Publications

Submitted
T. Bui-Thanh and Ghattas, O., “Bayes is Optimal,” ICES Report, vol. 15, no. 04, Submitted.
T. Bui-Thanh and Lan, S., “Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian Inverse Problems,” Submitted.
T. Bui-Thanh, “FEM-Based Discretization-Invariant MCMC Methods for PDE-constrained Bayesian Inverse Problems,” Submitted.
T. Bui-Thanh, “From Rankine-Hugoniot Condition to a Constructive Derivation of HDG Methods,” Lecture Notes in Computational Science and Engineering, Submitted.
T. Bui-Thanh, “Hybridized Discontinuous Galerkin Methods for Linearized Shallow Water Equations,” Submitted.
T. Bui-Thanh and Myers, A., “A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems,” SIAM Special Edition, Submitted.
2015
T. Bui-Thanh and Wilcox, L., “Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method,” Journal of Scientific Computing, no. 63, pp. 138--162, 2015.
T. Bui-Thanh, “From Godunov to A Unified Hybridized Discontinuous Galerkin Framework,” Journal of Computational Physics, no. 295, pp. 114-146, 2015.
E. Le and Bui-Thanh, T., “A Randomized Misfit Approach for Data Reduction in Large-Scale Inverse Problems,” SIAM CSE Conference. 2015.
T. Bui-Thanh and Ghattas, O., “A Scalable MAP Solver for Bayesian Inverse Problems with Besov Priors, Inverse Problems and Imaging,” Inverse Problems and Imaging, no. 9, pp. 27--53, 2015.
2014
T. Bui-Thanh and Ghattas, O., “A PDE-constrained Optimization Approach to the Discontinuous Petrov-Galerkin Method with a Trust Region Inexact Newton-CG Solver,” Computational Methods Applied Mechanical Engineering, no. 278, pp. 20--40, 2014.
T. Bui-Thanh and Girolami, M., “Solving Large-scale PDE-Constrained Bayesian Inverse Problems With Riemann Manifold Hamiltonian Monte Carlo,” Inverse Problems, Special Issue, no. 114014, pp. 30, 2014.
N. Roberts, Bui-Thanh, T., and Demkowicz, D., The DPG Method for the Stokes Problem, Computers & Mathematics with Applications. 67, 2014, pp. 966–995.
J. Chan, Heuer, N., Bui-Thanh, T., and Demkowicz, D., Robust DPG method for convection-dominated diffusion problems II: a natural in flow condition, Computers & Mathematics with Applications. 67, 2014, pp. 771–795.
T. Bui-Thanh and Ghattas, O., “An Analysis of Infinite Dimensional Bayesian Inverse Shape Acoustic Scattering and its Numerical Approximation,” SIAM Journal on Uncertainty Quantification, no. 2, pp. 203--222, 2014.
2013
T. Bui-Thanh and Ghattas, O., “Analysis of the Hessian for Inverse Scattering Problems Part III: Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions,” Inverse Problems and Imaging, vol. 7, pp. 1139–1155, 2013.
T. Bui-Thanh, Ghattas, O., Martin, J., and Stadler, G., “A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion,” SIAM Journal on Scientific Computing, vol. 35, pp. A2494–A2523, 2013.
T. Bui-Thanh, Demkowicz, L., and Ghattas, O., “Constructively Well-Posed Approximation Methods with Unity Inf-Sup and Continuity Constants for Partial Differential Equations,” Mathematics of Computation, vol. 82, no. 284, pp. 1923–1952, 2013.
T. Bui-Thanh, Demkowicz, L., and Ghattas, O., “A Unified Discontinuous Petrov-Galerkin Method and its Analysis for Friedrichs' Systems,” SIAM Journal on Numerical Analysis, vol. 51, no. 4, pp. 1933–1958, 2013.
2012
T. Bui-Thanh, “A Gentle Tutorial on Statistical Inversion using the Bayesian Paradigm,” ICES Report 12-18, 2012.

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