George Karniadakis


George Em Karniadakis

Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics

Brown University; also Research Scientist at MIT

George_Karniadakis at Brown.edu

 

"People who wish to analyze nature without using mathematics must settle for a reduced understanding", Richard Feynman

 

Courses:

 

An Introduction to Fractional Calculus, presented by Francesco Mainardi

 

 

2015-Spring Course: [APMA2560]

  • My interests are in stochastic multiscale modeling. Please see a detailed list of my publications per category HERE.
  • Please email me directly if you are interested to work with me as a PhD student or postoc (@Brown, MIT or PNNL).
  • New course on Fractional Calculus by Franscesco Mainardi, April-May, 2015, see syllabus HERE.
  • The impact of the work of my group has been recognized in two recent awards: (1) SIAM's 2015 Ralph E Kleinman Award for "many outstanding contributions to Applied Mathematics in a broad range of areas, including computational fluid dynamics, spectral methods and stochastic modeling.” (2) The 2015 MCS Wierdrehielm Award "for the most highly cited original article  in Microcirculation over the previous five year period for the paper, Blood Flow and Cell-Free Layer in Microvessels." 


Academic background:

George Karniadakis received his S.M. (1984) and Ph.D. (1987) from Massachusetts Institute of Technology. He was appointed Lecturer in the Department of Mechanical Engineering at MIT in 1987 and subsequently he joined the Center for Turbulence Research at Stanford / Nasa Ames. He joined Princeton University as Assistant Professor in the Department of Mechanical and Aerospace Engineering and as Associate Faculty in the Program of Applied and Computational Mathematics. He was a Visiting Professor at Caltech (1993) in the Aeronautics Department. He joined Brown University as Associate Professor of Applied Mathematics in the Center for Fluid Mechanics on January 1, 1994. He became a full professor on July 1, 1996.  He has been a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT since September 1, 2000. He was Visiting Professor at Peking University (Fall 2007 & 2013). He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM, 2010-), Fellow of the American Physical Society (APS, 2004-), Fellow of the American Society of Mechanical Engineers (ASME, 2003-) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA, 2006-). He received the CFD award (2007) and the J Tinsley Oden Medal (2013) by the US Association in Computational Mechanics. His h-index is 67 and he has been cited about 23,000 times (see my google scholar citations). See complete CV here. You can also check out our Geneaology Tree (remember to zoom in!).

 


Research Interests:

His research interests include diverse topics in computational science both on algorithms and applications. A main current thrust is stochastic simulation (in the context of uncertainty quantification and beyond), fractional PDEs, and multiscale modeling of physical and biological systems (especially the brain). Can you believe that we solve problems in 100 dimensions - check this out!. Read here about the exciting field of "New Biology" described by the National Research Council (2009). Read here about our work on sickle cell anemia and also on modeling malaria from first principles, which was also featured on the web site of the National Public Radio. Read here about our work on the first large multiscale modeling of a brain aneurysm (finalist in the Gordon Bell Award, Supercomputing'11). Our new area is neurovascular coupling in the brain, i.e., bridging the gap between neuroscience and vascular mechanics. New experimental evidence suggests the intriguing possibility that by slightly modulating the brain blood flow one can control information processing -- read our paper here! Recent feature article of our work ("Blood in Motion") in American Scientist.

Particular aspects include:

Fractional PDEs: A breakthrough paper!

Numerical solution of stochastic differential equations: SISC article, also PNAS article

Modeling uncertainty with polynomial chaos: PNAS article, CiSE, JCP

Biophysics - Multiscale modeling of biological systems: PNAS (sickle cell anemia); PNAS (blood viscosity); PNAS (malaria) article; PNAS (thrombosis) article, PRS article

Atomistic/Mesoscopic modeling - Dissipative Particle Dynamics: JCP (triple-decker); PRL (adaptive BCs)

Low Dimensional Modeling - Gappy Data - Data assimilation: JCP article

Ongoing Interests:

Spectral/hp Element and Discontinuous Galerkin methods : OUP Book
Turbulent Drag Reduction: Science article
DNS/LES of turbulence in complex geometries: JFM article
Flow-structure interactions: PRL article
Micro-transport and Dynamic self-assembly: Springer Book
Flow and heat control applications: JFM article
Parallel computing; Interactive/virtual reality computer graphics: CUP Book


 


Honors and Awards :

The USACM J Tinsley Oden Medal, 2013

The USACM Computational Fluid Dynamics Award, 2007
SIAM Fellow 2010

Associate Fellow of the American Institute of Aeronautics & Astronautics (AIAA) 2006

Fellow of the American Physical Society (APS) 2004

Fellow of the American Society of Mechanical Engineers (ASME) 2003

17th Robert Bruce Wallace Lecture Award, MIT, 2003
 Rheinstein Junior Faculty Award, Princeton University, 1992




 

  Publications By Category
  C++ / MPI Book
  Spectral Elements Book
  Microflows & Nanoflows Book
  Discontinuous Galerkin Methods Book
  Research Projects in the CRUNCH group
  George Karniadakis during a seminar on stochastic simulations

Where to contact George Karniadakis:

 

Professor George Karniadakis
Box F,
Division of Applied Mathematics,
Brown University,
Providence RI 02912, USA.



Additional Links:

 

SHORT COURSE ON FRACTIONAL PDES

MAY 22 - 31, 2013

INTERNATIONAL SYMPOSIUM ON FRACTIONAL PDES: 

THEORY, NUMERICS AND APPLICATIONS

JUNE 3 - 5, 2013

SALVE REGINA UNIVERSITY



Brown University