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T. Schorlepp, S. Tong, T. Grafke and G. Stadler, Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems, [arXiv:2303.11919]
T. Hartland, G. Stadler, M. Perego, K. Liegeois and N. Petra, Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initializaiton, [arXiv:2301.03644]
L. Holbach, M. Gurnis and G. Stadler, A Bayesian Level Set Method for Identifying SubsurfaceGeometries and Rheological Properties in Stokes Flow, [eartharXiv:4925]
H. Dinh, D. Giannakis, J. Slawinska, G. Stadler: Phase-field Models of Floe Fracture in Sea Ice, 2022, [ EGUsphere ]
M. Dunlop and G. Stadler, A gradient-free subspace-adjusting ensemble sampler for infinite-dimensional Bayesian inverse problems, 2022, [ arXiv:2202.11088 ]
S. Tong, G. Stadler, Large deviation theory-based adaptive importance sampling for rare events in high dimensions, SIAM/ASA Journal on Uncertainty Quantification, to appear, 2023 [ arXiv:2209.06278 ]
Y. Shih, C. Mehlmann, M. Losch, G. Stadler, Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models, Journal of Computational Physics, to appear [arXiv:2204.10822]
S. Tong, E. Vanden-Eijnden, G. Stadler, Estimating earthquake-induced tsunami height probabilities without sampling, Pure and Applied Geophysics, to appear, 2023 [arXiv:2111.14325]
A. Giuliani, F. Wechsung, A. Cerfon, M. Landreman, G. Stadler, Direct stellarator coil optimization for nested magnetic surfaces with precise quasisymmetry, Physics of Plasmas, 30, 042511, 2023, [ arXiv:2210.03248 ]
F. Wechsung, M. Landreman, A. Giuliani, A. Cerfon and G. Stadler, Precise stellarator quasi-symmetry can be achieved with electromagnetic coils, Proceedings of the National Academy of Sciences, 119(3), 2022, [ PNAS ]
Y. Shih, G. Stadler and F. Wechsung, Robust multigrid techniques for augmented Lagrangian preconditioning of incompressible Stokes equations with extreme viscosity variations, SIAM Journal on Scientific Computing, 2022, [arXiv:2107.00820 | SISC ]
A. Giuliani, F. Wechsung, M. Landreman, G. Stadler, A. Cerfon, Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasi-symmetry, Journal of Plasma Physics, 88(4), 905880401, 2022 [ arXiv:2202.11088 | JPP ]
J. Rudi, M. Gurnis and G. Stadler, Simultaneous inference of plate boundary stresses and mantle rheology using adjoints: Large-scale two-dimensional models, Geophysical Journal International, 231 (1), pp 597-614, 2022 [eartharXiv:10.31223 | GJI ]
F. Wechsung, A. Giuliani, M. Landreman, A. Cerfon, G. Stadler, Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design, Plasma Physics and Controlled Fusion, to appear [ arXiv:2203.10164 | PPCF ].
A. Giuliani, F. Wechsung, A. Cerfon, G. Stadler, M. Landreman, Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry, Journal of Computational Physics 459, 2022, [arXiv:2010:02033|JCP]
S. Mukerjee, T. Yang, G. Stadler and S. Gonzalez-Bailon, What Counts as a Weak Tie? A Comparison of Filtering Techniques to Analyze Co-Exposure to News, Social Networks, 68, 386-393, 2022 [ SSRN | SN ]
J. Hu, M. Gurnis, J. Rudi, G. Stadler, R. D. Müller, Dynamics of the abrupt change in Pacific Plate motion around 50 Ma, Nature Geoscience 15, 75-78, 2022 [NatureGeo].
Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization, De Gruyter, Edited by R. Herzog, M. Heinkenschloss, D. Kalise, G. Stadler and E. Trelat, 2022. [ DeGruyter]
S. Tong, E. Vanden-Eijnden, G. Stadler, Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis, Communications in Applied Mathematics and Computational Science, 16(2), pp 181-225, 2021, [ arXiv:2007:13930, CAMCOS]
A. Alexanderian, N. Petra, G. Stadler, I. Sunseri, Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you dont know, SIAM/ASA Journal on Uncertainty Quantification 9(1), 163-184, 2021 [ arXiv:2006.11939 | SIUQ ]
J. Rudi, Y. Shih and G. Stadler, Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies, Geochemistry, Geophysics Geosystems, 21(9), 2020, [ arXiv:2003.11115 | Gcubed link ]
I. Ambartsumyan, W. Boukaram, T. Bui-Thanh, O. Ghattas, D. Keyes, G. Stadler, G. Turkiyyah and S. Zampini, Hierarchical matrix approximations of Hessians arising in inverse problems governed by PDEs, SIAM Journal on Scientific Computing 42(5), A3397-A3426, 2020. [ arXiv:2003.10173 | SISC link ]
L. Lu, M. Morse, A. Rahimian, G. Stadler and D. Zorin, Scalable Simulation of Realistic Volume Fraction Red Blood Cell Flows through Vascular Networks, in ACM/IEEE Supercomputing SC19, 2019. [ arXiv:1909.11085 | SC link]
C. Li and G. Stadler, Sparse solutions in optimal control of PDEs with uncertain parameters: the linear case, SIAM Journal on Control and Optimization 57(1), pp. 633-658, 2019. [arXiv:1804.05678 | Sicon link]
L. Mertz, G. Stadler, J. Wylie, A Feynman-Kac formula approach for computing expectations and threshold crossing probabilities of non-smooth stochastic dynamical systems, Physica D: Nonlinear Phenomena, 397, pp 25-38, 2019. [arXiv:1704.02170 | link]
B. Crestel, G. Stadler and O. Ghattas, A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs, Inverse Problems 35(2) 2018. [arXiv:1808.05441 | link]
B. Crestel, A. Alexanderian, G. Stadler and O. Ghattas, A-optimal encoding weights for nonlinear inverse problems, with applications to the Helmholtz inverse problem, Inverse Problems, 33(7), 2017. [arXiv:1612.02358 | link]
D. Li, M. Gurnis and G. Stadler, Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity, Geophysical Journal International 209(1), pp. 86-105. [link], 2017.
J. Rudi, G. Stadler and O. Ghattas, Weighted BFBT Preconditioner for Stokes Flow Problems with Highly Heterogeneous Viscosity, SIAM Journal on Scientific Computing, 39(5), pp. 272–297, 2017. [arXiv:1607.03936 | link]
A. Alexanderian, N. Petra, G. Stadler and O. Ghattas: Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations, SIAM/ASA Journal on Uncertainty Quantification, 5(1), pp. 1166-1192, 2017. [arXiv:1602.07592 | link]
H. Zhu, N. Petra, G. Stadler, T. Isaac, T. J. R. Hughes, O. Ghattas. Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model. The Cryosphere, 10, 1477-1494, (2016). [link].
H. Zhu, S. Li, S. Fomel, G. Stadler and O. Ghattas. A Bayesian approach to estimate uncertainty for full waveform inversion with a priori information from depth migration, Geophysics, 81(5), pp. R307-R323, (2016). [link].
A. Alexanderian, N. Petra, G. Stadler and O. Ghattas: A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems, SIAM Journal on Scientific Computing, 38(1), A243-A272 (2016). [link | arXiv:1410.5899]
J. Rudi, A. C. I. Malossi, T. Isaac, G. Stadler, M. Gurnis, P. Staar, Y. Ineichen, C. Bekas, A. Curioni, O. Ghattas: An Extreme-Scale Implicit Solver for Complex PDEs: Highly Heterogeneous Flow in Earth’s Mantle, ACM/IEEE Supercomputing SC15, (2015), [ link ], Gordon Bell Prize.
T. Isaac, G. Stadler and O. Ghattas: Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics, SIAM Journal on Scientific Computing, 37(6), pp. B804-B833, (2015). [link | arXiv:1406.6573]
T. Isaac, N. Petra, G. Stadler and O. Ghattas: 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, Journal of Computational Physics 296, pp. 348-368 (2015). [link | arXiv:1410.1221]
H. Sundar, G. Stadler and G. Biros: Comparison of multigrid algorithms for high-order continuous finite element discretizations, Numerical Linear Algebra with Applications, 22(4), pp. 664-680, (2015). [arXiv:1402.5938 | link]. The corresponding Matlab implementation HoMG is available from Github.
L. C. Wilcox, G. Stadler, T. Bui-Thanh and O. Ghattas: Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method, Journal of Scientific Computing, 63(1), pp. 138-162, (2015). [arXiv:1311.6900 | link ]
V. Ratnaswamy, G. Stadler and M. Gurnis: Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples, Geophysical Journal International, 202(2), pp. 768-786, (2015). [ link ]
M. Perego, S. Price and G. Stadler: Optimal initial conditions for coupling ice sheet models to earth science models, Journal of Geophysical Research: Earth Surface, 119(9), pp. 1894-1917, (2014) [ JGR link ].
J. C. De los Reyes and G. Stadler: A nonsmooth model for discontinuous shear thickening fluids: analysis and numerical solution, Interfaces and Free Boundaries, 16(4), pp. 575-602, (2014) [ link pdf ].
