Douglas N. Arnold
Encyclopedia
Douglas Norman Arnold is a mathematician whose research focuses on the numerical analysis
of partial differential equation
s with applications in mechanics
and other fields in physics. , he is McKnight Presidential Professor of Mathematics at the University of Minnesota
.
Arnold studied mathematics as an undergraduate at Brown University
, gaining his B.A. in 1975. He continued his studies at the University of Chicago
, where he received a Ph.D. in 1979. He then moved to work at the University of Maryland, College Park
. In 1989, he moved to Penn State University where he occupied a chair until 2002. He became director of the Institute for Mathematics and its Applications
(IMA) in Minnesota in 2001. At the end of his term as director of the IMA, he becomes the McKnight Presidential Professor of Mathematics at the University of Minnesota. He is serving as president of the Society for Industrial and Applied Mathematics
in 2009 and 2010.
Arnold's research initially focused on the finite element method
for the solution of problems in elasticity
. This expanded to take other applications into account, like the collision of black hole
s.
Especially well known is Arnold's development of the finite element exterior calculus, a discrete version of exterior calculus that can be used to analyze the stability
of finite element methods. This was the topic of the plenary lecture Arnold gave at the 2002 International Congress of Mathematicians
.
Together with a colleague (Jonathan Rogness), Arnold produced a video explaining Möbius transformations which won an honorable mention in a contest sponsored by Science magazine
and the National Science Foundation
in 2007.
The video was watched over a million times at YouTube
.
Other honors include the award of a Guggenheim Fellowship
in 2008 and election as a foreign member of the Norwegian Academy of Science and Letters
in 2009.
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
of partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s with applications in mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
and other fields in physics. , he is McKnight Presidential Professor of Mathematics at the University of Minnesota
University of Minnesota
The University of Minnesota, Twin Cities is a public research university located in Minneapolis and St. Paul, Minnesota, United States. It is the oldest and largest part of the University of Minnesota system and has the fourth-largest main campus student body in the United States, with 52,557...
.
Arnold studied mathematics as an undergraduate at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
, gaining his B.A. in 1975. He continued his studies at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
, where he received a Ph.D. in 1979. He then moved to work at the University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
. In 1989, he moved to Penn State University where he occupied a chair until 2002. He became director of the Institute for Mathematics and its Applications
Institute for Mathematics and its Applications
The Institute for Mathematics and its Applications located at the University of Minnesota is an organization established in 1982 by the National Science Foundation of the United States...
(IMA) in Minnesota in 2001. At the end of his term as director of the IMA, he becomes the McKnight Presidential Professor of Mathematics at the University of Minnesota. He is serving as president of the Society for Industrial and Applied Mathematics
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
in 2009 and 2010.
Arnold's research initially focused on the finite element method
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
for the solution of problems in elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
. This expanded to take other applications into account, like the collision of black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s.
Especially well known is Arnold's development of the finite element exterior calculus, a discrete version of exterior calculus that can be used to analyze the stability
Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is related to the accuracy of the algorithm....
of finite element methods. This was the topic of the plenary lecture Arnold gave at the 2002 International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
.
Together with a colleague (Jonathan Rogness), Arnold produced a video explaining Möbius transformations which won an honorable mention in a contest sponsored by Science magazine
Science Magazine
Science Magazine was a half-hour television show produced by the Canadian Broadcasting Corporation from 1975 to 1979.The show was hosted by geneticist David Suzuki, who previously hosted the daytime youth programme Suzuki On Science...
and the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
in 2007.
The video was watched over a million times at YouTube
YouTube
YouTube is a video-sharing website, created by three former PayPal employees in February 2005, on which users can upload, view and share videos....
.
Other honors include the award of a Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
in 2008 and election as a foreign member of the Norwegian Academy of Science and Letters
Norwegian Academy of Science and Letters
The Norwegian Academy of Science and Letters is a learned society based in Oslo, Norway.-History:The University of Oslo was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Throndhjem had no university, but had a learned...
in 2009.