About me

I am a principal research scientist at the Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. My research interests include computational mechanics, molecular mechanics, nanophotonics, numerical simulation and optimization, scientific computing, and machine learning. My research projects focus on reduced basis methods for parametrized partial differential equations, hybridizable discontinuous Galerkin methods for multi-scale multi-physics simulations, hypersonic flow simulations, large eddy simulations, space weather prediction, atomistic and molecular simulations, nanoplasmonics, bandgap optimization, parallel computing on distributed systems, GPU computing. I am actively contributing to open source projects. In my spare time, I enjoy hanging around and traveling with my family.

Address: 77 Massachusetts Avenue, Office 37-371, Cambridge, MA 02139, USA. Administrative contact: Andres Forero at aforero@mit.edu and 617-253-4926.

Interests
  • Computational Mechanics
  • Molecular Mechanics
  • Nanophotonics
  • Scientific Computing
  • Machine Learning
Education

  • PhD in High Performance Computation for Engineered Systems, 2005

    National University of Singapore

  • BEng in Aeronautical Engineering, 2001

    Ho Chi Minh City University of Technology

Projects

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CESMIX SWQU AFOM LIP
Accelerated First-Order Methods in Simulations and Optimizations
We develop new computational methods and new theoretical analysis for important classes of large-scale simulation and soptimization problems arising in a variety of areas in engineering, science, data science, and applied mathematics. Towards this goal, we will develop and analyze new classes of principled first-order methods (FOMs) that are adapted to deal with the lack of smoothness of the objective function and/or the feasible domain. FOMs are appealing in several ways, as they need only work with gradients, they enjoy reasonably fast convergence, and they scale well in problem dimensions. These features make them suitable for truly large-scale applications, where the objective function is a sum (or average) of a huge number of component functions and the dimension of the optimization variable is huge. However, many existing state-of-the-art FOMs suffer from much slower convergence for a wide range of non-smooth problems. Indeed, without the smoothness condition, traditional FOMs and their accelerated versions do not converge either theoretically or empirically. The development of FOMs with improved and guaranteed convergence rates for solving non-smooth problems will not only advance theory but also broaden the scope of applicability of FOMs to important applications. The proposed research aims to discover new curvature or other mathematical structure conditions (beyond the smoothness condition traditionally required by FOMs) and accordingly, develop new first-order methods (or frameworks) for these conditions. We aim to establish rigorous convergence results to theoretically analyze the methods we will develop for non-smooth optimization problems. Finally, we apply our developed algorithms to solve very large-scale optimization problems in application areas both traditional and new. We will demonstrate the usefulness of our optimization algorithms on novel large-scale applications in the synergistic domains of medical imaging, quantum computing, molecular dynamics, and deep learning. This project is funded by AFOSR.
CESMIX Project
The Center for Exascale Simulation of Materials in Extreme Environments (CESMIX) seeks to advance the state-of-the-art in predictive simulation by connecting quantum and molecular simulations of materials with state-of-the-art programming languages, compiler technologies, and software performance engineering tools, underpinned by rigorous approaches to statistical inference and uncertainty quantification. Our motivating problem is to predict the degradation of complex (disordered and multi-component) materials under extreme loading, inaccessible to direct experimental observation. This application represents a technology domain of intense current interest, and exemplifies an important class of scientific problems - involving material interfaces in extreme environments. This project is supported by the Department of Energy’s Predictive Science Academic Alliance Program (PSAAP-III).
Project Website Open Source
Composable Next Generation Software Framework for Space Weather Data Assimilation and Uncertainty Quantification
The forecasting and reanalysis of space weather events poses a major challenge for many activities in space and beyond. For example, solar storms can damage the power supply infrastructure and computer networks on earth but also impact crucially space exploration and satellite traffic management. As a consequence, improved space weather prediction capabilities can unlock to tremendous societal and economic opportunities such as improved internet coverage via satellite mega-constellations. This multi-disciplinary project brings together teams from various institutions and fields to extend the computational capabilities in the realm of space weather modeling. As part of a larger NSF and NASA initiative motivated by the White House National Space Weather Strategy and Action Plan, the main objective of this project is to build a Julia-based, composable, sustainable, and portable open-source software framework for the model-based analysis of space weather. To that end, the project seeks to develop scalable algorithms for simulation of large-scale, high-fidelity models, reduced order modeling, data assimilation, and uncertainty propagation. These algorithms are then integrated and distributed to the wider space weather modeling community in form of a composable software framework build in Julia. This project is funded by NSF.
News Open Source
Lightning Initiation and Prevention
Prediction of lightning initiation from an aircraft in flight is still at an early stage of research. Even though the phenomenological description of lightning initiation from aircraft is well accepted, a predictive mathematical formulation is well beyond today’s understanding and computational capabilities. An improved physical description of the lightning initiation phenomena is important for prevention and protection. Our project has so far dealt with three areas (1) analytical and computational models of pre-strike electrostatics and leader initiation; (2) analytical and computational models of swept stroke physics; (3) lightning avoidance strategy based on a charge control method. This project is funded by the Boeing Company.