A. Alexanderian, N. Petra, G. Stadler and O. Ghattas: A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized l_0-sparsification, SIAM Journal on Scientific Computing, 36(5), pp. A2122-2148, (2014). [SISC link | arXiv:1308.4084]
N. Petra, J. Martin, G. Stadler and O. Ghattas: A computational framework for infinite-dimensional Bayesian inverse problems Part II: Stochastic Newton MCMC with application to ice sheet flow inverse problems, SIAM Journal on Scientific Computing, 36(4), pp. A1525-1555 (2014). [ SISC link | arXiv:1308.6221]
J. Worthen, G. Stadler, N. Petra, M. Gurnis and O. Ghattas: Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow, Physics of the Earth and Planatery Interiors, 234, 23-34 (2014). [ PEPI link ]
M. Hesse and G. Stadler: Joint inversion in coupled quasistatic poroelasticity, Journal of Geophysical Research: Solid Earth, 103, No. 2, 1425-1445. [ link ].
T. Bui-Thanh, O. Ghattas, J. Martin, and G. Stadler: A computational framework for infinite-dimensional Bayesian problems Part I: The linearized case, with applications to global seismic inversion, SIAM Journal on Scientific Computing, 35(6), A2494-2523, (2013). [ link | pdf | arXiv:1308.1313]
C. Burstedde, G. Stadler, L. Alisic, L. C. Wilcox, E. Tan, M. Gurnis, and O. Ghattas: Large-scale adaptive mantle convection simulations, Geophysical Journal International, 103 No. 3, pp. 889-906, (2013) [ link ].
T. Bui-Thanh, C. Burstedde, O. Ghattas, J. Martin, G. Stadler and L. C. Wilcox: Extreme-scale UQ for Bayesian inverse problems governed by PDEs, ACM/IEEE Supercomputing SC12, (2012), [ link ], Gordon Bell Prize Finalist.
H. Sundar, G. Biros, C. Burstedde, J. Rudi, O. Ghattas and G. Stadler: Parallel geometric-algebraic multigrid on unstructured forsts of octrees, ACM/IEEE Supercomputing SC12, (2012) [ link ]
L. Alisic, M. Gurnis, G. Stadler, C. Burstedde and O. Ghattas: Multi-scale dynamics and rheology of mantle flow with plates, Journal of Geophysical Research, 117, B10402 (2012) [ link ]
N. Petra, H. Zhu, G. Stadler, T. J. R. Hughes and O. Ghattas: An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model, Journal of Glaciology, 58, No. 211, (2012), [ link | pdf ]
R. Herzog, G. Stadler and G. Wachsmuth: Directional sparsity in optimal control of partial differential equations, SIAM Journal on Control and Optimization, 50, pp. 943-963, (2012), [ link | pdf ]. Please not the following ERRATUM: R. Herzog, G. Stadler and G. Wachsmuth: Erratum: Directional Sparsity In Optimal Control of Partial Differential Equations, SIAM Journal on Control and Optimization, 53(4), pp. 2722-2723, (2015), [ link ].
S. Yang, G. Stadler, R. Moser and O. Ghattas: A shape Hessian-based boundary roughness analysis of Navier-Stokes flow, SIAM Journal on Applied Mathematics, 71, Nr. 1, pp. 333-355, (2011). [ link | pdf ]
G. Stadler, C. Burstedde and M. Gurnis: Plattentektonik im Supercomputer, Spektrum der Wissenschaft, pp. 12-14, (April 2011).
N. Petra, G. Stadler: Model variational inverse problems governed by partial differential equations, ICES Report No. 11-05, The Institute for Computational Engineering and Sciences, The University of Texas at Austin, (2011). [ pdf | code ]
L.C. Wilcox, G. Stadler, C. Burstedde and O. Ghattas: A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media, Journal of Computational Physics, 229, Nr. 24, pp. 9373-9396, (2010). [ pdf | link ]
G. Stadler, M. Gurnis, C. Burstedde, L. C. Wilcox, L. Alisic and O. Ghattas: The Dynamics of Plate Tectonics and Mantle Flow: From Local to Global Scales, Science, 27 August 2010, 329, No. 5995, pp. 1033-1038 (2010). [ link | Supporting Online Material | Perspectives | CoS ]
C. Burstedde, O. Ghattas, M. Gurnis, T. Isaac, G. Stadler, T. Warburton, and L. C. Wilcox: Extreme-scale AMR, ACM/IEEE Supercomputing SC10 (2010), Gordon Bell Prize Finalist, 2010. [ link ]
L. Alisic, M. Gurnis, G. Stadler, C. Burstedde, L.C. Wilcox and O. Ghattas: Slab Stress and Strain Rate as Constraints on Global Mantle Flow, Geophysical Research Letters, 37, L22308 (2010). [ link ]
I. Figueiredo, P. Figueiredo, G. Stadler, O. Ghattas, and A. Araujo: Variational image segmentation for endoscopic human colonic aberrant crypt foci, IEEE Transactions on Medical Imaging, 29, Nr. 4, pp. 998-1011 (2010).
