Edit Profile (opens in new tab) Ghattas, Omar N. Co-Author Distance Author ID: ghattas.omar-n Published as: Ghattas, Omar; Ghattas, O.; Ghattas, Omar N. more...less Documents Indexed: 91 Publications since 1992, including 11 Additional arXiv Preprints 3 Contributions as Editor Co-Authors: 68 Co-Authors with 92 Joint Publications 1,590 Co-Co-Authors all top 5 Co-Authors 0 single-authored 21 Chen, Peng 19 Bui-Thanh, Tan 15 Stadler, Georg 12 O’Leary-Roseberry, Thomas 9 Villa, Umberto E. 8 Petra, Noemi 8 Willcox, Karen E. 7 Wilcox, Lucas C. 7 Wu, Keyi 6 Alger, Nick 6 van Bloemen Waanders, Bart G. 5 Alexanderian, Alen 5 Burstedde, Carsten 5 Cao, Lianghao 4 Biegler, Lorenz T. 4 Biros, George 4 Heinkenschloss, Matthias 4 Keyes, David Elliot 4 Oden, John Tinsley 3 Akcelik, Volkan 3 Bielak, Jacobo 3 Isaac, Tobin 3 Orozco, Carlos E. 2 Bark, Jai-Hyeong 2 Crestel, Benjamin 2 Demkowicz, Leszek F. 2 Hill, Judith C. 2 Lee, Jeonghun J. 2 Li, Xiaogang 2 Luo, Dingcheng 2 Marzouk, Youssef M. 2 Shewchuk, Jonathan Richard 1 Ambartsumyan, Ilona 1 Bao, Hesheng 1 Bashir, O. 1 Bollapragada, Srinivas 1 Boukaram, Wajih-Halim 1 Chaudhuri, Anirban 1 Chen, Joshua 1 Du, Xiaosong 1 Epanomeritakis, I. 1 Fidkowski, Krzysztof J. 1 Flath, H. P. 1 Galbally, D. 1 Gao, Longfei 1 Gloor, Philip J. 1 Haberman, Michael R. 1 Hartland, Tucker 1 Higdon, David M. 1 Hooker, John N. jun. 1 Jaramaz, Branislav 1 Jha, Prashant Kumar 1 Kallivokas, Loukas F. 1 Kim, Kitae 1 Lieberman, Chad 1 Malcevic, Ivan 1 Mallick, Bani K. 1 Martins, Joaquim R. R. A. 1 Moser, Robert D. 1 Myers, Aaron 1 O’Hallaron, David R. 1 Parno, Matthew D. 1 Rao, Vishwas 1 Rudi, Johann 1 Tenorio, Luis 1 Tu, Tiankai 1 Turkiyyah, George M. 1 Wang, Kainan 1 Xu, Jifeng 1 Yang, Shan 1 Zampini, Stefano all top 5 Serials 23 SIAM Journal on Scientific Computing 11 Journal of Computational Physics 9 Computer Methods in Applied Mechanics and Engineering 5 Inverse Problems 4 SIAM/ASA Journal on Uncertainty Quantification 3 International Journal for Numerical Methods in Engineering 2 AIAA Journal 2 Computers & Mathematics with Applications 2 SIAM Journal on Numerical Analysis 2 Journal of Scientific Computing 2 Inverse Problems and Imaging 1 Mathematics of Computation 1 ACM Transactions on Mathematical Software 1 Operations Research 1 Finite Elements in Analysis and Design 1 SIAM Journal on Applied Mathematics 1 International Journal of Computational Fluid Dynamics 1 Vietnam Journal of Mathematics 1 CMES. Computer Modeling in Engineering & Sciences 1 Acta Numerica 1 Lecture Notes in Computational Science and Engineering 1 Computational Science & Engineering 1 International Journal for Uncertainty Quantification 1 Bayesian Analysis all top 5 Fields 60 Numerical analysis (65-XX) 27 Partial differential equations (35-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 23 Statistics (62-XX) 20 Fluid mechanics (76-XX) 11 Operations research, mathematical programming (90-XX) 9 Computer science (68-XX) 7 Geophysics (86-XX) 5 Mechanics of deformable solids (74-XX) 4 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 76 Publications have been cited 2,155 times in 1,243 Documents Cited by ▼ Year ▼ p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees. Zbl 1230.65106 Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar 192 2011 A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. Zbl 1250.65011 Martin, James; Wilcox, Lucas C.; Burstedde, Carsten; Ghattas, Omar 130 2012 A computational framework for infinite-dimensional Bayesian inverse problems. I: The linearized case, with application to global seismic inversion. Zbl 1287.35087 Bui-Thanh, Tan; Ghattas, Omar; Martin, James; Stadler, Georg 121 2013 Model reduction for large-scale systems with high-dimensional parametric input space. Zbl 1196.37127 Bui-Thanh, T.; Willcox, K.; Ghattas, O. 120 2008 A computational framework for infinite-dimensional Bayesian inverse problems. II: stochastic Newton MCMC with application to ice sheet flow inverse problems. Zbl 1303.35110 Petra, Noemi; Martin, James; Stadler, Georg; Ghattas, Omar 85 2014 Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. I: The Krylov-Schur solver. Zbl 1091.65061 Biros, George; Ghattas, Omar 77 2005 A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. Zbl 1427.74071 Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar 77 2010 Parameter and state model reduction for large-scale statistical inverse problems. Zbl 1217.65123 Lieberman, Chad; Willcox, Karen; Ghattas, Omar 75 2010 Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations. Zbl 1229.65174 Flath, H. P.; Wilcox, L. C.; Akçelik, V.; Hill, Judith C.; Van Bloemen Waanders, B.; Ghattas, O. 72 2011 Nonlinear model reduction for uncertainty quantification in large-scale inverse problems. Zbl 1183.76837 Galbally, D.; Fidkowski, K.; Willcox, K.; Ghattas, O. 69 2010 Goal-oriented, model-constrained optimization for reduction of large-scale systems. Zbl 1123.65081 Bui-Thanh, T.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B. 67 2007 A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized \(\ell_0\)-sparsification. Zbl 1314.62163 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 49 2014 A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems. Zbl 06536072 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 47 2016 A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion. Zbl 1142.65052 Epanomeritakis, I.; Akçelik, V.; Ghattas, O.; Bielak, J. 44 2008 Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the antarctic ice sheet. Zbl 1352.86017 Isaac, Tobin; Petra, Noemi; Stadler, Georg; Ghattas, Omar 43 2015 Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations. Zbl 1391.93289 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 39 2017 Parallel Lagrange-Newton–Krylov-Schur methods for PDE-constrained optimization. II: The Lagrange-Newton solver and its application to optimal control of steady viscous flows. Zbl 1091.65062 Biros, George; Ghattas, Omar 38 2005 An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. Zbl 1306.65270 Bui-Thanh, Tan; Ghattas, Omar 37 2014 Optimal control of two-and three-dimensional incompressible Navier-Stokes flows. Zbl 0893.76067 Ghattas, Omar; Bark, Jai-Hyeong 35 1997 Hessian-based model reduction for large-scale systems with initial-condition inputs. Zbl 1195.76311 Bashir, O.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B.; Hill, J. 34 2008 On Bayesian A- and D-optimal experimental designs in infinite dimensions. Zbl 1359.62315 Alexanderian, Alen; Gloor, Philip J.; Ghattas, Omar 33 2016 Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers. Zbl 0961.74056 Bao, Hesheng; Bielak, Jacobo; Ghattas, Omar; Kallivokas, Loukas F.; O’Hallaron, David R.; Shewchuk, Jonathan R.; Xu, Jifeng 31 1998 Analysis of the Hessian for inverse scattering problems. I: Inverse shape scattering of acoustic waves. Zbl 1239.78006 Bui-Thanh, Tan; Ghattas, Omar 31 2012 A unified discontinuous Petrov-Galerkin method and its analysis for Friedrichs systems. Zbl 1278.65173 Bui-Thanh, Tan; Demkowicz, Leszek; Ghattas, Omar 30 2013 Large-scale PDE-constrained optimization. Zbl 1021.00015 28 2003 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 27 2011 hIPPYlib. An extensible software framework for large-scale inverse problems governed by PDEs. I: Deterministic inversion and linearized Bayesian inference. Zbl 07467976 Villa, Umberto; Petra, Noemi; Ghattas, Omar 26 2021 Real-time PDE-constrained optimization. Zbl 1117.49004 24 2007 Recursive algorithms for distributed forests of octrees. Zbl 1323.65105 Isaac, Tobin; Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar 23 2015 Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems. Zbl 1439.65071 Chen, Peng; Villa, Umberto; Ghattas, Omar 23 2017 Large-scale PDE-constrained optimization: an introduction. Zbl 1094.49500 Biegler, Lorenz T.; Ghattas, Omar; Heinkenschloss, Matthias; van Bloemen Waanders, Bart 22 2003 Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems. Zbl 1227.76027 Burstedde, Carsten; Ghattas, Omar; Stadler, Georg; Tu, Tiankai; Wilcox, Lucas C. 21 2009 Analysis of the Hessian for inverse scattering problems. II: Inverse medium scattering of acoustic waves. Zbl 1239.78007 Bui-Thanh, Tan; Ghattas, Omar 21 2012 Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty. Zbl 1451.65076 Chen, Peng; Villa, Umberto; Ghattas, Omar 21 2019 Learning physics-based models from data: perspectives from inverse problems and model reduction. Zbl 1520.65043 Ghattas, Omar; Willcox, Karen 20 2021 Parallel octree-based finite element method for large-scale earthquake ground motion simulation. Zbl 1232.86004 Bielak, J.; Ghattas, O.; Kim, E.