Principal Investigator (WAVE), Department of Mathematics (UMN), Simons Collaboration on Localization of Waves
Principal Investigator (WAVE), Department of Mathematics (UMN), Simons Collaboration on Localization of Waves
Numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields
Douglas N. Arnold is the McKnight Presidential Professor of Mathematics at the University of Minnesota. His research interests are in computational mathematics, centered on the design and analysis of numerical algorithms for partial differential equations and their application to physical problems ranging from the deformation of elastic shells to the collision of black holes. In a plenary lecture at the 2002 International Congress of Mathematicians, Arnold initiated the finite element exterior calculus, an approach to the stability of finite element methods based on geometric and topological structures underlying the relevant PDE, which has grown to be the subject of many hundreds of papers and dozens of PhD theses. His 2006 and 2010 joint papers establishing the foundations for this subject are each among the 30 most cited papers published in mathematics during their publication year (according to MathSciNet). His earlier work on discontinuous Galerkin methods is similarly highly cited, his thesis publication being the fourth most cited paper in mathematics in 1982, and a later joint work on the subject being the single most cited paper in all of mathematics in 2001.
From 2001 through 2008, Professor Arnold served as director of the Institute for Mathematics and its Applications (IMA). In 2009 and 2010, he was the elected President of the Society for Industrial and Applied Mathematics (SIAM), the world’s leading professional organization for applied mathematicians and computational scientists. He serves as Editor-in-Chief or on the editorial boards of numerous journals and is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics, and the American Association for the Advancement of Science. Among his other honors are a Guggenheim Fellowship, membership in the Norwegian Academy of Science and Letters, the SIAM Prize for Distinguished Service to the Profession, and the J. Tinsley Oden Medal of the US Association for Computational Mechanics. Arnold served on scientific boards including the Board of Mathematical Sciences and Applications of the National Research Council, the U.S. National Committee for Mathematics, the Mathematical and Physical Sciences Advisory Committee of the National Science Foundation, the Program Committees for both the International Congress of Mathematicians and the International Congress of Industrial and Applied Mathematics, and the boards of many research institutes including, currently, ICERM at Brown University and the Fine Institute for Theoretical Physics in Minnesota.
Read more on his University of Minnesota homepage.