G. Stadler: Elliptic optimal control problems with L1-control cost and applications for the placement of control devices, Computational Optimization and Applications, 44, Nr. 2, pp. 159-181, (2009). [ pdf | link ] Errata: The proof for Theorem 4.3 in the original publication is not correct. Please find the corrected proof here [ pdf ].
C. Burstedde, O. Ghattas, G. Stadler, T. Tu and L. C. Wilcox: Parallel scalable adjoint-based adaptive solution for variable-viscosity Stokes flows, Computer Methods Applied Mechanics and Engineering, 198, Nr. 21-26, pp. 1691-1700 (2009). [ link ]
S.L. Keeling, G. Propst, G. Stadler and W. Wackernagel: A mathematical model of the deformation of the eyeball by an elastic band, Mathematical Medicine and Biology, 26 Nr. 2 (2009). [ link ]
C. Burstedde, M. Burtscher, O. Ghattas, G. Stadler, T. Tu and L. C. Wilcox: ALPS: A framework for parallel adaptive PDE solution, Journal of Physics: Conference Series, 180, Issue 1, pp. 012009 (2009). [ link ]
C. Burstedde, O. Ghattas, M. Gurnis, G. Stadler, E. Tan, T. Tu, L. C. Wilcox, and S. Zhong: Scalable adaptive mantle convection simulation on petascale supercomputers, ACM/IEEE proceedings of SC08, 2008. Gordon Bell Prize finalist. [ link | pdf ]
C. Burstedde, O. Ghattas, G. Stadler, T. Tu and L. C. Wilcox: Towards Adaptive Mesh PDE Simulations on Petascale Computers, in Proceedings of Teragrid ‘08. [ pdf ] Winning paper of NSF Capability Computing Challenge.
S. Hueeber, G. Stadler and B. I. Wohlmuth: A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction, SIAM Journal on Scientific Computing, 30 Nr. 2, pp. 572-596 (2008) [ pdf | link ]
A. Araujo, D. Comissiong and G. Stadler: Numerical experiments for segmenting medical images using level sets, In Computational Vision and Medical Image Processing, Taylor & Francis Group, pp. 91-96 (2008).
L. Costa, I. Figueiredo, R. Leal, P. Oliveira and G. Stadler: Modeling and numerical study of actuator and sensor effects for a laminated piezoelectric plate, Computers and Structures 85, Nr. 7-8 pp. 385-403 (2007).
M. Hintermüller and G. Stadler: An infeasible primal-dual algorithm for TV-based inf-convolution-type image restoration, SIAM Journal on Scientific Computing, 28, Nr.1, pp. 1-23 (2006). [ pdf | link ]
G. Stadler, T. Steiner, J. Beiglböck: A practical map labeling algorithm utilizing mor phological image processing and force-directed methods, Cartography and Geographic Information Science, 33, Nr. 3, 207-215 (2006).
K. Kunisch and G. Stadler: Generalized Newton methods for the 2D-Signorini contact problem with friction in function space, Mathematical Modelling and Numerical Analysis, 39, Nr. 4, pp. 827-854 (2005). [ link ]
U. Hohenester and G. Stadler: Optimal quantum control in electron-phonon scatterings in artificial atoms, Physica E, 29, pp. 320-324 (2005).
Hohenester and G. Stadler: Quantum control of electron-phonon scatterings in artificial atoms, Physical Review Letters, 92, 196801 (2004). [ link ]
M. Hintermüller and G. Stadler: A semi-smooth Newton method for constrained linear-quadratic control problems, Zeitschrift fuer angewandte Mathematik und Mechanik (ZAMM), 83, Nr. 4, 219-237 (2003).
A. Borzi, G. Stadler and U. Hohenester: Optimal quantum control in nanostructures: Theory and application to a generic three-level system, Physical Review A, 66 053811 (2002).
G. Stadler: Infinite-Dimensional Semi-Smooth Newton and Augmented Lagrangian Methods for Friction and Contact Problems in Elasticity, PhD thesis, University of Graz, 2004. [ link ]
G. Stadler: Beschränkte linear-quadratische Optimalsteuerprozesse und eine primal-duale Strategie zur Lösung, Master thesis, University of Graz, 2001.