George Em Karniadakis
George Em Karniadakis
The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering
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The Wiener--Askey polynomial chaos for stochastic differential equations
D Xiu, GE Karniadakis
SIAM journal on scientific computing 24 (2), 619-644, 2002
Discontinuous Galerkin methods: theory, computation and applications
B Cockburn, GE Karniadakis, CW Shu
Springer Science & Business Media, 2012
Spectral/hp element methods for computational fluid dynamics
G Karniadakis, S Sherwin
Oxford University Press, 2013
Microflows and nanoflows: fundamentals and simulation
G Karniadakis, A Beskok, N Aluru
Springer Science & Business Media, 2006
High-order splitting methods for the incompressible Navier-Stokes equations
GE Karniadakis, M Israeli, SA Orszag
Journal of computational physics 97 (2), 414-443, 1991
Modeling uncertainty in flow simulations via generalized polynomial chaos
D Xiu, GE Karniadakis
Journal of computational physics 187 (1), 137-167, 2003
The MEMS handbook
M Gad-el-Hak
CRC press, 2001
Report: a model for flows in channels, pipes, and ducts at micro and nano scales
A Beskok, GE Karniadakis
Microscale thermophysical engineering 3 (1), 43-77, 1999
Micro flows: fundamentals and simulation
GE Karniadakis, A Beskok, M Gad-el-Hak
Appl. Mech. Rev. 55 (4), B76-B76, 2002
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M Raissi, P Perdikaris, GE Karniadakis
Journal of Computational Physics 378, 686-707, 2019
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
D Xiu, GE Karniadakis
Computer methods in applied mechanics and engineering 191 (43), 4927-4948, 2002
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
X Wan, GE Karniadakis
Journal of Computational Physics 209 (2), 617-642, 2005
Low‐dimensional models for complex geometry flows: application to grooved channels and circular cylinders
AE Deane, IG Kevrekidis, GE Karniadakis, SA Orszag
Physics of Fluids A: Fluid Dynamics 3 (10), 2337-2354, 1991
A multiscale red blood cell model with accurate mechanics, rheology, and dynamics
DA Fedosov, B Caswell, GE Karniadakis
Biophysical journal 98 (10), 2215-2225, 2010
Multi-element generalized polynomial chaos for arbitrary probability measures
X Wan, GE Karniadakis
SIAM Journal on Scientific Computing 28 (3), 901-928, 2006
Rarefaction and compressibility effects in gas microflows
A Beskok, GE Karniadakis, W Trimmer
Hidden physics models: Machine learning of nonlinear partial differential equations
M Raissi, GE Karniadakis
Journal of Computational Physics 357, 125-141, 2018
Three-dimensional dynamics and transition to turbulence in the wake of bluff objects
GE Karniadakis, GS Triantafyllou
Journal of fluid mechanics 238, 1-30, 1992
Dynamics and low-dimensionality of a turbulent near wake
X MA, GS Karamanos, GE Karniadakis
Journal of fluid mechanics 410, 29-65, 2000
Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations
M Raissi, P Perdikaris, GE Karniadakis
arXiv preprint arXiv:1711.10561, 2017
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