publisher: Springer
Release Date : 2012-01-06

Multiscale And Adaptivity Modeling Numerics And Applications written by Silvia Bertoluzza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.

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.