Book

Spectral Methods for Uncertainty Quantification, with Applications to Computational Fluid Dynamics

with Omar M. Knio, Springer Series Scientific Computation, (2010).

This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the stage for subsequent applications. These are demonstrated through detailed treatments of elementary problems, as well as in more elaborate examples involving vortex-dominated flows and compressible flows at low Mach numbers. Some recent developments are also outlined in the book, including iterative techniques (such as stochastic multigrids and Newton schemes), intrusive and non-intrusive formalisms, spectral representations using mixed and discontinuous bases, multi-resolution approximations, and adaptive techniques. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral approximation is helpful but not essential.
ISBN-10: 9048135192 # ISBN-13: 978-9048135196
Order here.

Book chapters

Multiresolution analysis for uncertainty quantification

O. Le Maître and O. Knio, in Handbook of Uncertainty Quantification, R. Ghanem, D. Higdon and H. Owhadi Editors, Springer, (2017).

A fast Poisson solver for OpenCL using Multigrid methods

S. Noury, S. Boivin and O. Le Maître, in GPU Pro2: Advanced Rendering Techniques, W. Engel Editor, (2011).

Journals

Preprints (submitted or in preparation)

[109] O.P. Le Maître, K. Mustapha and O. Knio. A Stochastic Galerkin method for uncertain time-fractional diffusion equations, (in preparation).

[108] J.F. Reis, O.P. Le Maître, P.M. Congedo and P. Mycek. Multipreconditioning Strategies for Solving Stochastic Elliptic Equations with Domain Decomposition Method, (in preparation).

[107] J.F. Reis, O.P. Le Maître, P.M. Congedo and P. Mycek. Stochastic Preconditioners for the Schwarz method, Comptes Rendus de Mathématiques, (in preparation).

[106] N. Leoni, P. Congedo, O. Le Maître and M.-G. Rodio. Bayesian Calibration with Adaptive Model Discrepancy, International Journal for Uncertainty Quantification, (in preparation).

2022

[105] A. del Val and O.P. Le Maître and P.M. Congedo and T.E. Magin. Stochastic calibration of a carbon nitridation model from plasma wind tunnel experiments using a Bayesian formulation, Carbon, 200, pp.199-214, (2022).

[104] G. Gori and O. Le Maître and P.M. Congedo. A confidence-based aerospace design approach robust to structural turbulence closure uncertainty, Computers and Fluids, 246, pp.105614, (2022).

[103] K. Mustapha, O.M. Knio and O.P. Le Maître. A second-order accurate time-scheme with graded meshes for the fractional Fokker-Planck equation, IMA Journal on Numerical Analysis, (2022).

[102] R. Lima, A.J. Conejo, L. Giraldi, O. Le Maître, I. Hoteit and O.M. Knio. Risk-averse stochastic programming vs. adaptive robust optimization: a virtual power plant application, INFORMS Journal on Computing, 12:3, pp.1795–1818, (2022).

[101] G. Gori, P.M. Congedo, O. Le Maître, T. Bellosta and A. Guardone, Modeling in-flight ice accretion under uncertain conditions, Journal of Aircraft, 59:3, pp.799–813,(2022).

[100] A. del Val, O.P. Le Maître, T.E. Magin, O. Chazot and P.M. Congedo. A Surrogate-based Optimal Likelihood Function for the Bayesian Calibration of the Catalytic Properties of Spacecraft Thermal Protection Materials, Applied Mathematical Modeling, 101, pp.791-810, (2022).

[99] S.M. Almohammadi, O.P. Le Maître and O.M. Knio. Computational challenges in sampling and representation of uncertain kinetic systems in large dimensions, Int. J. Uncertainty Quantification, 12:1, pp.1-24, (2022).

[98] M. Hantouche, S.M. Almohammadi, O.P. Le Maître and O.M. Knio. A Tangent Linear Approximation of the Ignition Delay Time. II: Sensitivity to Thermochemical Parameters, Combustion and Flame, 235:11677, (2022).

