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Journal Papers

  1. 1.M. Barrault, Y. Maday, N.C. Nguyen, A.T. Patera, An empirical interpolation method: Application to efficient reduced basis discretization of partial differential equations. C. R. Acad. Sci. Paris, Ser. I 339 (2004) 667--672.

  2. 2.S. Sen, K. Veroy, D.B.P. Huynh, S. Deparis, N.C. Nguyen, A.T. Patera, ``Natural norm'' a posteriori error estimators for reduced basis approximations. Journal of Computational Physics, 217 (2006) 37--62.

  3. 3.M.A. Grepl, Y. Maday, N.C. Nguyen, A.T. Patera, Efficient reduced basis treatment of nonaffine and nonlinear partial differential equations. ESAIM-Mathematical Modeling and Numerical Analysis (M2AN), 41 (2007) 575--605.

  4. 4.N.C. Nguyen, A. T. Patera, J. Peraire, A ``best points'' interpolation method for efficiet approximation of parametrized functions. International Journal of Numerical Methods in Engineering, 73  (2008) 521--543.

  5. 5.N.C. Nguyen, A posteriori error estimation and basis adaptivity for reduced basis approximation of nonaffine-parametrized linear elliptic partial differential equations. Journal of Computational Physics, 227 (2007) 983--1006.

  6. 6.N.C. Nguyen, A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales. Journal of Computational Physics, 227 (2007) 9807--9822.

  7. 7.N.C. Nguyen J. Peraire, An efficient reduced-order modeling approach for nonlinear parametrized partial differential equations. International Journal of Numerical Methods in Engineering, 76 (2008) 27--55.

  8. 8.Y. Maday, N.C. Nguyen, A.T. Patera, G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Communications on Pure and Applied Analysis, 8 (2009) 384--404. A special issue on A tribute to Professor P. G. Ciarlet on his 70th birthday.

  9. 9.N.C. Nguyen J. Peraire, B. Cockburn, An implicit high-order hybridazable discontinuous Galerkin method for linear convection-diffusion equations. Journal of Computational Physics, 228 (2009) 3232--3254.

  10. 10.N.C. Nguyen J. Peraire, B. Cockburn, An implicit high-order hybridazable discontinuous Galerkin method for nonlinear convection-diffusion equations. Journal of Computational Physics, 228 (2009) 8841--8855.

  11. 11.Boyaval, C Le Bris, Y Maday, NC Nguyen, and AT Patera, A Reduced Basis Approach for Variational Problems with Stochastic Parameters: Application to Heat Conduction with Variable Robin Coefficient. Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3187--3206.

  12. 12.N.C. Nguyen, G. Rozza, A. T Patera, Reduced Basis Approximation and A Posteriori Error Estimation for the Time-Dependent Viscous Burgers Equation. Calcolo, 46 (2009) 157--185. 

  13. 13.N.C. Nguyen J. Peraire, B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow. Computer Methods in Applied Mechanics and Engineering, 199 (2010) 582--597.

  14. 14.B. Cockburn, J. Gopalakrishnan, N.C. Nguyen, J. Peraire, F.-J. Sayas, Analysis of HDG methods for Stokes flow. Mathematics of Computation, 2009. Accepted.

  15. 15.H. Men, N.-C. Nguyen, R.M. Freund, P.A. Parrilo, J. Peraire. Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods. Journal of Computational Physics, 2009. To appear.

  16. 16.N.C. Nguyen, J. Peraire, B. Cockburn, A comparison of HDG methods for Stokes flow. Journal of Scientific Computing, 2009. To appear.

Ph.D. Dissertation

Book Chapters

  1. 1.N.C. Nguyen, K. Veroy, A.T. Patera, Certified real-time solution of parametrized partial differential equations. In Handbook of Materials Modeling, pp. 1523--1558. Springer 2005.

  2. 2.M.A. Grepl, N.C. Nguyen, K. Veroy, A.T. Patera, G.R. Liu, Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. In Real-Time PDE-Constrained Optimization, pp. 197--212. SIAM Computational Science and Engineering Book Series 2007.

  3. 3.E. Cances, C. LeBris, Y. Maday, N.C. Nguyen, A.T. Patera, G.S.H. Pau, Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. In High-dimensional Partial Differential Equations in Science and Engineering, pp. 15--47. American Mathematical Society, CRM proceedings series, volume 41, 2007.

  4. 4.N. C. Nguyen, G. Rozza, D.B.P. Huynh, and A. T. Patera, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Parabolic PDEs; Application to Real-Time Bayesian Parameter Estimation. In Computational Methods for Large Scale Inverse Problems and Uncertainty Quantification, John Wiley & Sons, 2009.

Papers in Review

  1. 1.N.C. Nguyen, An uncertainty quantification method for parameter estimation in elliptic partial differential equations. Submitted to Computer Methods in Applied Mechanics and Engineering, 2009.

  2. 2.N.C. Nguyen, J. Peraire, B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Submitted to Journal of Computational Physics, 2009.

  3. 3.D. J. Knezevic, N.C. Nguyen, A.T. Patera, Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Submitted to Mathematical Models and Methods in Applied Sciences, 2009.

  4. 4.B. Cockburn, J. Gopalakrishnan, F. Li, N.C. Nguyen, J. Peraire, Hybridization and postprocessing techniques for mixed eigenfunctions. Submitted to SIAM Numerical Analysis, 2009.

  5. 5.S. Boyaval, C. Le Bris, T. Lelievre, Y. Maday, N.C. Nguyen A.T. Patera, Reduced basis techniques for stochastic problems. Submitted to Archivesof Computational Methods in Engineering, 2009.

Conference Papers

  1. 1.N.C. Nguyen, P.O. Persson, J. Peraire, RANS Solutions using high order discontinuous Galerkin methods. In Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2007-0914, Reno, NV, January 2007.

  2. 2.N.C. Nguyen, J. Peraire, An interpolation method for the reconstruction and recognition of face images. In Proceedings of the 2nd International Conference on Computer Vision Theory and Applications, pp. 91–96, March 2007.

  3. 3.G. Rozza, D.B.P. Huynh, N.C. Nguyen, A.T. Patera, Real-Time Reliable Simulation of Heat Transfer Phenomena. Paper HT2009-88212. ASME Summer Heat Transfer Conference, San Francisco, California, July 19-23, 2009.

  4. 4.G. Rozza, N.C. Nguyen, S. Deparis, A.T. Patera, Reduced Basis Methods and A Posteriori Error Estimators for Heat Transfer Problems. Paper HT2009-88211. ASME Summer Heat Transfer Conference, San Francisco, California, July 19-23, 2009.

  5. 5.N.C. Nguyen, J. Peraire, B. Cockburn, Hybridizable  discontinuous Galerkin methods. Submitted to the ICOSAHOM proceedings in a special volume of the book series Lecture Notes in computational Science and Engineering, 2009.

  6. 6.N.C. Nguyen, J. Peraire, B. Cockburn, A Hybridizable Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations. In Proceedings of the 48th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2010-362, Orlando, Florida, January 2010.

  7. 7.J. Peraire, N.C. Nguyen, B. Cockburn, A Hybridizable Discontinuous Galerkin Method for the compressible Euler and Navier-Stokes Equations. In Proceedings of the 48th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2010-363, Orlando, Florida, January 2010.

Other Notes