-J. 19 2005 Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics. Zbl 1327.65242 Isaac, Tobin; Stadler, Georg; Ghattas, Omar 17 2015 Analysis of an \(hp\)-nonconforming discontinuous Galerkin spectral element method for wave propagation. Zbl 1250.65120 Bui-Thanh, Tan; Ghattas, Omar 16 2012 A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem. Zbl 1370.65064 Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg; Ghattas, Omar 15 2017 Optimal design of truss structures by logic-based branch and cut. Zbl 1163.90827 Bollapragada, S.; Ghattas, O.; Hooker, J. N. 14 2001 Analysis of the Hessian for inverse scattering problems. III: Inverse medium scattering of electromagnetic waves in three dimensions. Zbl 1292.78012 Bui-Thanh, Tan; Ghattas, Omar 14 2013 Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs. Zbl 1507.62299 O’Leary-Roseberry, Thomas; Villa, Umberto; Chen, Peng; Ghattas, Omar 14 2022 Nearly orthogonal two-dimensional grid generation with aspect ratio control. Zbl 0990.65132 Akcelik, Volkan; Jaramaz, Branislav; Ghattas, Omar 13 2001 A randomized maximum a posteriori method for posterior sampling of high dimensional nonlinear Bayesian inverse problems. Zbl 1386.35391 Wang, Kainan; Bui-Thanh, Tan; Ghattas, Omar 13 2018 Optimal design of acoustic metamaterial cloaks under uncertainty. Zbl 07511447 Chen, Peng; Haberman, Michael R.; Ghattas, Omar 13 2021 A variational finite element method for stationary nonlinear fluid-solid interaction. Zbl 0924.76057 Ghattas, Omar; Li, Xiaogang 12 1995 Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method. Zbl 1319.65051 Wilcox, Lucas C.; Stadler, Georg; Bui-Thanh, Tan; Ghattas, Omar 12 2015 Weighted BFBT preconditioner for Stokes flow problems with highly heterogeneous viscosity. Zbl 1392.65039 Rudi, Johann; Stadler, Georg; Ghattas, Omar 11 2017 Hessian-based sampling for high-dimensional model reduction. Zbl 1498.62106 Chen, Peng; Ghattas, Omar 11 2019 Adaptive Hessian-based nonstationary Gaussian process response surface method for probability density approximation with application to Bayesian solution of large-scale inverse problems. Zbl 1257.62035 Bui-Thanh, Tan; Ghattas, Omar; Higdon, David 11 2012 A reduced SAND method for optimal design of nonlinear structures. Zbl 0895.73050 Orozco, Carlos E.; Ghattas, Omar N. 10 1997 A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors. Zbl 1347.49045 Bui-Thanh, Tan; Ghattas, Omar 10 2015 Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters. Zbl 1473.65072 Chen, Peng; Ghattas, Omar 10 2021 A PDE-constrained optimization approach to the discontinuous Petrov-Galerkin method with a trust region inexact Newton-CG solver. Zbl 1425.65151 Bui-Thanh, Tan; Ghattas, Omar 9 2014 Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. Zbl 1453.65289 Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano 8 2020 Tensor train construction from tensor actions, with application to compression of large high order derivative tensors. Zbl 1465.35370 Alger, Nick; Chen, Peng; Ghattas, Omar 8 2020 Constructively well-posed approximation methods with unity inf-sup and continuity constants for partial differential equations. Zbl 1281.65129 Bui-Thanh, Tan; Demkowicz, Leszek; Ghattas, Omar 8 2013 Bayesian inference of heterogeneous epidemic models: application to COVID-19 spread accounting for long-term care facilities. Zbl 1502.62098 Chen, Peng; Wu, Keyi; Ghattas, Omar 7 2021 A shape Hessian-based boundary roughness analysis of Navier-Stokes flow. Zbl 1215.35122 Yang, Shan; Stadler, Georg; Moser, Robert; Ghattas, Omar 6 2011 A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs. Zbl 1412.65197 Crestel, Benjamin; Stadler, Georg; Ghattas, Omar 6 2019 A fast and scalable computational framework for large-scale high-dimensional Bayesian optimal experimental design. Zbl 1514.62153 Wu, Keyi; Chen, Peng; Ghattas, Omar 5 2023 Large-scale Bayesian optimal experimental design with derivative-informed projected neural network. Zbl 1519.35348 Wu, Keyi; O’Leary-Roseberry, Thomas; Chen, Peng; Ghattas, Omar 5 2023 Dynamic-mesh finite element method for Lagrangian computational fluid dynamics. Zbl 1059.76036 