Paul Davis offers a detailed overview of some of the invited talks, prize lectures, and minisymposia presentations at CSE19.
Quantization—an efficient means of producing low-precision DNNs—yields interesting mathematical issues.
Could Hopf bifurcation be responsible for fluctuating wait times? Jamol Pender investigates at CSE19.
Roy Goodman presents an overview of Markdown, a lightweight markup language that is well suited for smaller writing projects.
Panelists at a CSE19 discussion on diversity spoke about ongoing efforts towards equal representation in academia.
View a multitude of prize photos from CSE19 and GS19, which took place earlier this year.
Exceptional mathematician with background in number theory and/or recursive function theory sought to help prepare paper.
IPAM seeks proposals from the mathematical, statistical, and scientific communities for long programs and workshops.
2018 / xii + 120 pages / Softcover / 978-1-611975-53-6 / List $54.00 / SIAM Member $37.80 / SIAM Member $48.30 / Order Code: CB93
Keywords: finite element method, mixed method, PDE, finite element exterior calculus, de Rham complex, Hodge theory, thermodynamics, fluid flow, solid deformation, elasticity, electricity and magnetism, numerical methods
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.