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notre dame
stanford

Thesis

  • M. J. Zahr, Adaptive Model Reduction to Accelerate Optimization Problems Governed by Partial Differential Equations. PhD thesis, Stanford University, August 2016. [ bib | thesis ]

Book chapters

  • A. Shi, P.-O. Persson, and M. J. Zahr, “High-order implicit shock tracking (HOIST),” in Mesh Generation and Adaptation: Cutting-Edge Techniques (R. Sevilla, S. Perotto, and K. Morgan, eds.), pp. 233--259, Springer International Publishing, 2022. [ bib | DOI | link ]

  • M. J. Zahr and P.-O. Persson, “Energetically optimal flapping wing motions via adjoint-based optimization and high-order discretizations,” in Frontiers in PDE-Constrained Optimization, Springer, 2018. [ bib | paper ]

Journal papers

  • J. Vandergrift and M. J. Zahr, “Preconditioned iterative solvers for constrained high-order implicit shock tracking methods,” Journal of Computational Physics, vol. 514, p. 113234, October 2024. [ bib | arxiv ]

  • J. M. Kaufmann and M. J. Zahr, “Symmetric, optimization-based, cross-element compatible nodal distributions for high-order finite elements,” Communications in Applied Mathematics and Computational Science, in review 2024. [ bib | arxiv ]

  • T. Wen and M. J. Zahr, “An inexact augmented Lagrangian trust-region method to accelerate optimization problems with PDE constraints,” International Journal for Numerical Methods in Fluids, in review 2024. [ bib | arxiv ]

  • H. Gao and M. J. Zahr, “Adaptive model reduction with local enrichment: empirical quadrature, error estimation, adaptivity,” International Journal of Computational Fluid Dynamics, vol. 37, pp. 451--473, March 2024. [ bib | arxiv ]

  • C. J. Naudet and M. J. Zahr, “A space-time high-order implicit shock tracking method for shock-dominated unsteady flows,” Journal of Computational Physics, vol. 501, p. 112792, March 2024. [ bib | arxiv ]

  • T. Huang, C. J. Naudet, and M. J. Zahr, “High-order implicit shock tracking boundary conditions for flows with parametrized shocks,” Journal of Computational Physics, vol. 495, p. 112517, December 2023. [ bib | arxiv ]

  • M. Mirhoseini and M. J. Zahr, “Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature,” International Journal for Numerical Methods in Fluids, vol. 96, pp. 102--124, September 2023. [ bib | arxiv ]

  • V. Zucatti and M. J. Zahr, “An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots,” International Journal for Numerical Methods in Fluids, vol. 96, pp. 189--208, September 2023. [ bib | arxiv ]

  • T. Wen and M. J. Zahr, “A globally convergent method to accelerate large-scale optimization using on-the-fly model hyperreduction: Application to shape optimization,” Journal of Computational Physics, vol. 484, p. 112082, July 2023. [ bib | arxiv ]

  • M. Mirhoseini and M. J. Zahr, “Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking,” Journal of Computational Physics, vol. 473, p. 111739, January 2023. [ bib | DOI | link | arxiv ]

  • H. Gao, M. J. Zahr, and J.-X. Wang, “Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems,” Computer Methods in Applied Mechanics and Engineering, vol. 390, p. 114502, February 2022. [ bib | arxiv ]

  • C. J. Naudet, J. Töger, and M. J. Zahr, “Accurate quantification of blood flow wall shear stress using simulation-based imaging: a synthetic, comparative study,” Engineering with Computers, pp. 1--17, August 2022. [ bib | DOI | arxiv ]

  • T. Huang and M. J. Zahr, “A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows,” Journal of Computational Physics, vol. 454, p. 110981, April 2022. [ bib | DOI | arxiv ]

  • A. Shi, P.-O. Persson, and M. J. Zahr, “Implicit shock tracking for unsteady flows by the method of lines,” Journal of Computational Physics, vol. 454, p. 110906, April 2022. [ bib | arxiv ]

  • A. Schein, K. T. Carlberg, and M. J. Zahr, “Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection,” International Journal for Numerical Methods in Engineering, vol. 122, no. 14, pp. 3368--3399, 2021. [ bib | arxiv ]

