PUBLICATIONS

2012

C.Y. Lee and Boris Rozovskii. On stochastic Navier-Stokes equations driven by stationary white noise, 2012.

B. Wen and N. Zabaras.  Investigating variability of fatigue indicator parameters of two-phase nickel-based superalloy microstructures, Computational Materials Science, Vol. 51 (1), pp. 455-481, 2012.

X. Yang, M. Choi, G. Lin, and G.E. Karniadakis. Adaptive ANONVA decomposition of stochastic incompressible and compressible flows, J. Comp. Phys., 231, 1587-1614, (doi: 10.1016/j.jcp.2011.10.028) 2012.

2011

W. Cao and Z. Zhang. Mean square stability of two-step Maruyama methods for stochastic delay differential equations, under review, Journal of Computational and Applied Mathematics, 2011.

M. Cheng, T.Y. Hou, and P. Yan. A Data-driven stochastic method, submitted  2011

Y. Chen, J.S. Hesthaven, Y. Maday, J. Rodriguez, and X. Zhu. Certified reduced methods for electromagnetic scattering and radar cross section estimation, submitted 2011.

J.L. Eftang, D.J. Knezevic, and A.T. Patera. An hp certified reduced basis method for parametrized parabolic partial differential equations, Mathematical and Computer Modelling of Dynamical Systems, 17(4):395-422, (doi:10.1080/13873954.2011.547670) 2011.

J.L. Eftang, D.B.P. Huynh, D.J. Knezevic, and A.T. Patera. A two-step certified reduced basis method, Journal of Scientific Computing, (doi: 10.1007/s10915-011-9494-2) 2011.

B. Fares, J.S. Hesthaven, Y. Maday, and B. Stamm. The reduced basis method for the electric field integral equation, J. Comput. Phys. 230(14), 5532-5555, (doi: 10.1016/j.jcp.2011.03.023) 2011.

M. Ganesh, J.S. Hesthaven, and B. Stamm. A reduced basis method for multiple electromagnetic scattering in three dimensions, submitted 2011.

Z.Gao and J.S. Hesthaven. Efficient solution of ordinary differential equations with high-dimensional parametrized uncertainty, Comm. Comput. Phys. 10(2), 253-278, 2011.

J.S. Hesthaven and S. Zhang. On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations, submitted 2011.

J.S. Hesthaven, B. Stamm, and S. Zhang. Certified reduced basis methods for the electric field integral equation,  submitted 2011.

J.S. Hesthaven, B. Stamm, and S. Zhang. Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods, submitted  2011.

T.Y. Hou and Z. Shi. Data-driven time-frequency analysis, preprint, submitted  2011.

T. Y. Hou, Z. Shi, and S. Wang. The dual role of convection in 3D Navier-Stokes equations, to appear in Proceedings of 2011 Congress of Foundation of Computational Mathematics, Budapest,  Lecture Notes in Applied Mathematics, 2011

X. Hu, G. Lin, T.Y. Hou and P. Yan. An adaptive ANOVA-based data-driven stochastic method for elliptic PDE with random coefficient, submitted 2011.

D.B.P. Huynh, D.J Knezevic, and A.T Patera.  Certified reduced basis model characterization: a frequentistic uncertainty framework, Computer Methods in Applied Mechanics and Engineering, accepted   (doi: 10.1016/j.cma.2011.09.011) 2011.

D.B.P. Huynh, D.J. Knezevic, and A.T Patera. A Laplace transform certified reduced basis method; application to the heat equation and wave equation, CR Acad Sci Paris Series I, 349(7-8):401-405, 2011.

D.B.P. Huynh, D.J Knezevic, J.W Peterson, and A.T Patera.  High-fidelity real-time simulation on deployed platforms, Computers and Fluids, 43(1):74-81 (doi:10.1016/j.compfluid.2010.07.007) 2011.

D.B.P. Huynh, D.J. Knezevic, and A.T. Patera.  A static condensation reduced basis element methods: approximation and A posteriori error estimation, Mathematical Modelling and Numerical Analysis, submitted 2011.

D.J Knezevic and J.W. Peterson. A High-performance parallel implementation of the certified reduced basis method, Comput. Methods Appl. Mech. Engrg. 200(13-16), 1455-1566, (doi: 10.1016/j.cma.2010.12.026) 2011.

D.J. Knezevic, N.C Nguyen, and A.T Patera.  Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations, Mathematical Models and Methods in Applied Sciences, 21(7): 1415-1442, 2011, (doi: 10.1142/S0218202511005441)

M. Liu, Z. Gao and J.S. Hesthaven. Adaptive sparse grid algorithms with applications to electromagnetics scattering under uncertainty, Appl. Numer. Math. 61(1), 24-37, (doi:10.1016/j.apnum.2010.08.002) 2011.

S. Lototsky and B.L.Rozovskii, D. Selesi.  On generalized Malliavin calculus, J. Stochastic  Processes and Applications, submitted 2011.

X. Ma and N. Zabaras. Kernel principal component analysis for stochastic input model reduction, Journal of Computational Physics, Vol. 230 (19), pp. 7311-7331, 2011.