Malcevic, Ivan; Ghattas, Omar 4 2002 A data scalable augmented Lagrangian KKT preconditioner for large-scale inverse problems. Zbl 1422.65090 Alger, Nick; Villa, Umberto; Bui-Thanh, Tan; Ghattas, Omar 4 2017 Learning high-dimensional parametric maps via reduced basis adaptive residual networks. Zbl 1507.68273 O’Leary-Roseberry, Thomas; Du, Xiaosong; Chaudhuri, Anirban; Martins, Joaquim R. R. A.; Willcox, Karen; Ghattas, Omar 4 2022 Stein variational reduced basis Bayesian inversion. Zbl 1467.62042 Chen, Peng; Ghattas, Omar 4 2021 Scalable Matrix-free adaptive product-convolution approximation for locally translation-invariant operators. Zbl 1461.41001 Alger, Nick; Rao, Vishwas; Myers, Aaron; Bui-Thanh, Tan; Ghattas, Omar 4 2019 A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers. Zbl 1480.49027 Cao, Lianghao; Ghattas, Omar; Oden, J. Tinsley 4 2022 A compiler for parallel finite element methods with domain-decomposed unstructured meshes. Zbl 0817.65079 Shewchuk, Jonathan Richard; Ghattas, Omar 3 1994 Infeasible path optimal design methods with applications to aerodynamic shape optimization. Zbl 0900.76216 Orozco, Carlos E.; Ghattas, Omar N. 3 1996 Domain decomposition methods for sensitivity analysis of a nonlinear aeroelasticity problem. Zbl 0939.74064 Ghattas, O.; Li, X. 3 1998 Sparse approach to simultaneous analysis and design of geometrically nonlinear structures. Zbl 0761.73078 Orozco, Carlos E.; Ghattas, Omar N. 3 1992 Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm. Zbl 07690209 Luo, Dingcheng; Cao, Lianghao; Chen, Peng; Ghattas, Omar; Oden, J. Tinsley 3 2023 Inexactness issues in the Lagrange-Newton-Krylov-Schur method for PDE-contrained optimization. Zbl 1062.65069 Biros, George; Ghattas, Omar 2 2003 An offline-online decomposition method for efficient linear Bayesian goal-oriented optimal experimental design: application to optimal sensor placement. Zbl 07673279 Wu, Keyi; Chen, Peng; Ghattas, Omar 2 2023 Residual-based error correction for neural operator accelerated Infinite-dimensional Bayesian inverse problems. Zbl 07788122 Cao, Lianghao; O’Leary-Roseberry, Thomas; Jha, Prashant K.; Oden, J. Tinsley; Ghattas, Omar 1 2023 A fast and scalable computational framework for large-scale high-dimensional Bayesian optimal experimental design. Zbl 1514.62153 Wu, Keyi; Chen, Peng; Ghattas, Omar 5 2023 Large-scale Bayesian optimal experimental design with derivative-informed projected neural network. Zbl 1519.35348 Wu, Keyi; O’Leary-Roseberry, Thomas; Chen, Peng; Ghattas, Omar 5 2023 Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm. Zbl 07690209 Luo, Dingcheng; Cao, Lianghao; Chen, Peng; Ghattas, Omar; Oden, J. Tinsley 3 2023 An offline-online decomposition method for efficient linear Bayesian goal-oriented optimal experimental design: application to optimal sensor placement. Zbl 07673279 Wu, Keyi; Chen, Peng; Ghattas, Omar 2 2023 Residual-based error correction for neural operator accelerated Infinite-dimensional Bayesian inverse problems. Zbl 07788122 Cao, Lianghao; O’Leary-Roseberry, Thomas; Jha, Prashant K.; Oden, J. Tinsley; Ghattas, Omar 1 2023 Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs. Zbl 1507.62299 O’Leary-Roseberry, Thomas; Villa, Umberto; Chen, Peng; Ghattas, Omar 14 2022 Learning high-dimensional parametric maps via reduced basis adaptive residual networks. Zbl 1507.68273 O’Leary-Roseberry, Thomas; Du, Xiaosong; Chaudhuri, Anirban; Martins, Joaquim R. R. A.; Willcox, Karen; Ghattas, Omar 4 2022 A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers. Zbl 1480.49027 Cao, Lianghao; Ghattas, Omar; Oden, J. Tinsley 4 2022 hIPPYlib. An extensible software framework for large-scale inverse problems governed by PDEs. I: Deterministic inversion and linearized Bayesian inference. Zbl 07467976 Villa, Umberto; Petra, Noemi; Ghattas, Omar 26 2021 Learning physics-based models from data: perspectives from inverse problems and model reduction. Zbl 1520.65043 Ghattas, Omar; Willcox, Karen 20 2021 Optimal design of acoustic metamaterial cloaks under uncertainty. Zbl 07511447 Chen, Peng; Haberman, Michael R.; Ghattas, Omar 13 2021 Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters. Zbl 1473.65072 Chen, Peng; Ghattas, Omar 10 2021 Bayesian inference of heterogeneous