PUBLICATIONS

2014

H. Cho, D. Venturi and G.E. Karniadakis, Statistical analysis and simulation of random shocks in Burgers turbulence, Submitted to Royal Society A, 2014.

M. Choi, T. Sapsis and G.E. Karniadakis, On the equivalence of dynamically orthogonal and dynamically bi-orthogonal methods: Theory and numerical simulations. J. Comput. Phys., 270, 1-20, 2014.

M. Ci, T.Y. Hou and Z. Shi, A multiscale model reduction method for partial differential equations, ESAIM:M2An, 48, 449-474, 2014.

T.Y. Hou, Z. Shi and P. Tavalali, Convergence of a data-driven time-frequency analysis method, Applied and Comput. Harmonic Analysis, 37(2), 235-270, 2014.

L. Ng and K. Willcox, Aircraft conceptual design under uncertainty, In Proceedings of the 10th AIAA Multidisciplinary Design Optimization Conference, Baltimore, MD, January 2014. Submitted to Journal of Aircraft.

B. Peherstofer, D. Butnaru, K. Willcox and H. Bungartz, Localized discrete empirical interpolation methods, Accepted for publication, SIAM Journal on Scientific Computing.

K. Urban and A.T. Patera, An Improved Error Bound for Reduced Basis Approximation of Linear Parabolic Problems, Submitted to Mathematics of Computation, 83(288), 1599-1615, 2014

doi: 10.1090/S0025-5718-2013-02782-2.

S. Vallaghe and A.T. Patera, The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model, SIAM Journal on Scientific Computing,36(3), B294-B320, 2014.

D. Venturi and G.E. Karniadakis, Convolutionless Nakajima-Z2wanzig equations for stochastic analysis in large scale simulations, Royal Society A, 470, 20130754, 2014.

M. Yano, A.T. Patera and K. Urban, A space-time hp-interpolation-based certified reduced basis method for Burgers' equation, Mathematical Models and Methods in Applied Sciences, 24(9), 2014.

M. Zayernouri and G.E. Karniadakis, Exponentially accurate spectral and spectral element methods for fractional ODEs, J. Comput. Phys., 257, Part A, 460-480, 2014.

M. Zayernouri and G.E. Karniadakis, Fractional spectral collocation methods, SIAM J. Sci. Comput., 36(1) A40-A62, 2014.

M. Zayernouri and G.E. Karniadakis, Fractional spectral collocation methods for linear and nonlinear variable order FPDEs, Submitted to J. Comput. Physics, Special Issue on Fractional PDEs, 2014.

M. Zheng and G.E. Karnidakis, Numerical Methods for SPDEs with tempered stable processes, Submitted to SIAM J. Sci. Comput. 2014.

2013

I. Bilionis and N. Zabaras, Solution of inverse problems with limited forward solver evaluations: a fully Bayesian framework, Inverse problems (under review) 2013.

I. Bilionis and N. Zabaras, A stochastic optimization approach to coarse-graining using a relative framework, The Journal of Chemical Physics, 138(4), 044313, 2013.

I. Bilionis, N. Zabaras, B.A. Konomi, and G. Lin, Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification, J. of Comput. Physics. 241, 212-239, 2013.

W. Cao, Z. Zhang and G.E. Karniadakis, Numerical methods for stochastic delay differential equations via the Wong-Zakai approximation, Submitted to SIAM J. Sci. Comput. 2013.

P. Chen and N. Zabaras, A nonparametric belief propagation method for uncertainty quantification with applications to flow in random porous media, J. Comput. Physics, 240, 615-643, 2013.

P. Chen and N. Zabaras, Adaptive locally weighted projection regression method for uncertainty quantification", Communications in Computational Physics (CiCP), 14(4), 851-878, 2013, doi: 10.4208/cicp.060712.281212a.

M. Cheng, T. Y. Hou, and Z. Zhang, A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equations II: Adaptivity and Generalizations, J. Comput. Phys. 242, 753-776, 2013, DOI: 10.1016/j.jcp2013.02.020.

M. Cheng, T.Y. Hou, M. Yan and Z. Zhang, A data-driven stochastic method for elliptic PDEs with Random coefficients, SIAM/ASA J. for Uncertainty Quantification 1, 452-493,  2013.

H. Cho, D. Venturi and G. Karniadakis, Adaptive discontinuous Galerkin method for response-excitation PDF equations,SIAM J. Sci. Comput. 35(4), B90-B911, 2013.