  • M. Yano, T. Huang, and M. J. Zahr, “A globally convergent method to accelerate topology optimization using on-the-fly model reduction,” Computer Methods in Applied Mechanics and Engineering, vol. 375, p. 113635, 2021. [ bib | DOI | link | arxiv ]

  • M. J. Zahr and J. M. Powers, “High-order resolution of multidimensional compressible reactive flow using implicit shock tracking,” AIAA Journal, vol. 59, no. 1, pp. 150--164, 2021. [ bib | DOI | link ]

  • J. Töger, M. J. Zahr, N. Aristokleous, K. Markenroth Bloch, M. Carlsson, and P.-O. Persson, “Blood flow imaging by optimal matching of computational fluid dynamics to 4D flow data,” Magnetic Resonance in Medicine, vol. 84, no. 4, pp. 2231--2245, 2020. [ bib | DOI | link ]

  • H. Gao, J.-X. Wang, and M. J. Zahr, “Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning,” Physica D: Nonlinear Phenomena, vol. 412, p. 132614, 2020. [ bib | DOI | link | arxiv ]

  • D. Z. Huang, W. Pazner, P.-O. Persson, and M. J. Zahr, “High-order partitioned spectral deferred correction solvers for multiphysics problems,” Journal of Computational Physics, vol. 412, p. 109441, 2020. [ bib | DOI | link | arxiv ]

  • M. J. Zahr, A. Shi, and P.-O. Persson, “Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method,” Journal of Computational Physics, vol. 410, p. 109385, 2020. [ bib | DOI | link | arxiv ]

  • M. J. Zahr, K. Carlberg, and D. P. Kouri, “An efficient, globally convergent method for optimization under uncertainty using adaptive model reduction and sparse grids,” SIAM/ASA Journal on Uncertainty Quantification, vol. 7, no. 3, pp. 877--912, 2019. [ bib | DOI | link | arxiv ]

  • M. J. Zahr and P.-O. Persson, “An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions,” Journal of Computational Physics, vol. 365, pp. 105 -- 134, 2018. [ bib | DOI | link | arxiv | paper ]

  • D. Z. Huang, P.-O. Persson, and M. J. Zahr, “High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit-explicit Runge-Kutta schemes,” Computer Methods in Applied Mechanics and Engineering, vol. 346, pp. 674 -- 706, 2018. [ bib | DOI | link | arxiv ]

  • M. J. Zahr, P. Avery, and C. Farhat, “A multilevel projection-based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics,” International Journal for Numerical Methods in Engineering, vol. 112, no. 8, pp. 855--881, 2017. [ bib | DOI | link ]

  • M. J. Zahr, P.-O. Persson, and J. Wilkening, “A fully discrete adjoint method for optimization of flow problems on deforming domains with time-periodicity constraints,” Computers & Fluids, vol. 139, pp. 130 -- 147, 2016. [ bib | DOI | arxiv | link ]

  • M. J. Zahr and P.-O. Persson, “An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems,” Journal of Computational Physics, vol. 326, pp. 516 -- 543, 2016. [ bib | DOI | arxiv | link ]

  • D. Amsallem, M. J. Zahr, and K. Washabaugh, “Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction,” Advances in Computational Mathematics, pp. 1--44, 2015. [ bib | DOI | link ]

  • M. J. Zahr and C. Farhat, “Progressive construction of a parametric reduced-order model for PDE-constrained optimization,” International Journal for Numerical Methods in Engineering, vol. 102, no. 5, pp. 1111--1135, 2015. [ bib | DOI | arxiv | link ]

  • D. Amsallem, M. J. Zahr, Y. Choi, and C. Farhat, “Design optimization using hyper-reduced-order models,” Structural and Multidisciplinary Optimization, pp. 1--22, 2014. [ bib | DOI | link ]

  • D. Amsallem, M. J. Zahr, and C. Farhat, “Nonlinear model order reduction based on local reduced-order bases,” International Journal for Numerical Methods in Engineering, vol. 92, no. 10, pp. 891--916, 2012. [ bib | DOI | link ]