epidemic models: application to COVID-19 spread accounting for long-term care facilities. Zbl 1502.62098 Chen, Peng; Wu, Keyi; Ghattas, Omar 7 2021 Stein variational reduced basis Bayesian inversion. Zbl 1467.62042 Chen, Peng; Ghattas, Omar 4 2021 Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs. Zbl 1453.65289 Ambartsumyan, Ilona; Boukaram, Wajih; Bui-Thanh, Tan; Ghattas, Omar; Keyes, David; Stadler, Georg; Turkiyyah, George; Zampini, Stefano 8 2020 Tensor train construction from tensor actions, with application to compression of large high order derivative tensors. Zbl 1465.35370 Alger, Nick; Chen, Peng; Ghattas, Omar 8 2020 Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty. Zbl 1451.65076 Chen, Peng; Villa, Umberto; Ghattas, Omar 21 2019 Hessian-based sampling for high-dimensional model reduction. Zbl 1498.62106 Chen, Peng; Ghattas, Omar 11 2019 A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs. Zbl 1412.65197 Crestel, Benjamin; Stadler, Georg; Ghattas, Omar 6 2019 Scalable Matrix-free adaptive product-convolution approximation for locally translation-invariant operators. Zbl 1461.41001 Alger, Nick; Rao, Vishwas; Myers, Aaron; Bui-Thanh, Tan; Ghattas, Omar 4 2019 A randomized maximum a posteriori method for posterior sampling of high dimensional nonlinear Bayesian inverse problems. Zbl 1386.35391 Wang, Kainan; Bui-Thanh, Tan; Ghattas, Omar 13 2018 Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations. Zbl 1391.93289 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 39 2017 Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems. Zbl 1439.65071 Chen, Peng; Villa, Umberto; Ghattas, Omar 23 2017 A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem. Zbl 1370.65064 Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg; Ghattas, Omar 15 2017 Weighted BFBT preconditioner for Stokes flow problems with highly heterogeneous viscosity. Zbl 1392.65039 Rudi, Johann; Stadler, Georg; Ghattas, Omar 11 2017 A data scalable augmented Lagrangian KKT preconditioner for large-scale inverse problems. Zbl 1422.65090 Alger, Nick; Villa, Umberto; Bui-Thanh, Tan; Ghattas, Omar 4 2017 A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems. Zbl 06536072 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 47 2016 On Bayesian A- and D-optimal experimental designs in infinite dimensions. Zbl 1359.62315 Alexanderian, Alen; Gloor, Philip J.; Ghattas, Omar 33 2016 Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the antarctic ice sheet. Zbl 1352.86017 Isaac, Tobin; Petra, Noemi; Stadler, Georg; Ghattas, Omar 43 2015 Recursive algorithms for distributed forests of octrees. Zbl 1323.65105 Isaac, Tobin; Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar 23 2015 Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics. Zbl 1327.65242 Isaac, Tobin; Stadler, Georg; Ghattas, Omar 17 2015 Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method. Zbl 1319.65051 Wilcox, Lucas C.; Stadler, Georg; Bui-Thanh, Tan; Ghattas, Omar 12 2015 A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors. Zbl 1347.49045 Bui-Thanh, Tan; Ghattas, Omar 10 2015 A computational framework for infinite-dimensional Bayesian inverse problems. II: stochastic Newton MCMC with application to ice sheet flow inverse problems. Zbl 1303.35110 Petra, Noemi; Martin, James; Stadler, Georg; Ghattas, Omar 85 2014 A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized \(\ell_0\)-sparsification. Zbl 1314.62163 Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar 49 2014 An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. Zbl 1306.65270 Bui-Thanh, Tan; Ghattas, Omar 37 2014 A PDE-constrained optimization approach to the discontinuous Petrov-Galerkin method with a trust region inexact Newton-CG solver. Zbl 1425.65151 Bui-Thanh, Tan; Ghattas, Omar 9 2014 A computational framework for infinite-dimensional Bayesian inverse problems. I: The linearized case, with application to global seismic inversion. Zbl 1287.35087 Bui-Thanh, Tan; Ghattas, Omar; Martin, James; Stadler, Georg 121 2013 A unified discontinuous Petrov-Galerkin method and its analysis for Friedrichs systems. Zbl 1278.65173 Bui-Thanh, Tan; Demkowicz, Leszek; Ghattas, Omar 30 2013 Analysis of the Hessian for inverse scattering problems. III: Inverse