Featured Research

Jordi Vila-Perez, R. Loek Van Heyningen, Ngoc Cuong Nguyen, Jaume Peraire
January, 2022 arXiv, 2022
Exasim: Generating Discontinuous Galerkin Codes for Numerical Solutions of Partial Differential Equations on Graphics Processors

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Ngoc Cuong Nguyen, Sebastien Terrana, Jaime Peraire
January, 2022 AIAA Journal 60(5), 3060-3077
Large-Eddy Simulation of Transonic Buffet Using Matrix-Free Discontinuous Galerkin Method

We present an implicit large-eddy simulation of transonic buffet over the OAT15A supercritical airfoil at Mach number 0.73, angle of attack 3.5 degrees, and Reynolds number 3 millions. The simulation is performed using a matrix-free discontinuous Galerkin (DG) method and a diagonally implicit Runge-Kutta scheme on graphics processor units. We propose a Jacobian-free Newton-Krylov method to solve nonlinear systems arising from the discretization of the Navier?Stokes equations. The method successfully predicts the buffet onset, the buffet frequency, and turbulence statistics owing to the high-order DG discretization and an efficient mesh refinement for the laminar and turbulent boundary layers. A number of physical phenomena present in the experiment are captured in our simulation, including periodical low-frequency oscillations of shock wave in the streamwise direction, strong shear layer detached from the shock wave due to shock-wave/boundary-layer interaction and small-scale structures broken down by the shear-layer instability in the transition region, and shock-induced flow separation. The pressure coefficient, the root mean square of the fluctuating pressure, and the streamwise range of the shock wave oscillation agree well with the experimental data. The results suggest that the proposed method can accurately predict the onset of turbulence and buffet phenomena at high Reynolds numbers without a subgrid scale model or a wall model.
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Publications

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Jaime Manriquez, Ngoc Cuong Nguyen, Manuel Solano (2022). A dissimilar non-matching HDG discretization for Stokes flows. Computer Methods in Applied Mechanics and Engineering 399, 115292.

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Jordi Vila-Perez, R. Loek Van Heyningen, Ngoc Cuong Nguyen, Jaume Peraire (2022). Exasim: Generating Discontinuous Galerkin Codes for Numerical Solutions of Partial Differential Equations on Graphics Processors. arXiv, 2022.

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Ngoc Cuong Nguyen, Sebastien Terrana, Jaime Peraire (2022). Large-Eddy Simulation of Transonic Buffet Using Matrix-Free Discontinuous Galerkin Method. AIAA Journal 60(5), 3060-3077.

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Lee R. Strobel, Ngoc Cuong Nguyen, Carmen Guerra-Garcia (2022). Multiscale Modeling of Streamers: High-Fidelity Versus Computationally Efficient Methods. AIAA SCITECH 2022 Forum, 2124.

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Manuel A. Sanchez, Shukai Du, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaime Peraire (2022). Symplectic Hamiltonian finite element methods for electromagnetics. Computer Methods in Applied Mechanics and Engineering 396, 114969.

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F. Vidal-Codina, Ngoc Cuong Nguyen, C. Ciraci, S. H. Oh, J. Peraire (2021). A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures. Journal of Computational Physics 429, 110000.