H. Cho, D. Venturi, and G.E. Karniadakis, Karhunen-Loeve expansion for multi-correlated stochastic processes, Probabilistic Engineering Mechanics, 34, 147-167, 2013.

M. Choi, T. Sapsis, and G.E. Karniadakis, A convergence study for the SPDEs using combined polynomial chaos and dynamically orthogonal schemes, J. Comp. Phys. 245, 281-301, 2013.

Y. Efendiev, J. Galvis and T.Y. Hou, Generalized multiscale finite element methods (GMsFEM), J. Comput. Phys.,251, 116-135, 2013.

J.L. Eftang and A.T. Patera, A port-reduced static condensation reduced basis element method for large component-synthesized structures: Approximation and a posteriori error estimation. Advanced Modeling and Simulation in Engineering Sciences (SpringerOpen) 1:3, 2013.

J.L. Eftang, D.B.P. Huynh, D.J. Knezevic, E.M. Rønquist and A.T. Patera, Adaptive Port Reduction in Static Condensation: Proceedings of the 7th Vienna Conference on Mathematical Modelling - MATHMOD2012 ) DOI: 10.3182/20120215-3-AT-3016.00123, vol. 7, part 1, pp. 695-699, 2013.

J.S. Hesthaven, B. Stamm, and S. Zhang, Efficient greedy algorithms for high-dimensional parameter spaces with application so empirical interpolation and reduced basis methods, Mathematical Modeling and Numerical Analysis, Published online by Cambridge University Press, July 16, 2013, DOI: http://dx.doi.org/10.105/m2an/2013100

T. Y. Hou and Z. Shi, Data-driven Time-Frequency Analysis', Applied and Comput. Harmonic Analysis, 35(2), 284, 308, 2013.  http://dx.doi.org/10.1016/j.acha.2012.10.001.

T.Y. Hou, X. Hu and F. Hussain, Multiscale modeling of incompressible turbulent flows, J. Comput. Phys., 232, 383, 396, 2013. http://dx.doi.org/10.1016/j.jcp2012.08.029.

D.B.P. Huynh, D.J. Knezevic and A.T. Patera, A Static Condensation Reduced Basis Element Method: Complex Problems: Computer Methods In Applied Mechanics and Engineering, 259(1), 197-216, 2013, DOI: 10.1016/u.cma.2013.02.013.

D.B.P. Huynh, D.J. Knezevic and A.T. Patera, A Static Condensation Reduced Basis Element Method: Approximation and A Posteriori Error Estimation, Mathematical Modeling and Numerical Analysis, 47(1), 213-251, 2013, DOI: 10.1051/m2an/2012022.

J. Kristensen, I. Bilionis and N. Zabaras, Relative entropy as model selection tool in cluster expansion, Phys. Rev. B, 87, 174112, May 2013.

C. Lieberman and K. Willcox, Nonlinear goal-oriented Bayesian inference: Application to carbon capture and storage, Submitted to SIAM J. Sci. Comput., 2013.

C. Lieberman and K. Willcox, Goal-oriented inference: Approach, linear theory, and application to advection-diffusion, SIAM Review, 55(3), 493-519, 2013.

C. T. Miller, C. N. Dawsonb, M. W. Farthing, T. Y. Hou, J.F. Huange, C. E. Kees, C.T. Kelley, H.P. Langtangen Numerical Simulation of Water Resources Problems: Models, Methods, and Trends', Advances in Water Resources, 51, 405-437, 2013. DOI: 10.1016/j.advwatres.2012.05.008.

L. Ng, and K. Willcox, Aircraft Conceptual Design Under Uncertainty,10th AIAA Multidisciplinary Design Optimization Conference, DOI:10.2514/6.2014-0802.

L. Ng and K. Willcox, Multifidelity approaches for optimization under uncertainty, Submitted to International Journal for Numerical Methods in Engineering, 2013.

B. Peherstofer, D. Butnaru, K. Willcox and H. Bungartz, Localized Discrete Empirical Interpolation Method, Aerospace Computational Design Lab Technical Report ACDL-TR-2013, Submitted to SIAM Journal on Scientific Computing, 2013

L. Ng and K. Willcox, Aircraft Conceptual Design under Uncertainty, Submitted to AIAA 2014 SciTech Conference.

B. Rozovky and X. Wan, Wick-Malliavin approximation of elliptic problems with long-normal random coefficients, Submitted 2013.

S. Vallaghe, D.B.P. Huynh, D. Knezevic and A.T. Patera, Component-based reduced basis for eigenproblems Submitted July 2013 to Computers & Structures.