medium scattering of electromagnetic waves in three dimensions. Zbl 1292.78012 Bui-Thanh, Tan; Ghattas, Omar 14 2013 Constructively well-posed approximation methods with unity inf-sup and continuity constants for partial differential equations. Zbl 1281.65129 Bui-Thanh, Tan; Demkowicz, Leszek; Ghattas, Omar 8 2013 A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. Zbl 1250.65011 Martin, James; Wilcox, Lucas C.; Burstedde, Carsten; Ghattas, Omar 130 2012 Analysis of the Hessian for inverse scattering problems. I: Inverse shape scattering of acoustic waves. Zbl 1239.78006 Bui-Thanh, Tan; Ghattas, Omar 31 2012 Analysis of the Hessian for inverse scattering problems. II: Inverse medium scattering of acoustic waves. Zbl 1239.78007 Bui-Thanh, Tan; Ghattas, Omar 21 2012 Analysis of an \(hp\)-nonconforming discontinuous Galerkin spectral element method for wave propagation. Zbl 1250.65120 Bui-Thanh, Tan; Ghattas, Omar 16 2012 Adaptive Hessian-based nonstationary Gaussian process response surface method for probability density approximation with application to Bayesian solution of large-scale inverse problems. Zbl 1257.62035 Bui-Thanh, Tan; Ghattas, Omar; Higdon, David 11 2012 p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees. Zbl 1230.65106 Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar 192 2011 Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations. Zbl 1229.65174 Flath, H. P.; Wilcox, L. C.; Akçelik, V.; Hill, Judith C.; Van Bloemen Waanders, B.; Ghattas, O. 72 2011 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 27 2011 A shape Hessian-based boundary roughness analysis of Navier-Stokes flow. Zbl 1215.35122 Yang, Shan; Stadler, Georg; Moser, Robert; Ghattas, Omar 6 2011 A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. Zbl 1427.74071 Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar 77 2010 Parameter and state model reduction for large-scale statistical inverse problems. Zbl 1217.65123 Lieberman, Chad; Willcox, Karen; Ghattas, Omar 75 2010 Nonlinear model reduction for uncertainty quantification in large-scale inverse problems. Zbl 1183.76837 Galbally, D.; Fidkowski, K.; Willcox, K.; Ghattas, O. 69 2010 Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems. Zbl 1227.76027 Burstedde, Carsten; Ghattas, Omar; Stadler, Georg; Tu, Tiankai; Wilcox, Lucas C. 21 2009 Model reduction for large-scale systems with high-dimensional parametric input space. Zbl 1196.37127 Bui-Thanh, T.; Willcox, K.; Ghattas, O. 120 2008 A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion. Zbl 1142.65052 Epanomeritakis, I.; Akçelik, V.; Ghattas, O.; Bielak, J. 44 2008 Hessian-based model reduction for large-scale systems with initial-condition inputs. Zbl 1195.76311 Bashir, O.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B.; Hill, J. 34 2008 Goal-oriented, model-constrained optimization for reduction of large-scale systems. Zbl 1123.65081 Bui-Thanh, T.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B. 67 2007 Real-time PDE-constrained optimization. Zbl 1117.49004 24 2007 Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. I: The Krylov-Schur solver. Zbl 1091.65061 Biros, George; Ghattas, Omar 77 2005 Parallel Lagrange-Newton–Krylov-Schur methods for PDE-constrained optimization. II: The Lagrange-Newton solver and its application to optimal control of steady viscous flows. Zbl 1091.65062 Biros, George; Ghattas, Omar 38 2005 Parallel octree-based finite element method for large-scale earthquake ground motion simulation. Zbl 1232.86004 Bielak, J.; Ghattas, O.; Kim, E.-J. 19 2005 Large-scale PDE-constrained optimization. Zbl 1021.00015 28 2003 Large-scale PDE-constrained optimization: an introduction. Zbl 1094.49500 Biegler, Lorenz T.; Ghattas, Omar; Heinkenschloss, Matthias; van Bloemen Waanders, Bart 22 2003 Inexactness issues in the Lagrange-Newton-Krylov-Schur method for PDE-contrained optimization. Zbl 1062.65069 Biros, George; Ghattas, Omar 2 2003 Dynamic-mesh finite element method for Lagrangian computational fluid dynamics. Zbl 1059.76036 Malcevic, Ivan; Ghattas, Omar 4 2002 Optimal design of truss structures by logic-based branch and cut. Zbl 1163.90827 Bollapragada, S.; Ghattas, O.; Hooker, J. N. 14 2001 Nearly orthogonal two-dimensional grid generation with