2021

[97] P. Sochala, A. Gesret and O.P. Le Maître. Polynomial Surrogates for Bayesian traveltime tomography, International Journal on Geomathematics, 12:20, (2021).

[96] J.M. Armengol, O.P. Le Maître and R. Vicquelin. Bayesian calibration of a methane-air global scheme and uncertainty propagation to flame-vortex interactions, Combustion and Flame, 234, 111642 (2021).

[95] G. Gori, O.P. Le Maître and P.M. Congedo. On the Sensitivity of Structural Turbulence Uncertainty Estimates to Time and Space Resolution, Computers and Fluids, 229 , pp.105081, (2021).

[94] H.H. Hal-Zahrani, M. Lucchesi, K. Mustapha, O.P. Le Maître and O.M. Knio. Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation, J. Physics Commu., 5:8, pp.085014, (2021).

[93] J.F. Reis, O.P. Le Maître, P.M. Congedo and P. Mycek. Acceleration of Domain Decomposition Methods for Stochastic Elliptic Equations, Computer Methods in Applied Mechanics and Engineering, 381, pp.113845, (2021).

[92] S.M. Almohammadi, M. Hantouche, O.P. Le Maître and O.M. Knio. A Tangent Linear Approximation of the Ignition Delay Time. I: Sensitivity to Rate Parameters, Combustion and Flame, 230, pp.111426, (2021).

[91] R. Lima, A.J. Conejo, L. Giraldi, O. Le Maître, I. Hoteit and O.M. Knio. Sample average approximation for risk-averse problems: A virtual power plant scheduling application, EURO Journal on Computational Optimization, 9, pp.100005, (2021).

[90] C. Sabater, O.P. Le Maître, P.M. Congedo and S. Görtz. Optimization under Uncertainty of Large Dimensional Problems using Quantile Bayesian Regression, Computer Methods in Applied Mechanics and Engineering, 376, pp.113632, (2021).

[89] I. Hoteit et al. Towards an End-to-End Analysis and Prediction System for Weather, Climate, and Marine Applications in the Red Sea, Bulletin of the American Meteorological Society, 102:1, pp.E99-E122, (2021).

[88] M. Sacher, O. Le Maître, R. Duvigneau, F. Hauville and M. Durand, A Non-Nested Infilling Strategy for Multi-Fidelity based Efficient Global Optimization, Int. J. Uncertainty Quantification, 11:1, pp.1-30, (2021).

2020

[87] M. Jornet, J. Calatayud, O. Le Maître and J.C. Cortés, Variance reduction methods and multilevel Monte Carlo strategy for the density estimation of random second order linear differential equations solutions, J. Uncertainty Quantification, 10:5, pp.467-497, (2020).

[86] W. Boukaram, M. Lucchesi, G. Turkiyyah, O. Le Maître, O. Knio and D. Keyes, Hierarchical Matrix Approximation for Space-Fractional Diffusion Equations, Computer Methods in Applied Mechanics and Engineering, 369, pp.113191, (2020).

[85] G. Gori, M. Zocca, A. Guardone, O.P. Le Maître and P.M. Congedo, Bayesian calibration of thermodynamic models from vapor flow experiments, Computers and Fluids, 205, pp.104505, (2020).

[84] A. Siripatana, O. Le Maitre, O. Knio, C. Dawson and I. Hoteit, Bayesian Inference of Spatially-Varying Manning’s n Coefficients in the Coastal Ocean Using a Generalized Karhunen-Loeve Expansion and Polynomial Chaos, Ocean Dynamics, 70, pp.1103-1127, (2020).

[83] M. Jornet, J. Calatayud, O. Le Maître and J.C. Cortés, Second order linear differential equations with analytic uncertainties: stochastic analysis via the computation of the probability density function, J. Computational and Applied Mathematics, 374, pp.112770, (2020).

[82] P. Sochala, F. De Martin and O. Le Maitre, Model reduction for large-scale simulations of earthquake in uncertain 3D medium, International Journal on Uncertainty Quantification, 10:2, pp.101-127, (2020).