Conference papers

  • T. Huang, M. J. Zahr, K. R. Holst, A. Baker, J. Freels, P. Batten, N. Bachchan, J. B. Maeng, T. C. Fisher, J. Park, S. Jee, and W. J. White, “High-Fidelity CFD Verification Workshop 2024 Summary: Shock-Dominated Flows,” in AIAA Aviation Forum and Exposition (Aviation 2024), (Las Vegas, Nevada), American Institute of Aeronautics and Astronautics, AIAA Paper 2024-3695, 7/29/2024 -- 8/2/2024. [ bib | link ]

  • C. J. Naudet, B. Taylor, and M. J. Zahr, “High-order implicit shock tracking for finite-source spherical blast waves,” in AIAA Aviation Forum and Exposition (Aviation 2023), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2023-3863, 6/12/2023 -- 6/16/2023. [ bib | link ]

  • T. Wen and M. J. Zahr, “An augmented Lagrangian trust-region method to accelerate equality-constrained shape optimization problems using model hyperreduction,” in AIAA Science and Technology Forum and Exposition (SciTech2023), (National Harbor, Maryland), American Institute of Aeronautics and Astronautics, AIAA Paper 2023-1423, 1/23/2023 -- 1/27/2023. [ bib | link ]

  • K. Holst, C. Kim, and M. J. Zahr, “High-Fidelity CFD Verification Workshop 2024: Shock-Dominated Flows,” in AIAA Science and Technology Forum and Exposition (SciTech2023), (National Harbor, Maryland), American Institute of Aeronautics and Astronautics, AIAA Paper 2023-1242, 1/23/2023 -- 1/27/2023. [ bib | link ]

  • T. Huang and M. J. Zahr, “High-order implicit shock tracking boundary conditions for supersonic flow over a smoothed rectangle,” in AIAA Science and Technology Forum and Exposition (SciTech2023), (National Harbor, Maryland), American Institute of Aeronautics and Astronautics, AIAA Paper 2023-1977, 1/23/2023 -- 1/27/2023. [ bib | link ]

  • O. Rasheed, T. Huang, and M. J. Zahr, “High-order implicit shock tracking for a supersonic biplane airfoil,” in AIAA Aviation Forum and Exposition (Aviation 2022), (Chicago, Illinois), American Institute of Aeronautics and Astronautics, AIAA Paper 2022-4082, 6/27/2022 -- 7/1/2022. [ bib ]

  • T. Huang and M. J. Zahr, “High-order implicit shock tracking with targeted mesh optimization and PDE-based smoothing,” in AIAA Aviation Forum and Exposition (Aviation 2021), (Washington, D.C.), American Institute of Aeronautics and Astronautics, AIAA Paper 2021-2710, 6/7/2021 -- 6/11/2021. [ bib | link ]

  • M. J. Zahr and P.-O. Persson, “An r-adaptive, high-order discontinuous Galerkin method for flows with attached shocks,” in AIAA Science and Technology Forum and Exposition (SciTech2020), (Orlando, Florida), American Institute of Aeronautics and Astronautics, AIAA Paper 2020-0537, 1/6/2020 -- 1/10/2020. [ bib | link ]

  • A. Shi, P.-O. Persson, and M. J. Zahr, “An optimization-based discontinuous Galerkin approach for high-order accurate shock tracking with guaranteed mesh quality,” in AIAA Science and Technology Forum and Exposition (SciTech2019), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2019-1151, 1/7/2019 -- 1/11/2019. [ bib | paper | link ]

  • M. Franco, P.-O. Persson, W. Pazner, and M. J. Zahr, “An adjoint method using fully implicit Runge-Kutta schemes for optimization of flow problems,” in AIAA Science and Technology Forum and Exposition (SciTech2019), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2019-0351, 1/7/2019 -- 1/11/2019. [ bib | paper | link ]

  • D. Z. Huang, P.-O. Persson, and M. J. Zahr, “A high-order partitioned solver for general multiphysics problems and its applications in optimization,” in AIAA Science and Technology Forum and Exposition (SciTech2019), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2019-1697, 1/7/2019 -- 1/11/2019. [ bib | paper | link ]

  • M. J. Zahr and P.-O. Persson, “An optimization-based discontinuous Galerkin approach for high-order accurate shock tracking,” in AIAA Science and Technology Forum and Exposition (SciTech2018), (Kissimmee, Florida), American Institute of Aeronautics and Astronautics, AIAA Paper 2018-0063, 1/8/2018 -- 1/12/2018. [ bib | paper | link ]