aspect ratio control. Zbl 0990.65132 Akcelik, Volkan; Jaramaz, Branislav; Ghattas, Omar 13 2001 Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers. Zbl 0961.74056 Bao, Hesheng; Bielak, Jacobo; Ghattas, Omar; Kallivokas, Loukas F.; O’Hallaron, David R.; Shewchuk, Jonathan R.; Xu, Jifeng 31 1998 Domain decomposition methods for sensitivity analysis of a nonlinear aeroelasticity problem. Zbl 0939.74064 Ghattas, O.; Li, X. 3 1998 Optimal control of two-and three-dimensional incompressible Navier-Stokes flows. Zbl 0893.76067 Ghattas, Omar; Bark, Jai-Hyeong 35 1997 A reduced SAND method for optimal design of nonlinear structures. Zbl 0895.73050 Orozco, Carlos E.; Ghattas, Omar N. 10 1997 Infeasible path optimal design methods with applications to aerodynamic shape optimization. Zbl 0900.76216 Orozco, Carlos E.; Ghattas, Omar N. 3 1996 A variational finite element method for stationary nonlinear fluid-solid interaction. Zbl 0924.76057 Ghattas, Omar; Li, Xiaogang 12 1995 A compiler for parallel finite element methods with domain-decomposed unstructured meshes. Zbl 0817.65079 Shewchuk, Jonathan Richard; Ghattas, Omar 3 1994 Sparse approach to simultaneous analysis and design of geometrically nonlinear structures. Zbl 0761.73078 Orozco, Carlos E.; Ghattas, Omar N. 3 1992 all cited Publications top 5 cited Publications all top 5 Cited by 2,297 Authors 41 Ghattas, Omar N. 24 Bui-Thanh, Tan 23 Chen, Peng 22 Marzouk, Youssef M. 21 Willcox, Karen E. 19 Stadler, Georg 18 Cui, Tiangang 16 Carlberg, Kevin T. 16 Gibou, Frédéric 15 Kronbichler, Martin 14 Alexanderian, Alen 13 Demkowicz, Leszek F. 13 Farhat, Charbel H. 11 Chan, Jesse 11 Petra, Noemi 11 Saibaba, Arvind Krishna 10 Badia, Santiago 10 Bangerth, Wolfgang 10 Biros, George 10 Gugercin, Serkan 10 Heister, Timo 10 Heltai, Luca 10 Maier, Matthias Sebastian 10 Peherstorfer, Benjamin 10 Quarteroni, Alfio M. 10 Ruthotto, Lars 10 Villa, Umberto E. 9 Burstedde, Carsten 9 Choi, Youngsoo 9 Choo, Jinhyun 9 Girolami, Mark A. 9 Mang, Andreas 9 Navon, Ionel Michael 9 Pelteret, Jean-Paul 9 Stuart, Andrew M. 9 Turcksin, Bruno 8 Arndt, Daniel 8 Kallivokas, Loukas F. 8 Martín, Alberto F. 8 Mazzieri, Ilario 8 Rozza, Gianluigi 8 San, Omer 8 Schwab, Christoph 8 Sundar, Hari 7 Aquino, Wilkins 7 Barone, Matthew F. 7 Borggaard, Jeff T. 7 Capistrán, Marcos A. 7 Dede’, Luca 7 Gassner, Gregor J. 7 Haber, Eldad 7 Helin, Tapio 7 Keith, Brendan 7 Lee, Sanghyun 7 Manzoni, Andrea 7 Perego, Mauro 7 Petrov, Igor’ Borisovich 7 Rüde, Ulrich 7 Wheeler, Mary Fanett 7 Wohlmuth, Barbara I. 7 Zampini, Stefano 6 Bardsley, Johnathan M. 6 Davydov, Denis 6 De los Reyes, Juan Carlos 6 Ganapathysubramanian, Baskar 6 Hintermüller, Michael 6 Isaac, Tobin 6 Kaipio, Jari P. 6 Kalashnikova, Irina 6 Kouri, Drew P. 6 Li, Jinglai 6 Nguyen, Ngoc Cuong 6 Shen, Chunyu 6 Zhou, Tao 5 Afkham, Babak Maboudi 5 Amsallem, David 5 Anitescu, Mihai 5 Antonietti, Paola Francesca 5 Benner, Peter 5 Bielak, Jacobo 5 Bonnet, Marc 5 Bordas, Stéphane Pierre Alain 5 Cai, Xiao-Chuan 5 Christen, J. Andrés 5 Chung, Tsz Shun Eric 5 Erceg, Marko 5 Fang, Fangxin 5 Fehling, Marc 5 Fernando, Milinda 5 Fung, Samy Wu 5 Gauger, Nicolas R. 5 Gholami, Amir 5 Givoli, Dan 5 Hagstrom, Thomas M. 5 Hansen, Per Christian 5 Hesthaven, Jan S. 5 Hyvönen, Nuutti 5 Iliescu, Traian 5 Jiang, Lijian 5 Keyes, David Elliot ...and 2,197 more Authors all top 5 Cited in 181 Serials 194 Journal of Computational Physics 167 Computer Methods in Applied Mechanics and Engineering 133 SIAM Journal on Scientific Computing 49 Inverse Problems 49 SIAM/ASA Journal on Uncertainty Quantification 40 International Journal for Numerical Methods in Engineering 36 Journal of Scientific Computing 31 Computers & Mathematics with Applications 20 Journal of Computational and Applied Mathematics 19 Computers and Fluids 16 Advances in Computational Mathematics 15 Computational Geosciences 13 Computational Mechanics 13 Inverse Problems and Imaging 12 Applied Mathematics and Computation 12 Inverse Problems in Science and Engineering 10 International Journal for Numerical Methods in Fluids 10 Optimization and Engineering 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Statistics and Computing 8 Numerische Mathematik 8 Applied Mathematical Modelling 8 SIAM Journal on Optimization 