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Manuel Solano, Sebastien Terrana, Ngoc Cuong Nguyen, Jaime Peraire (2021). An HDG method for dissimilar meshes. IMA Journal of Numerical Analysis 42(2), 1665-1699.

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Manuel A. Sanchez, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaime Peraire (2021). Symplectic Hamiltonian finite element methods for linear elastodynamics. Computer Methods in Applied Mechanics and Engineering 381, 113843.

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N. Pares, Ngoc Cuong Nguyen, P. Diez, J. Peraire (2021). A posteriori goal-oriented bounds for the Poisson problem using potential and equilibrated flux reconstructions: Application to the hybridizable discontinuous Galerkin method. Computer Methods in Applied Mechanics and Engineering 386, 114088.

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C. Pavan, P. Fontanes, M. Urbani, Ngoc Cuong Nguyen, M. Martinez-Sanchez, J. Peraire, J. Montanya, C. Guerra-Garcia (2020). Aircraft Charging and its Influence on Triggered Lightning. Journal of Geophysical Research Atmospheres 125(1), e2019JD031245.

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Carmen Guerra-Garcia, Pol Fontanes, Michele Urbani, Joan Montanya, Theodore Mouratidis, Manuel Martinez-Sanchez, Ngoc Cuong Nguyen (2020). Controlled Electric Charging of an Aircraft in Flight using Corona Discharge. AIAA Scitech 2020 Forum, 1887.

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C. Guerra-Garcia, Ngoc Cuong Nguyen, T. Mouratidis, M. Martinez-Sanchez (2020). Corona Discharge in Wind for Electrically Isolated Electrodes. Journal of Geophysical Research Atmospheres 125(16), e2020JD032908.

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Sebastien Terrana, Ngoc Cuong Nguyen, Jaime Peraire (2020). GPU-accelerated Large Eddy Simulation of Hypersonic Flows. AIAA Scitech 2020 Forum, 1062.

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C. Ciuca, P. Fernandez, A. Christophe, Ngoc Cuong Nguyen, J. Peraire (2020). Implicit hybridized discontinuous Galerkin methods for compressible magnetohydrodynamics. Journal of Computational Physics X 5, 100042.

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Ferran Vidal-Codina, Luis Martin-Moreno, Cristian Ciraci, Daehan Yoo, Ngoc Cuong Nguyen, Sang-Hyun Oh, Jaime Peraire (2020). Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits. Opt. Express 28(6), 8701-8715.

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Ngoc Cuong Nguyen, Sebastien Terrana, Jaime Peraire (2020). Wall-resolved implicit large eddy simulation of transonic buffet over the OAT15A airfoil using a discontinuous Galerkin method. AIAA Scitech 2020 Forum, 2062.

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S. Terrana, Ngoc Cuong Nguyen, J. Bonet, J. Peraire (2019). A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures. Computer Methods in Applied Mechanics and Engineering 352, 561-585.

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F. Vidal-Codina, J. Saa-Seoane, Ngoc Cuong Nguyen, J. Peraire (2019). A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals. Journal of Computational Physics X 2, 100016.

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Daehan Yoo, Ferran Vidal-Codina, Cristian Ciraci, Ngoc Cuong Nguyen, David R Smith, Jaime Peraire, Sang-Hyun Oh (2019). Modeling and observation of mid-infrared nonlocality in effective epsilon-near-zero ultranarrow coaxial apertures. Nature Communications 10(1), 4476.

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F. Vidal-Codina, Ngoc Cuong Nguyen, S. H. Oh, J. Peraire (2018). A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures. Journal of Computational Physics 355, 548-565.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2018). A physics-based shock capturing method for large-eddy simulation. arXiv, 2018.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2018). A physics-based shock capturing method for unsteady laminar and turbulent flows. 2018 AIAA Aerospace Sciences Meeting, 0062.

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Ngoc Cuong Nguyen, P. Fernandez, R. M. Freund, J. Peraire (2018). Accelerated Residual Methods for the Iterative Solution of Systems of Equations. SIAM Journal on Scientific Computing 40(5), A3157-A3179.

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Carmen Guerra-Garcia, Ngoc Cuong Nguyen, Jaime Peraire, Manuel Martinez-Sanchez (2018). Charge Control Strategy for Aircraft-Triggered Lightning Strike Risk Reduction. AIAA Journal 56(5), 1988-2002.