D. Venturi, D.M. Tartakovsky, A.M. Tartakovsky and G.E. Karniadakis, Exact PDF equations and closure approximations for advective-reactive transport, J Comput. Phys., 243, 323-343, 2013.

D. Venturi and G.E. Karniadakis, Goal-oriented probability density function methods for stochastic dynamic al systems, Submitted to PNAS, 2013.

D. Venturi, R. Mikulevicius, B. Rozovskii, and G.E. Karniadakis, Wick-Malliavin approximation to nonlinear stochastic PDEs: Analysis and simulations, Accepted for publication in Proceedings of the Royal Society A, 2013.

J. Wan and N. Zabaras, A probabilistic graphical model approach to stochastic multiscale partial differential equations, J. Comput. Physics, 250, 477-510, 2013.

X. Yang, and G.E. Karniadakis Reweighted minimization method for stochastic elliptic differential equations, J. Comput. Phys, 248, 87-108, 2013.

M. Yano and A.T Patera, A space-time variational approach to hydrodynamic stability theory. Proceedings of the Royal Society A, 469(2155), article number 20130036, July 2013.  doi: 10.1098/rspa.2013.0036

M. Yano, A reduced basis method with exact-solution certificates for symmetric coercive equations, Submitted in November 2013 to Computer Methods in Applied Mechanics and Engineering.

M. Yano, A space-time Petrov-Galerkin certified reduced basis method: Application to the Boussinesq equations, SIAM Journal on Scientific Computing, Accepted November 2013.

N. Zabaras, Adaptive local weighted projection regression method for uncertainty quantification, Communications in Computational Physics (in press) 2013.

M. Zayernouri, S-W. Park, D. Tartakovsky and G.E. Karniadakis, Stochastic smoothed profile method for modeling random roughness in flow problems, CMAME, 263, 99-112, 2013.

M. Zayernouri, and G.E. Karniadakis, Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation, J. Comput. Phys., 252, 495-517, 2013.

M. Zayernouri, W. Cao and G.E. Karniadakis, Spectral and discontinuous spectral element methods for fractional delay equations, Submitted to SIAM J. Sci. Comput., 2013.

M. Zayernouri, I. Alvey and G.E. Karniadakis, Discontinuous Petrov-Galerkin methods for time and space-fractional advection equations, Submitted to SIAM J. Sci. Comput. 2013.

M. Zayernouri, M. Ainsworth and G.E. Karniadakis, A unified Petrov-Galerkin spectral method for fractional PDEs, Submitted to CMAME, 2013.

Z. Zhang, X. Hu, T.Y. Hou, G. Lin and M. Yan, An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficients, Submitted to Communications in Computational Physics, 2013.

Z. Zhang, M. Ci and T.Y Hou, A multiscale-data-driven stochastic method for elliptic PDEs with random coefficients, Submitted to SIAM Multiscale Modeling and Simulation, 2013.

Z. Zhang, M. Ci and T.Y. Hou, A multiscale multilevel Monte Carlo method for elliptic PDEs with random coefficients, In preparation, 2013.

Z. Zhang, X. Yang, G. Lin and G.E. Karniadakis, Numerical solution for the Stratnovich- and Ito-Euler equations: Application to the stochastic piston problem, J. Comput. Phys., 236, 15-27, 2013.

Z. Zhang, B. Rozovskii and G.E. Karniadakis, The method of lines for stochastic differential equations driven by white noise: A spectral approach, In preparation 2013.

Z. Zhang, M.V. Tretyakov, B. Rozovskii and G.E. Karniadakis, Wiener chaos vs stochastic collcation methods for linear advection-diffusion-reaction equations with multiplicative white noise, Submitted to SIAM J. on Numerical Analysis, 2013.

Z. Zhang, M.V. Tretyakov, B. Rozovskii and G.E. Karniadakis, A recursive sparse grid collocation method for differential equations with white noise, Submitted to SIAM J. Sci. Comput. 2013.

M. Zheng, X. Wan, and G.E. Karniadakis, Adaptive-multi-element polynomial chaos with discrete measure: Algorithms and application to SPDEs, Submitted to Applied Numerical Mathematics, 2013.

2012

I. Bilionis and N. Zabaras, Multi-output local Gaussian process regression: Application to uncertainty quantification, J. Comp. Phys., 231, 5718-5746, 2012.

I. Bilionis and P. S. Koutsourelakis. Free energy computations by minimization of Kullback-Leibler divergence: An efficient adaptive biasing potential method for sparse representation, Journal of Computational Physics, 231, 3849-3870, 2012.