8 Journal of Numerical Mathematics 8 Communications in Computational Physics 7 Computer Physics Communications 7 Applied Numerical Mathematics 7 SIAM Journal on Imaging Sciences 6 Journal of Mathematical Imaging and Vision 6 Computational Optimization and Applications 6 Archives of Computational Methods in Engineering 6 GEM - International Journal on Geomathematics 5 Journal of Mathematical Analysis and Applications 5 International Journal of Computer Mathematics 5 International Journal of Computational Fluid Dynamics 4 Mathematics of Computation 4 Journal of Optimization Theory and Applications 4 SIAM Journal on Numerical Analysis 4 SIAM Review 4 Engineering Analysis with Boundary Elements 4 Mathematical Problems in Engineering 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Nonlinear Analysis. Real World Applications 4 Computational Methods in Applied Mathematics 4 Multiscale Modeling & Simulation 4 Acta Numerica 3 Applicable Analysis 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 ACM Transactions on Mathematical Software 3 Applied Mathematics and Optimization 3 Calcolo 3 Mathematics and Computers in Simulation 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 SIAM Journal on Control and Optimization 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Matrix Analysis and Applications 3 Computational Statistics 3 SIAM Journal on Applied Mathematics 3 Mathematical Programming. Series A. Series B 3 ETNA. Electronic Transactions on Numerical Analysis 3 Computing and Visualization in Science 3 Vietnam Journal of Mathematics 3 Optimization Methods & Software 3 Foundations of Computational Mathematics 3 Journal of Machine Learning Research (JMLR) 3 Structural and Multidisciplinary Optimization 3 Journal of Theoretical Biology 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Communications on Applied Mathematics and Computation 3 Electronic Research Archive 3 Foundations of Data Science 3 SIAM Journal on Mathematics of Data Science 2 Journal of Mathematical Biology 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Scandinavian Journal of Statistics 2 Wave Motion 2 Statistical Science 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Computational Mathematics and Mathematical Physics 2 Computational and Applied Mathematics 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Lobachevskii Journal of Mathematics 2 Communications on Pure and Applied Analysis 2 SIAM Journal on Applied Dynamical Systems 2 GAMM-Mitteilungen 2 The Annals of Applied Statistics 2 Advances in Mathematical Physics 2 SMAI Journal of Computational Mathematics 1 Acta Mechanica 1 Classical and Quantum Gravity 1 International Journal of Heat and Mass Transfer 1 Journal of the Franklin Institute 1 Moscow University Mathematics Bulletin 1 Physica A 1 Transport Theory and Statistical Physics 1 The Annals of Statistics ...and 81 more Serials all top 5 Cited in 39 Fields 876 Numerical analysis (65-XX) 344 Partial differential equations (35-XX) 319 Fluid mechanics (76-XX) 253 Statistics (62-XX) 196 Mechanics of deformable solids (74-XX) 153 Calculus of variations and optimal control; optimization (49-XX) 96 Computer science (68-XX) 92 Geophysics (86-XX) 87 Operations research, mathematical programming (90-XX) 79 Probability theory and stochastic processes (60-XX) 68 Systems theory; control (93-XX) 49 Biology and other natural sciences (92-XX) 44 Optics, electromagnetic theory (78-XX) 32 Information and communication theory, circuits (94-XX) 20 Dynamical systems and ergodic theory (37-XX) 20 Statistical mechanics, structure of matter (82-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 17 Operator theory (47-XX) 16 Approximations and expansions (41-XX) 16 Classical thermodynamics, heat transfer (80-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Functional analysis (46-XX) 8 Mechanics of particles and systems (70-XX) 7 Ordinary differential equations (34-XX) 6 Quantum theory (81-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Astronomy and astrophysics (85-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Integral equations (45-XX) 2 Measure and integration (28-XX) 2 Relativity and gravitational theory (83-XX) 2 Mathematics education (97-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year