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F. Vidal-Codina, Ngoc Cuong Nguyen, J. Peraire (2018). Computing parametrized solutions for plasmonic nanogap structures. Journal of Computational Physics 366, 89-106.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2018). Entropy-stable hybridized discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations. arXiv, 2018.

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P. Fernandez, A. Christophe, S. Terrana, Ngoc Cuong Nguyen, J. Peraire (2018). Hybridized discontinuous Galerkin methods for wave propagation. Journal of Scientific Computing 77(3), 1566-1604.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2018). On the ability of discontinuous Galerkin methods to simulate under-resolved turbulent flows. arXiv, 2018.

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Ngoc Cuong Nguyen, Yanlai Chen (2018). Reduced-basis method for the iterative solution of parametrized symmetric positive-definite linear systems. arXiv, 2018.

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Daehan Yoo, Daniel A. Mohr, Ferran Vidal-Codina, Aurelian John-Herpin, Minsik Jo, Sunghwan Kim, Joseph Matson, Joshua D. Caldwell, Heonsu Jeon, Ngoc Cuong Nguyen, Luis Martin-Moreno, Jaime Peraire, Hatice Altug, Sang-Hyun Oh (2018). High-Contrast Infrared Absorption Spectroscopy via Mass-Produced Coaxial Zero-Mode Resonators with Sub-10 nm Gaps. Nano Letters 18(3), 1930-1936.

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Ngoc Cuong Nguyen, C. Guerra-Garcia, J. Peraire, M. Martinez-Sanchez (2017). Computational study of glow corona discharge in wind: Biased conductor. Journal of Electrostatics 89, 1-12.

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D. Moro, Ngoc Cuong Nguyen, J. Peraire, M. Drela (2017). Mesh Topology Preserving Boundary-Layer Adaptivity Method for Steady Viscous Flows. AIAA Journal 55(6), 1970-1985.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2017). Subgrid-scale modeling and implicit numerical dissipation in DG-based Large-Eddy Simulation. 23rd AIAA Computational Fluid Dynamics Conference, 3951.

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M. A. Sanchez, C. Ciuca, Ngoc Cuong Nguyen, J. Peraire, B. Cockburn (2017). Symplectic Hamiltonian HDG methods for wave propagation phenomena. Journal of Computational Physics 350, 951-973.

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Pablo Fernandez, Ngoc Cuong Nguyen, Jaime Peraire (2017). The hybridized discontinuous Galerkin method for implicit large-eddy simulation of transitional turbulent flows. Journal of Computational Physics 336, 308-329.

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F. Vidal-Codina, Ngoc Cuong Nguyen, M. B. Giles, J. Peraire (2016). An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations. SIAM/ASA Journal on Uncertainty Quantification 4(1), 244-265.

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M Stanglmeier, Ngoc Cuong Nguyen, J Peraire, B Cockburn (2016). An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Computer Methods in Applied Mechanics and Engineering 300, 748-769.

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C Guerra-Garcia, Ngoc Cuong Nguyen, J Peraire, M Martinez-Sanchez (2016). Arc reattachment driven by a turbulent boundary layer: implications for the sweeping of lightning arcs along aircraft. Journal of Physics D Applied Physics 49(37), 375204.

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B. Cockburn, Ngoc Cuong Nguyen, J. Peraire (2016). Chapter 8 - HDG Methods for Hyperbolic Problems. Handbook of Numerical Methods for Hyperbolic Problems 17, 173-197.

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David Moro, Ngoc Cuong Nguyen, Jaime Peraire (2016). Dilation-based shock capturing for high-order methods. International Journal for Numerical Methods in Fluids 82(7), 398-416.

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Ngoc Cuong Nguyen, H. Men, R. M. Freund, J. Peraire (2016). Functional Regression for State Prediction Using Linear PDE Models and Observations. SIAM Journal on Scientific Computing 38(2), B247-B271.

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Ngoc Cuong Nguyen, J. Peraire (2016). Gaussian functional regression for output prediction: Model assimilation and experimental design. Journal of Computational Physics 309, 52-68.