[81] K. Mustapha, K. Furati, O.M. Knio and O.P. Le Maître. A finite difference method for space fractional differential equations with variable diffusivity coefficients, Communications on Applied Mathematics and Computation, 2, pp.671–688, (2020).

[80] M. Botti, D. Di Pietro, O. Le Maitre and P. Sochala, Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods, Computer Methods in Applied Mechanics and Engineering, 263:1, pp. 112736, (2020).

[79] S. Allouch, M. Lucchesi, O.P. Le Maître, K. Mustapha, and O.M. Knio. Particle Simulation of Fractional Diffusion Equations, Computational Particle Mechanics, 7, pp. 491-507, (2020)

2019

[78] A.Siripatana, L.Giraldi, O. Le Maitre, I. Hoteit and O.Knio, Combining Ensemble Kalman Filter with Multiresolution Analysis for Efficient Assimilation into Adaptive Mesh Models, Computational Geosciences, 23:6, pp. 1259-1276, (2019).

[77] P. Sochala and O.P. Le Maître. A level point Polynomial Chaos method for uncertain stiff problems, J. Scientific Computing, 83:3, pp. 1987-2009,(2019).

[76] F. Sanson, O. Le Maître and P.M. Congedo. Uncertainty Propagation in Systems of Solvers, Computer Methods in Applied Mechanics and Engineering, 352, pp. 32-55, (2019).

2018

[75] F. Rizzi, K. Morris, K. Sargsyan, P. Mycek, C. Safta, O. Le Maître, O.M. Knio, B.J. Debusschere. Partial differential equations preconditioner resilient to soft and hard faults, The International Journal of High Performance Computing Application, 32:5, pp. 658-673, (2018).

[74] D. Lucor and O.P. Le Maître. Cardiovascular modeling with adapted parametric inference, ESAIM: Procedings and Survey, 62, pp. 91-107, (2018).

[73] M. Navarro, O.P. Le Maître, I. Hoteit, K. Mandly, D. Georges and O.M. Knio. Surrogate based parameter inference in a debris flow model, Computational Geosciences, 22:6, pp. 1447-1463, (2018).

[72] A. Contreras, P. Mycek, O. Le Maître, F. Rizzi, B. Debusschere and O. Knio. Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations. Part B: Accelerated Monte-Carlo Sampling with Local PC Expansions, SIAM J. Sci. Comp., 40:4, pp. C547-580, (2018).

[71] A. Contreras, P. Mycek, O. Le Maître, F. Rizzi, B. Debusschere and O. Knio. Parallel Domain Decomposition Strategies for Stochastic Elliptic Equations. Part A: Local KL Representations,SIAM J. Sci. Comp., 40:4, pp. C520-546, (2018).

[70] M. Sacher, R. Duvigneau, O. Le Maître, M. Durand, E. Bérrini, F. Hauville and J.A. Astolfi. A classification approach to Efficient Global Optimization in the presence of non-computable domains, Structural and Multidisciplinary Optimization, 58:4, pp. 1537-1557, (2018).

[69] A. Siripatana, T. Mayo, O. Knio, C. Dawson, O. Le Maître and I. Hoteit. Ensemble Kalman filter inference of spatially varying Manning's n coefficient in the coastal ocean, Journal of Hydrology, 562, pp. 664-684, (2018).

[68] L. Giraldi, O.P. Le Maître, I. Hoteit and O.M. Knio. Optimal projection of observations in a Bayesian setting, Computational Statistics and Data Analysis, 124, pp. 252-276, (2018).

[67] M. Sacher, M. Durand, E. Bérrini, F. Hauville, R. Duvigneau, O. Le Maître, J.-A. Astolfi. Flexible hydrofoil optimization for the 35th America's Cup with constrained EGO method, Ocean Engineering, 157, pp. 62-72, (2018).

[66] F. Rizzi, K. Morris, K. Sargsyan, P. Mycek, C. Safta, O. Le Maître, O.M. Knio, B.J. Debusschere. Exploring the Interplay of Resilience and Energy Consumption for a Task-Based Partial Differential Equations Preconditioner, Parallel Computing, 73, pp. 16-27, (2018).

