Mathematical Foundations of Finite Elements and Iterative Solvers
Seiten
2022
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-708-0 (ISBN)
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-1-61197-708-0 (ISBN)
Describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. The book examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis.
This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author's decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems.
Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.
This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author's decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems.
Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.
Paolo Gatto is senior lecturer at the Institute of Analysis and Scientific Computing at Vienna University of Technology. He has held postdoctoral positions at Brown University, École Polytechnique Fédérale de Lausanne (EPFL), and RWTH Aachen. His research interests include hp-finite elements, fast algorithms for integral equations, and numerical linear algebra.
| Erscheinungsdatum | 03.05.2022 |
|---|---|
| Reihe/Serie | Computational Science and Engineering |
| Verlagsort | New York |
| Sprache | englisch |
| Gewicht | 416 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik | |
| ISBN-10 | 1-61197-708-8 / 1611977088 |
| ISBN-13 | 978-1-61197-708-0 / 9781611977080 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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