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Daehan Yoo, Ngoc Cuong Nguyen, Luis Martin-Moreno, Daniel A Mohr, Sol Carretero-Palacios, Jonah Shaver, Jaime Peraire, Thomas W Ebbesen, Sang-Hyun Oh (2016). High-throughput fabrication of resonant metamaterials with ultrasmall coaxial apertures via atomic layer lithography. Nano letters 16(3), 2040-2046.

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Pablo Fernandez, Ngoc Cuong Nguyen, Xevi Roca, Jaime Peraire (2016). Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method. 54th AIAA Aerospace Sciences Meeting, 1332.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2015). A class of embedded discontinuous Galerkin methods for computational fluid dynamics. Journal of Computational Physics 302, 674-692.

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F. Vidal-Codina, Ngoc Cuong Nguyen, M.B. Giles, J. Peraire (2015). A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations. Journal of Computational Physics 297, 700-720.

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Ngoc Cuong Nguyen, J. Peraire, F. Reitich, B. Cockburn (2015). A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation. Journal of Computational Physics 290, 318-335.

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Ngoc Cuong Nguyen, J. Peraire (2015). Gaussian functional regression for linear partial differential equations. Computer Methods in Applied Mechanics and Engineering 287, 69-89.

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Hyeong-Ryeol Park, Xiaoshu Chen, Ngoc Cuong Nguyen, Jaime Peraire, Sang-Hyun Oh (2015). Nanogap-enhanced terahertz sensing of 1 nm thick lambda/106 dielectric films. Acs Photonics 2(3), 417-424.

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J. Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, J. Peraire (2015). Spectral approximations by the HDG method. Mathematics of Computation 84(293), 1037-1059.

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Han Men, Robert M. Freund, Ngoc Cuong Nguyen, Joel Saa-Seoane, Jaime Peraire (2014). Fabrication-Adaptive Optimization with an Application to Photonic Crystal Design. Operations Research 62(2), 418-434.

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LNT Huynh, Ngoc Cuong Nguyen, J Peraire, BC Khoo (2013). A high-order hybridizable discontinuous Galerkin method for elliptic interface problems. International Journal for Numerical Methods in Engineering 93(2), 183-200.

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David Moro, Ngoc Cuong Nguyen, Mark Drela, Jaime Peraire (2013). A High-Order Self-Adaptive Monolithic Solver for Viscous-Inviscid Interacting Flows. 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 857.

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Ngoc Cuong Nguyen, Xevi Roca, David Moro, Jaime Peraire (2013). A Hybridized Multiscale Discontinuous Galerkin Method for Compressible Flows. 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 689.

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Hemant K. Chaurasia, Ngoc Cuong Nguyen, Jaime Peraire (2013). A Time-Spectral Hybridizable Discontinuous Galerkin Method for Periodic Flow Problems. 21st AIAA Computational Fluid Dynamics Conference, 2861.

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David Moro, Ngoc Cuong Nguyen, Jaime Peraire, Mark Drela (2013). Advances in the development of a High Order, Viscous-Inviscid Interaction Solver. 21st AIAA Computational Fluid Dynamics Conference, 2943.

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Aycil Cesmelioglu, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire (2013). Analysis of HDG methods for Oseen equations. Journal of Scientific Computing 55(2), 392-431.

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K. C. Hoang, B. C. Khoo, G. R. Liu, Ngoc Cuong Nguyen, A. T. Patera (2013). Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Inverse Problems in Science and Engineering 21(8), 1310-1334.

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Xevi Roca, Ngoc Cuong Nguyen, Jaime Peraire (2013). Scalable parallelization of the hybridized discontinuous Galerkin method for compressible flow. 21st AIAA Computational Fluid Dynamics Conference, 2939.

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D. Moro, Ngoc Cuong Nguyen, J. Peraire (2012). A hybridized discontinuous Petrov-Galerkin scheme for scalar conservation laws. International Journal for Numerical Methods in Engineering 91(9), 950-970.

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J Saa-Seoane, Ngoc Cuong Nguyen, H Men, R Freund, J Peraire (2012). Binary optimization techniques for linear PDE-governed material design. Appl. Phys. A - Mater. Sci. Process. 109(4), 1023-1030.

