Finite Element Exterior Calculus (Paperback)

Douglas N. Arnold

ISBN 10: 1611975530 / ISBN 13: 9781611975536

Published by Society for Industrial & Applied Mathematics,U.S., New York, 2019

About this Item

Paperback. Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical worldwave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many moreare described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs. Presents the fundamentals of finite element exterior calculus, including the geometrical and functional analysis preliminaries, quickly and in one place. The book is also for mathematicians from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781611975536

Bibliographic Details

• Title: Finite Element Exterior Calculus (Paperback)
• Publisher: Society for Industrial & Applied Mathematics,U.S., New York
• Publication Date: 2019
• Language: English
• ISBN 10: 1611975530
• ISBN 13: 9781611975536
• Binding: Paperback
• Condition: new

About this title

Synopsis

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

About the Author

Douglas N. Arnold is McKnight Presidential Professor of Mathematics at the University of Minnesota. He is a mathematician and educator whose research focuses on numerical analysis, PDEs, mechanics, and the interplay among these fields. He is known as the originator of FEEC, first presented in his plenary lecture at the International Congress of Mathematicians in 2002. Professor Arnold's many accomplishments include the award of a Guggenheim Fellowship; election as a foreign member of the Norwegian Academy of Science and Letters;Fellowship in the Society for Industrial and Applied Mathematics (SIAM), the American Association for the Advancement of Science (AAAS), and the American Mathematical Society (AMS);and serving as president of SIAM and director of the Institute of Mathematics and Its Applications (IMA). He received the SIAM Prize for Distinguished Service to the Profession and the J. Tinsley Oden Medal of the U.S. Association for Computational Mechanics. In 2007 he coauthored an award-winning video, Möbius Transformations Revealed, which has garnered over two million views on YouTube.