I. Bilionis and N. Zabaras, Multidimensional adaptive relevance vector machines for Uncertainty Quantification", SIAM Journal for Scientific Computing, 34(6), B881-B908, 2012.

Y. Chen, J.S. Hesthaven, Y. Maday, J. Rodriguez, and X. Zhu. Certified reduced methods for electromagnetic scattering and radar cross section estimation, Comput. Methods Appl. Mech. Engin., 233, 92-108, 2012.

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, 51(1), 28-59, (doi: 10.1007/s10915-011-9494-2) 2012.

J.L. Eftang and B. Stamm, Parameter multi-domain "hp" empirical interpolation, International Journal for Numerical Methods in Engineering, 90(4), 412-428, doi: 10.1002/nme.3327, 2012.

M. Ganesh, J.S. Hesthaven, and B. Stamm. A reduced basis method for multiple electromagnetic scattering in three dimensions, J. Comput. Phys. 231(23), 7756-7779, 2012.

J.S. Hesthaven, B. Stamm, and S. Zhang. Certified reduced basis methods for the electric field integral equation SIAM J. Sci. Comput., 34(3), A1777-A1799, 2012.

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, 201-204, 13-24  (doi: 10.1016/j.cma.2011.09.011) 2012.

C.Y. Lee and Boris Rozovskii. On stochastic Navier-Stokes equations driven by stationary white noise, In: Malliavin Calculus and Stochastic Analysis, F. Viends et al, Editors, pp. 219-250.

C. Lieberman and K. Willcox, Goal-oriented inference: Approach, linear theory, and application to advection-diffusion, SIAM J. Sci. Comput. 34(4), 1880-1904, 2012.

S. Lototsky and B.L. Rozovskii, D. Selesi.  On generalized Malliavin calculus, J. Stochastic  Processes and Applications, 122, 808-843, 2012.

R. Mikulevicius, B. L. Rozovsky, On unbiased stochastic Navier-Stokes equation, On unbiased stochastic Navier-Stokes equations, Probab. Theory Related Fields, 154, 787-834, 2012.

L. Ng, D.B.P. Huynh and K. Willcox, Multifidelity uncertainty propagation for optimization under uncertainty, 12th AIAA Aviation Technology, Integration and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Chapter DOI: 10.2514/6.2012-5602, September 17-19 2012.

A.T. Patera and E.M. Ronquist, Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data, CR Acad. Sci. Paris, Series 1, 350(9-10), 543-547, 2012.

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, 350(3-4), 203-207, 2012.

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., 468, 759-793 2012 (doi: 10.1098/rspa.2011.0186).

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, Comp. Physics, 231, 7450-7474, 2012.

D. Venturi and G.E. Karniadakis. Differential constraints for the probability density function of stochastic solutions to the wave equation,  Int. J. Uncertainty Quantification, 2(3), 195-213, 2012.

D. Venturi, M. Choi, and G.E. Karniadakis. Supercritical quasi-conduction states in stochastic Rayleigh Benard convection, Int. J. of Heat & Mass Transfer, 55(13-14), 3732-3743, 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.

B. Wen and N. Zabaras, A multiscale approach for model reduction of random microstructures, Computational Materials Science, Vol. 63, pp. 269-285, 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.

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., 34(2) A1165-A1186, 2012

Z. Zhang, B. Rozovskii, M.V. Tretyakov, G.E. Karniadakis, A multi-stage Wiener chaos expansion method for stochastic advection-diffusion-reaction equations, SIAM J. Sci. Comput. 34(2), A914-A936, 2012.

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.

JL Eftang, AT Patera, and EM Rønquist, An “hp” Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations. JS Hesthaven and EM Rønquist (eds.), Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, 76:179–187, 2011.  doi: 0.1007/978-3-642-15337-2-15

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.

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.

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. 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.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)

P.S. Koutsourelakis and E. Bilionis. Scalable Bayesian reduced-order models for simulating high-dimensional multiscale dynamical systems, SIAM Multiscale Modeling & Simulation, 9(1), 449-485, 2011..

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.

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).

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.

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.

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).

B. Kouchmeshky and N. Zabaras.  Microstructure model reduction and uncertainty quantification in multiscale deformation processes, Computational Materials Science, 48:213--227, 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, 4(2), 271-297, 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.

S. Lototsky, B. Rozovskii, and X. Wan. Elliptic equations of higher stochastic order, J. Math. Modeling and Numerical Anal,44(5), 1135-1153, 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.