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Ngoc Cuong Nguyen, Jaume Peraire (2012). Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics. Journal of Computational Physics 231(18), 5955-5988.

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David Moro, Ngoc Cuong Nguyen, Jaime Peraire, Jay Gopalakrishnan (2011). A Hybridized Discontinuous Petrov-Galerkin Method for Compresible Flows. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 197.

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Ngoc Cuong Nguyen, Jaime Peraire (2011). An adaptive shock-capturing HDG method for compressible flows. 20th AIAA Computational Fluid Dynamics Conference, 3060.

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Jaime Peraire, Ngoc Cuong Nguyen, Bernardo Cockburn (2011). An embedded discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations. 20th AIAA Computational Fluid Dynamics Conference, 3228.

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Han Men, Ngoc Cuong Nguyen, Robert M Freund, Kian-Meng Lim, Pablo A Parrilo, Jaime Peraire (2011). Design of photonic crystals with multiple and combined band gaps. Physical Review E 83(4), 046703.

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Xevi Roca, Ngoc Cuong Nguyen, Jaime Peraire (2011). GPU-accelerated sparse matrix-vector product for a hybridizable discontinuous Galerkin method. 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition , 687.

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Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn (2011). High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics. Journal of Computational Physics 230(10), 3695-3718.

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Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn (2011). Hybridizable discontinuous Galerkin methods. Spectral and High Order Methods for Partial Differential Equations, 63-84. Springer.

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Ngoc Cuong Nguyen, Jaume Peraire, Bernardo Cockburn (2011). Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwells equations. Journal of Computational Physics 230(19), 7151-7175.

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David Moro, Ngoc Cuong Nguyen, Jaime Peraire (2011). Navier-Stokes solution using hybridizable discontinuous Galerkin methods. 20th AIAA computational fluid dynamics conference, 3407.

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David J Knezevic, Ngoc Cuong Nguyen, Anthony T Patera (2011). Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Mathematical Models and Methods in Applied Sciences 21(07), 1415-1442.

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Bernardo Cockburn, Jayadeep Gopalakrishnan, Ngoc Cuong Nguyen, Jaime Peraire, Francisco-Javier Sayas (2011). Analysis of HDG methods for Stokes flow. Mathematics of Computation 80 (274), 723-760.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2011). An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. Journal of Computational Physics 230 (4), 1147-1170.

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Sebastien Boyaval, Claude Le Bris, Tony Lelievre, Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera (2010). Reduced Basis Techniques for Stochastic Problems. Archives of Computational methods in Engineering 17 (4), 435-454.

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Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire (2010). A comparison of HDG methods for Stokes flow. Journal of Scientific Computing 45(1), 215-237.

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Jaime Peraire, Ngoc Cuong Nguyen, Bernardo Cockburn (2010). A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations. 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 363.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2010). A hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. 48th AIAA Aerospace Sciences meeting including the new horizons forum and aerospace exposition, 362.

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Han Men, Ngoc Cuong Nguyen, Robert M Freund, Pablo A Parrilo, Jaume Peraire (2010). Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. Journal of Computational Physics 229(10), 3706-3725.

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B. Cockburn, J. Gopalakrishnan, F. Li, Ngoc Cuong Nguyen, J. Peraire (2010). Hybridization and Postprocessing Techniques for Mixed Eigenfunctions. SIAM Journal on Numerical Analysis 48(3), 857-881.

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Ngoc Cuong Nguyen, Gianluigi Rozza, Phuong Huynh, Anthony T Patera (2010). Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real-Time Bayesian Parameter Estimation. Large-Scale Inverse Problems and Quantification of Uncertainty, 151-177.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2010). A hybridizable discontinuous Galerkin method for Stokes flow. Computer Methods in Applied Mechanics and Engineering 199 (9-12), 582-597.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2009). An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations. Journal of Computational Physics 228 (23), 8841-8855.

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Sebastien Boyaval, Claude Le Bris, Yvon Maday, Ngoc Cuong Nguyen, Anthony T Patera (2009). 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(41-44), 3187-3206.

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G. Rozza, D. B. P. Huynh, Ngoc Cuong Nguyen, A. T. Patera (2009). Real-Time Reliable Simulation of Heat Transfer Phenomena. Heat Transfer Summer Conference, 851-860. ASME.