2017

[65] F. Rizzi, K. Morris, K. Sargsyan, P. Mycek, C. Safta, O. Le Maître, O.M. Knio, B.J. Debusschere. Partial differential equations preconditioner resilient to soft and hard faults, Int. Journal of High Performance Computing and Applications, 32:5, pp. 658-673, (2017).

[64] A. Siripatana, T. Mayo, I. Sraj, O. Knio, C. Dawson, O. Le Maître, and I. Hoteit. Assessing an ensemble Kalman filter inference of Manning’s n coefficient of a storm surge model against a polynomial chaos-based MCMC, Ocean Dynamics, 67:8, pp. 1067-1094, (2017).

[63] L. Giraldi, O.P. Le Maître, K.T. Mandli, C.N. Dawson, I. Hoteit and O.M. Knio. Bayesian inference of earthquake parameters from buoy data using a polynomial chaos based surrogate, Computational Geosciences, 21:4, pp. 683-699, (2017).

[62] P. Mycek, A. Contreras, O. Le Maître, K. Sargsyan, F. Rizzi, K. Morris, C. Safta, B. Debusschere and O. Knio. A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs, Computer Physics Communications, 216, pp. 18-34, (2017).

[61] M. Navarro Jimenez, O.P. Le Maître and O.M. Knio. Non-intrusive Polynomial Chaos expansions for sensitivity analysis in stochastic differential Equations, SIAM/ASA J. Uncertainty Quantification, 5:1, pp. 378-402, (2017).

[60] P. Mycek, F. Rizzi, O. Le Maître , K. Sargsyan, K. Morris, C. Safta, B. Debusschere and O. Knio. Discrete a priori bounds for the detection of corrupted PDE solutions in exascale computations, SIAM J. Sci. Comp., 39:1, pp. 1-28, (2017).

[59] M. Sacher, F. Hauville, R. Duvigneau, O. Le Maître, N. Aubin and M. Durand. Efficient Optimization Procedure in Non-Linear Fluid-Structure Interaction Problem: Application to Mainsail Trimming in Upwind Conditions, J. Fluids and Structures, 60, pp. 209-231, (2017).

2016

[58] M. Navarro Jimenez, O.P. Le Maître and O.M. Knio. Global sensitivity analysis in stochastic simulators of uncertain reaction networks, J. Chem. Phys., 145, pp. 244106, (2016).

[57] A. Contreras, O.P. Le Maître, W. Aquino and O.M. Knio. Multi-Model Polynomial Chaos Surrogate Dictionary for Bayesian Inference in Elasticity Problems, Probabilistic Engineering Mechanics, 46, pp. 107-119, (2016).

[56] T. Wang, O.P. Le Maître, I. Hoteit and O.M. Knio. Path planing in uncertain flow using ensemble method, Ocean Dynamics, 66:10, pp. 1231-1251, (2016).

[55] G. Li, M. Iskandarani, M. Le Henaff, J. Winokur, O.P. Le Maître and O. Knio. Quantifying intial and wind forcing uncertainty in the Gulf of Mexico, Computational Geosciences, 20:5, pp. 1133-1153,(2016).

[54] J. Winokur, D. Kim, F. Bisetti, O.P. Le Maître and O. Knio. Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification, Journal of Scientific Computing, 68:2, pp. 596- 623, (2016).

[53] M. Schick, V. Heuveline and O. Le Maître. A Newton-Galerkin Method for Fluid Flow Exhibiting Uncertain Dynamics, SIAM Review, 58:1, pp. 119-140, (2016).

[52] I. Sraj, O.P. Le Maître, I. Hoteit and O. Knio. Coordinates Transformation and Polynomial Chaos for the Bayesian inference of a Gaussian Field with Parametrized Prior Covariance Function, Computer Methods in Applied Mechanics and Engineering, 298, pp. 205-228, (2016).