X. Ma and N. Zabaras. A stochastic mixed finite element heterogeneous multiscale method for flow in porous media, Journal of Computational Physics, Vol. 230 (12), pp. 4696-4722, 2011.

J. Park, B. Rozovsky, and R. Sowers. Efficient nonlinear filtering of a singularly perturbed stochastic hybrid system,  London Math. Society J. of Computation and Mathematics, 2011, (doi: 10.1112/S146115701000029X).

K. Urban and A.T. Patera.  A new error bound for reduced basis approximation of parabolic partial differential equations, CR Acad. Sci. Paris Series 1, submitted 2011.

D. Venturi. A fully symmetric nonlinear biorthogonal decomposition theory for random fields,

Physica D, 240(4-5), 415-25, 2011, (doi: 10.1016/j.physd.2010.10.005) 2011.

D. Venturi, T. Sapsis, H. Cho, and G.E. Karniadakis. A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems, Proc. Roy. Soc. A., 2011 (doi: 10.1098/rspa.2011.0186).

D. Venturi and G.E. Karniadakis. Differential constraints for the probability density function of stochastic solutions to the wave equation, in press:  Int. J. Uncertainty Quantification.

D. Venturi and G.E. Karniadakis. New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs, Submitted to J. Comp. Physics, 2011.

D. Venturi, M. Choi, and G.E. Karniadakis. Supercritical quasi-conduction states in stochastic Rayleigh Benard convection, submitted to the Int. J. of Heat & Mass Transfer, 2011.

J. Wan and N. Zabaras. A Bayesian approach to multiscale inverse problems using a sequential monte carlo method, Inverse Problems, Vol. 27 (10), 2011.

B. Wen, Z. Li and N. Zabaras.  Thermal response variability of random polycrystalline microstructures, Communications in Computational Physics, Vol. 10 (3), pp. 607-634, 2011.

H. Xin, T.Y. Hou, and F. Hussain. A mathematically derived multiscale turbulence closure,

submitted 2011.

Z. Zhang, M. Choi, and G.E. Karniadakis. Error estimates for the ANOVA method with polynomial chaos interpolation: Tensor product functions, SIAM J. Sci. Comp., to appear, 2011.

2010

I. Bilionis and P. S. Koutsourelakis.  Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations, Journal of Computational Physics, submitted  2010.

J.L. Eftang, M.A. Grepl, and A.T. Patera. A posteriori error bounds for the empirical interpolation method, CR Acad Sci Paris Series I, 348(9-10): 575-579, 2010.

J.L. Eftang, A.T. Patera, and E.M Rønquist.  An “hp” certified reduced basis method for parametrized elliptic partial differential equations, SIAM Journal on Scientific Computing, 32(6):3170-3200,  2010, (doi: 10.1137/090780122).

Z. Gao and J.S. Hesthaven. On ANOVA expansions and strategies for choosing the anchor point, Appl. Math. and Comp. 217, 3274-3285, 2010, (doi:10.1016/j.amc.2010.08.061).

Z. Gao and J.S. Hesthaven.  Efficient solution of ordinary differential equations with high-dimensional parametrized uncertainty, Comm. Comput. Phys. 10(2), 253-279, 2011, (doi: 10.4208/cicp.090110.080910a).

B. Kouchmeshky and N. Zabaras.  Microstructure model reduction and uncertainty quantification in multiscale deformation processes, Computational Materials Science, 48:213--227, 2010.

P.S. Koutsourelakis and E. Bilionis. Scalable Bayesian reduced-order models for simulating high-dimensional multiscale dynamical systems, SIAM Multiscale Modeling & Simulation, submitted 2010.

C.-Y. Lee and B. Rozovskii. A stochastic finite element method for stochastic parabolic equations driven by purely spatial noise, Communications on Stochastic Analysis, (accepted),  2010.

C.-Y. Lee, B. Rozovskii, and H. M. Zhow. Randomization of forcing in large systems of PDE for improvement of energy estimates, SIAM J. Multiscale Modeling and Simulation, 8(4), 1419-1438, 2010.

Z. Li, B. Wen, and N. Zabaras. Computing mechanical response variability of polycrystalline microstructures through dimensionality reduction techniques, Computational Materials Science, Vol. 49 (3), pp. 568-581, 2010.

X. Ma and N. Zabaras. An adaptive high-dimensional stochastic model representation technique for the solution of stochastic PDEs, J. Comp. Phys., 229:3884--3915, 2010.

X. Ma and N. Zabaras. An adaptive high-dimensional stochastic model representation technique for the solution of stochastic PDEs, Journal of Computational Physics, Vol. 229 (10), pp. 3884-3915, 2010.

D. Venturi, X. Wan, and G.E. Karniadakis. Stochastic bifurcation analysis of Rayleigh-Benard Convection, Journal of Fluid Mechanics 650, 391-413, 2010.

Z. Zhang, M. Choi and G.E. Karniadakis. Anchor points matter in ANOVA decomposition, Proceedings of ICOSAHOM’09, Springer, eds. E. Ronquist & J. Hesthaven, 2010.

2009

S. Lototsky, B. Rozovskii, and X. Wan. Elliptic equations of higher stochastic order, J. Math. Modeling and Numerical Anal, (accepted), 2009.