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Ngoc Cuong Nguyen, Gianluigi Rozza, Anthony T. Patera (2009). Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers equation. Calcolo 46 (3), 157-185.

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G. Rozza, Ngoc Cuong Nguyen, A. T. Patera, S. Deparis (2009). Reduced Basis Methods and a Posteriori Error Estimators for Heat Transfer Problems. Heat Transfer Summer Conference, 753-762.

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Ngoc Cuong Nguyen, Jaime Peraire, Bernardo Cockburn (2009). An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations. Journal of Computational Physics 228 (9), 3232-3254.

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Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera, George S. H. Pau (2009). A general multipurpose interpolation procedure: the magic points. Communications on Pure & Applied Analysis 8 (1), 383.

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Ngoc Cuong Nguyen (2008). A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales. Journal of Computational Physics 227(23), 9807-9822.

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Ngoc Cuong Nguyen, Jaime Peraire (2008). An efficient reduced-order modeling approach for non-linear parametrized partial differential equations. International Journal for Numerical Methods in Engineering 76(1), 27-55.

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Ngoc Cuong Nguyen, Anthony T. Patera, Jaime Peraire (2008). A best points interpolation method for efficient approximation of parametrized functions. International journal for numerical methods in engineering 73 (4), 521-543.

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Ngoc Cuong Nguyen (2007). A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations. Journal of Computational Physics 227(2), 983-1006.

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Martin A Grepl, Ngoc Cuong Nguyen, Karen Veroy, Anthony T Patera, Gui R Liu (2007). Certified rapid solution of partial differential equations for real-time parameter estimation and optimization. Real-time PDE-constrained optimization, 199-216. SIAM.

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Martin A. Grepl, Ngoc Cuong Nguyen, Karen Veroy, Anthony T. Patera, Gui R. Liu (2007). Certified Rapid Solution of Partial Differential Equations for Real-Time Parameter Estimation and Optimization. Real-Time PDE-Constrained Optimization, 199-216, SIAM.

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Eric Cances, Claude Le Bris, Ngoc Cuong Nguyen, Y Maday, Anthony T Patera, George Shu Heng Pau (2007). Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. Proceedings of the workshop for high-dimensional partial differential equations in science and engineering (Montreal), 15-57.

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Ngoc Cuong Nguyen, Per-Olof Persson, Jaime Peraire (2007). RANS solutions using high order discontinuous Galerkin methods. 45th AIAA Aerospace Sciences Meeting and Exhibit, 914.

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Martin A Grepl, Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera (2007). Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Mathematical Modelling and Numerical Analysis 41 (3), 575-605.

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Sugata Sen, Karen Veroy, Dinh Bao Phuong Huynh, Simone Deparis, Ngoc Cuong Nguyen, Anthony T Patera (2006). ?Natural norm? a posteriori error estimators for reduced basis approximations. Journal of Computational Physics 217(1), 37-62.

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Ngoc Cuong Nguyen (2006). A Note on Tikhonov Regularization of Linear Ill-Posed Problems. Massachusetts Institute of Technology, 1-4.

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Ngoc Cuong Nguyen (2005). Reduced-basis approximation and a posteriori error bounds for nonaffine and nonlinear partial differential equations: Application to inverse analysis. National University of Singapore.

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Ngoc Cuong Nguyen (2005). Turbulence modeling. Department of Aeronautics and Astronautics, MIT, 1-6.

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Ngoc Cuong Nguyen, Karen Veroy, Anthony T. Patera (2005). Certified real-time solution of parametrized partial differential equations. Handbook of materials modeling, 1529-1564.

Cite Link

Maxime Barrault, Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera (2004). An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Mathematique 339 (9), 667-672.

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Department of Aeronautics & Astronautics, MIT
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Course description: Covers advanced topics in numerical methods for the discretization, solution, and control of problems governed by partial differential equations. Specific topics include the Discontinuous Galerkin finite element method for systems of conservations laws, therory and implementation, applications involving compressible, viscous flows, grid generation, optimal control of PDEconstrained systems, a posteriori error estimation and adaptivity.

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