2015

[51] K. Sargsyan, F. Rizzi, P. Mycek, C. Safta, K. Morris, H. Najm, O. Le Maître, O. Knio, B. Debusschere. Faults Resilient Decomposition Preconditioner for PDEs, SIAM J. Sci. Comp., 37:5, pp. 2317-2345, (2015).

[50] P. Dutta, M.W. Urban, O.P. Le Maître, J.F. Greenleaf and W. Aquino. Simultatneous Identification of Elastic Properties, Thickness, and Diameter of Arteries excited with Ultrasound Radiation Force, Physics in Medecine and Biology, 60:13, pp. 5279, (2015).

[49] O.P. Le Maître, O. Knio and A. Moraes. Variance decomposition in stochastic simulators, J. Chemical Physics, 142, pp. 244115, (2015).

[48] O. Le Maître and O. Knio. PC analysis of stochastic differential equations driven by Wiener noise, Reliability Engineering and System Safety, 135, pp. 107-124 (2015).

2014

[47] L. Tamellini, O. Le Maître and A. Nouy. Model reduction based on Proper Generalized Decomposition for the stochastic steady incompressible Navier-Stokes equations, SIAM J. Sci. Comp., 36:3, pp. 1089-1117, (2014).

[46] M. Schick, O. Le Maitre and V. Heuveline. A Newton Galerkin Method for fluid flow exhibiting uncertain periodic dynamics, SIAM/ASA J. Uncertainty Quantification, 2, pp. 153-173, (2014).

[45] A. Alexanderian, F. Rizzi, M. Rathinam, O. Le Maître and O. Knio. Preconditioned Bayesian Regression for Stochastic Chemical Kinetics, Journal of Scientific Computing, 58:3, pp. 592-626, (2014).

2013

[44] P. Sochala and O. Le Maître. Polyomial Chaos expansion for subsurface flows with uncertain parameters, Advances in Water Resources, 62-A, pp. 139-154, (2013).

2012

[43] L. Mathelin and O. Le Maître. Uncertainty quantification in a chemical system using error estimate-based mesh adaptation, Theo. and Comp. Fluid Dynamics, 28:5, pp. 415-434, (2012).

[42] J. Tryoen, O. Le Maître and A. Ern. Adaptive Anisotropic Spectral Stochastic Methods for Uncertain Scalar Conservation Laws, SIAM J. Sci. Comp., 34:5, pp. 2459-2481, (2012).

[41] M. Salloum, A. Alexanderian, O.P. Le Maître, H. Najm and O. Knio. A simplified CSP analysis of a stiff stochastic ODE system, Computer Methods in Applied Mechanics and Engineering, 217–220, pp. 121-138, (2012).

[40] M. Rousseau, O. Cerdan, A. Ern, O. Le Maître and P. Sochala. Study of overland flow with uncertain infiltration using stochastic tools, Advances in Water Resources, 38, pp. 1-12, (2012).

[39] A. Alenxanderian, O.P. Le Maître, H.N. Najm, M. Iskandarani, O.M. Knio. Multiscale stochastic preconditioners in non-intrusive spectral projection, J. Scientific Computing, 50:7, pp. 306-340, (2012).

[38] L. Mathelin, L. Pastur and O. Le Maître. A compressed-sensing approach for closed-loop optimal control of nonlinear systems, Theo. Comp. Fluid Dyn., 26:1, pp. 319-337, (2012).

2011

[37] Y. Duguet, O. Le Maître and P. Schlatter. Stochastic and deterministic motion of laminar-turbulent interface in a shear flow, Phys. Rev. E, 84, 066315 (2011).

2010

[36] O. Le Maître, L. Mathelin, O. Knio and Y.M. Hussaini. Asynchroneous time integration for polynomial Chaos expansions of uncertain periodic dynamics, Discrete and Continuous Dynamical Systems, 28(1), pp. 199-226, (2010).

[35] V. Daru, P. Le Quéré, M.-C. Duluc and O. Le Maître. A numerical method for the simulation of low Mach number liquid-gaz flows, J. Comp. Phys., 235(2), pp. 491-506, (2010).