  • J. Wang, M. J. Zahr, and P.-O. Persson, “Energetically optimal flapping flight based on a fully discrete adjoint method with explicit treatment of flapping frequency,” in 23rd AIAA Computational Fluid Dynamics Conference, (Denver, Colorado), American Institute of Aeronautics and Astronautics, AIAA Paper 2017-4412, 6/5/2017 -- 6/9/2017. [ bib | paper | link ]

  • K. Washabaugh, M. J. Zahr, and C. Farhat, “On the use of discrete nonlinear reduced-order models for the prediction of steady-state flows past parametrically deformed complex geometries,” in AIAA Science and Technology Forum and Exposition (SciTech 2016), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2016-1814, 1/4/2016 -- 1/8/2016. [ bib | link ]

  • D. De Santis, M. J. Zahr, and C. Farhat, “Gradient-based aerodynamic shape optimization using the FIVER embedded boundary method,” in AIAA Science and Technology Forum and Exposition (SciTech 2016), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2016-0807, 1/4/2016 -- 1/8/2016. [ bib | paper | link ]

  • M. J. Zahr and P.-O. Persson, “High-order, time-dependent aerodynamic optimization using a discontinuous Galerkin discretization of the Navier-Stokes equations,” in AIAA Science and Technology Forum and Exposition (SciTech 2016), (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2016-0064, 1/4/2016 -- 1/8/2016. [ bib | paper | link ]

  • M. J. Zahr and P.-O. Persson, “Performance tuning of Newton-GMRES methods for discontinuous Galerkin discretizations of the Navier-Stokes equations,” in 21st AIAA Computational Fluid Dynamics Conference, (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2013-2685, 6/24/2013 -- 6/27/2013. [ bib | paper | link ]

  • M. J. Zahr, D. Amsallem, and C. Farhat, “Construction of parametrically-robust CFD-based reduced-order models for PDE-constrained optimization,” in 21st AIAA Computational Fluid Dynamics Conference, (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2013-2685, 6/24/2013 -- 6/27/2013. [ bib | paper | link ]

  • K. Washabaugh, D. Amsallem, M. J. Zahr, and C. Farhat, “Nonlinear model reduction for CFD problems using local reduced-order bases,” in 42nd AIAA Fluid Dynamics Conference and Exhibit, Fluid Dynamics and Co-located Conferences, (New Orleans, Louisiana), American Institute of Aeronautics and Astronautics, AIAA Paper 2012-2686, 6/25/2012 -- 6/28/2012. [ bib | paper | link ]

  • K. Carlberg, J. Cortial, D. Amsallem, M. J. Zahr, and C. Farhat, “The GNAT nonlinear model reduction method and its application to fluid dynamics problems,” in 6th AIAA Theoretical Fluid Mechanics Conference, (Honolulu, Hawaii), American Institute of Aeronautics and Astronautics, AIAA Paper 2011-3112, 6/27/2011 -- 6/30/2011. [ bib | link ]

  • D. Amsallem, M. J. Zahr, and C. Farhat, “On the robustness of residual minimization for constructing POD-based reduced-order CFD models,” in 43rd AIAA Fluid Dynamics Conference and Exhibit, (San Diego, California), American Institute of Aeronautics and Astronautics, AIAA Paper 2013-2447, 6/27/2011 -- 6/30/2011. [ bib | paper | link ]

Technical reports

  • M. J. Zahr and S. Govindjee, “Theoretical and numerical foundations for the use of microcolumns as angular motion sensors,” tech. rep., University of California, Berkeley, 2011. [ bib | paper ]

  • M. J. Zahr, K. Carlberg, D. Amsallem, and C. Farhat, “Comparison of model reduction techniques on high-fidelity linear and nonlinear electrical, mechanical, and biological systems,” tech. rep., University of California, Berkeley, 2010. [ bib | paper ]

  • M. J. Zahr, N. Luco, and H. Ryu, “Mitigation of seismic risk pertaining to non-ductile reinforced concrete buildings using seismic risk maps,” tech. rep., United States Geologic Survey (USGS), 2009. [ bib | paper ]