Multiscale, Multiphysics, Multifidelity Simulations

This theme encompasses the new discretization and solution computational tools required to treat systems with a wide range of spatial and/or temporal scales, a wide variety of different coupled physical phenomena, and many different demands/contexts as regards output dimensionality, fidelity, and response. Verification and a posteriori error estimation play a key role in model selection and certification and “safe”/robust use by third parties.

Related Publications

Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media
DW Holmes, JR Williams, & P Tilke. International Journal for Numerical and Analytical Methods in Geomechanics, 35(4):419-437, 2011

Coupled ocean-acoustic prediction of transmission loss in a continental shelfbreak region: predictive skill, uncertainty quantification and dynamical sensitivities
PFJ Lermusiaux, J Xu, CF Chen, S Jan, LY Chiu, and Y-J Yang. IEEE Journal of Oceanic Engineering. 35(4):895-916, 2010.
doi: 10.1109/JOE.2010.2068611.

Multiscale two-way embedding schemes for free-surface primitive-equations in the Multidisciplinary Simulation, Estimation and Assimilation System
PJ Haley and PFJ Lermusiaux. Ocean Dynamics, 60(6):1497-1537, 2010.

A natural-norm successive constraint method for inf-sup lower bounds
DBP Huynh, DJ Knezevic, Y Chen, JS Hesthaven, & AT Patera. Computer Methods in Applied Mechanics and Engineering, 199(29-32):1963-1975, 2010.

A posteriori error bounds for the empirical interpolation method
JL Eftang, MA Grepl, AT Patera. Comptes Rendus Mathematique, 348(9-10):575-579, 2010.

Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
YM Marzouk and HN Najm. Journal of Computational Physics, 228(6): 1862–1902, 2009.

Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G Rozza, DBP Huynh, & AT Patera. Archives of Computational Methods in Engineering, 15(3):229-275, 2008.

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms
R Juanes & FX Dub.  Computational Geosciences, 12(3):273-295, 2008.

Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
MA Grepl, Y Maday, NC Nguyen, & AT Patera. Mathematical Modelling and Numerical Analysis (M2AN), 41(3):575-605, 2007.

A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
MA Grepl & AT Patera.  Mathematical Modelling and Numerical Analysis, 39(1):157-181, 2005.

Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds
K Veroy & AT Patera. International Journal for Numerical Methods in Fluids, 47(8-9):773-788, 2005.

Multiscale-stabilized solutions to one-dimensional systems of conservation laws
R Juanes & TW Patzek. Computer Methods in Applied Mechanics and Engineering, 194(25-26:2781-2805, 2005.

A variational multiscale finite element method for multiphase flow in porous media
R Juanes.  Finite elements in analysis and design, 41(7-8):763-777, 2005.

A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
M Paraschivoiu, J Peraire, & AT Patera. Computer Methods in Applied Mechanics and Engineering, 150(1-4):289-312, 1997. 

Heterogeneous atomistic-continuum representations for dense fluid systems
NG Hadjiconstantinou, AT Patera.  International Journal of Modern Physics C, 8(4):967-976, 1997.

A spectral element method for fluid-dynamics — Laminar-flow in a channel expansion
AT Patera. Journal of Computational Physics, 54(3):468-488, 1984.