[34] J. Tryoen, O. Le Maître, M. Ndjinga and A. Ern. Roe solver with entropy corrector for uncertain hyperbolic systems, J. Comput. and Appl. Math., 235(2), pp. 491-506, (2010).

[33] J. Tryoen, O. Le Maître, M. Ndjinga and A. Ern. Multi-resolution analysis and upwinding for uncertain nonlinear hyperbolic systems, J. Comp. Phys., 228(18), pp. 6485-6511, (2010).

[32] O. Le Maître and L. Mathelin. Equation free model reduction for complex dynamical systems, Int. J. Num. Meth. Fluids, 63(2), pp. 163-184, (2010).

[31] K. Sargsyan, B. Debusschere, H. Najm and O. Le Maître. Spectral representation and reduced order mod- eling of the dynamics of stochatic reaction networks via adaotive data partitioning, J. Sci. Comp., 31(6), pp. 4395-4421, (2010).

2009

[30] H. Najm, B. Debusschere, Y. Marzouk, W. Widmer and O. Le Maître. Uncertainty quantification in chemical systems, Int. J. Num. Meth. Eng., 80(6), pp. 789-814, (2009).

[29] M.-C. Duluc, O. Le Maître, V. Daru and P. Le Quéré. **Numerical study of liquid inclusion oscillations inside a closed 1-D micro-channel filled with gas, Microfluidics and Nanofluidics, 6, pp. 163-177, (2009).**

[28] A. Nouy and O. Le Maître. Generalized Spectral Decomposition for Stochastic Non Linear Problems, J. Comp. Phys., 228(1), pp. 202-235, (2009).

[27] O. Le Maître. A Newton Method for the Resolution of Steady Stochastic Navier-Stokes Equations, J. Comput. \& Fluids, 38(8), pp. 1566-1579, (2009).

[26] L. Mathelin and O. Le Maître. Robust Model Reduction and Control of the Flow Past a Cylinder with Uncertainty, J. Comp. Fluids, 38(6), pp. 1168-1182, (2009).

[25] T. Crestaux, O. Le Maître and J.M. Martinez. Polynomial Chaos Expansion of Sensitivity Analysis, J. Rel. Eng. Syst. Safety, 94(7), pp. 1161-1182, (2009).

2008

[24] M. Snyder, O. Knio, J. Katz and O. Le Maître. Numerical Study on the Motion of Microscopic Oil Droplets in High Intensity Isotropic Turbulence, Physics of Fluids, 29(7), (2008).

2007

[23] L. Mathelin and O. Le Maître. Dual-based aposteriori error estimate for stochastic finite element methods, Comm. Appl. Math. and Comp. Sci., 2(1), pp. 83-115, (2007).

[22] O.P. Le Maître and O.M. Knio. A stochastic particle-mesh scheme for uncertainty propagation in vortical flows, J. Comp. Phys., 226(1), pp. 645-671, (2007).

[21] M. Snyder, O. Knio, J. Katz and O. Le Maître. Statistical analysis of small bubbles dynamics in isotropic turbulence, Physics of Fluids, 19, (2007).

[20] O.P. Le Maître, H.N. Najm, P.P. Pébay, R.G. Ghanem and O.M. Knio. Multi-resolution analysis for uncertainty quantification in chemical systems, SIAM J. Sci. Comp., 29, pp. 864-889, (2007).

[19] O. Cadot and O. Le Maître. The turbulent flow between two rotating stirrers : similitude laws and transitions for the driving torques, European Journal of Mechanics B-Fluids, 26(6), pp. 258-270, (2007).

2006

[18] O.P. Le Maître. Polynomial chaos expansion of a Lagrangian model for the flow around an airfoil, Comptes Rendus de Mécanique, 334(11), pp. 693-698, (2006).

[17] V. Daru, M.C. Duluc, O. Le Maître, D. Juric and P. Le Quéré. Modélisation et simulation numérique du changement de phase liquide-vapeur en cavité, Comptes Rendus de Mécanique, 334, pp. 25-33, (2006).

[16] O. Knio and O. Le Maître. Uncertainty Propagation in CFD Using Polynomial Chaos Decompositions, Fluid Dynamics Research, 38(9), pp. 616-640, (2006).

[15] M. Luersen, R. Le Riche, D. Lemosse and O. Le Maître. A computationally efficient approach to swimming monofin optimization, Structural and Multidisciplinary Optimization, 31(6), pp. 488-496, (2006).

2004

[14] M.T. Reagan, H.N. Najm, B.J. Debusschere, O.P. Le Maître, O.M. Knio, and R.G. Ghanem. Spectral Stochastic Uncertainty Quantification in Chemical Systems, Combustion Theory and Modelling, 8, pp. 607- 632, (2004).

[13] O.P. Le Maître, M.T. Reagan, H.N. Najm, R.G. Ghanem, and O.M. Knio. Natural Convection in a Closed Cavity under Stochastic, Non-Boussinesq Conditions, SIAM J. Sci. Comp., 26(2), pp. 375-394, (2004).

[12] B. Debusschere, H. Najm, P. Pébay, O. Knio, R. Ghanem and O. Le Maître. Numerical Challenges in the use of Polynomial Chaos Representations for Stochastic Processes, SIAM J. Sci. Comp., 26(2), pp. 698-719, (2004).

[11] O.P. Le Maître, H.N. Najm, R.G. Ghanem, and O.M. Knio. Multi-Resolution Analysis of Wiener-Type Uncertainty Propagation Schemes, J. Comp. Phys., 197(2), pp. 502-531, (2004).

[10] O.P. Le Maître, O.M. Knio, H.N. Najm and R.G. Ghanem. Uncertainty Propagation using Wiener-Haar Expansions, J. Comp. Phys., 197(1), pp. 28-57, (2004).

2003

[9] O.P. Le Maître, O.M. Knio, B.J. Debusschere, H.N. Najm, and R.G. Ghanem. A Multigrid solver for two- dimensional stochastic diffusion equations, Comp. Meth. App. Mech. and Eng., 192(41-42), pp. 4723-4744, (2003).

[8] B. Debusschere, H. Najm, A. Matta, O. Knio, R. Ghanem and O. Le Maître. Protein Labeling Reactions in Electrochemical Flow : Numerical Simulation and Uncertainty Propagation, Physics of Fluids, 15(8), pp. 2238-2250, (2003).

[7] O.P. Le Maître, R.H. Scanlan and O.M. Knio. Numerical estimation of the flutter derivatives of a NACA airfoil by means of Navier-Stokes simulation, J. Fluids and Structures, 17(1), pp. 1-28, (2003).

2002

[6] O.P. Le Maître, M.T. Reagan, O.M. Knio, H.N. Najm and R.G. Ghanem. A stochastic projection method for fluid flow. II. Random Process, J. Comp. Phys., 181(1), pp. 9-44, (2002).

2001

[5] O.P. Le Maître, O.M. Knio, H.N. Najm and R.G. Ghanem. A stochastic projection method for fluid flow. I. Basic formulation, J. Comp. Phys., 173(2), pp. 481-511, (2001).

[4] O. Le Maître, J. Levin, M. Iskandarani, and O. Knio. A Multiscale Pressure Splitting of the Shallow Water Equations, I. Formulation and 1D Tests, J. Comp. Phys., 166, pp. 116-151, (2001).

1999

[3] O. Le Maître, S. Huberson and J.E. Souza de Cursi. Unsteady Model of Sail and Flow Interaction, J. Fluids and Structures, 13(1), pp. 37-59, (1999).

1998

[2] O. Le Maître, J.E. Souza de Cursi and S. Huberson. Large displacements analysis for ideally flexible sails, Europ. J. Mechanics (A/Solid), 17(4), pp. 619-636, (1998).

1996

[1] O. Le Maître, S. Huberson and J.E. Souza de Cursi. Application of a non-convex model of fabric deformations to sail cut analysis, J. Wind Eng. and Ind. Appl., 63(1-3), pp. 77-93, (1996).

Olivier Le Maître