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[1]
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O. G. Ernst, B. Sprungk, and C. Zhang, “Uncertainty modeling and propagation
for groundwater flow: A comparative study of surrogates,” International
Journal on Geomathematics, vol. 15, no. 1, Article 11, 2024.
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[2]
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K. Kurgyis, P. Achtziger-Zupančič, M. Bjorge, M. S. Boxberg,
M. Broggi, J. Buchwald, O. G. Ernst, J. Flügge, A. Ganopolski, T. Graf,
P. Kortenbruck, J. Kowalski, P. Kreye, P. Kukla, S. Mayr, S. Miro, T. Nagel,
W. Nowak, S. Oladyshkin, A. Renz, J. Rienäcker-Burschil, K.-J.
Röhlig, O. Sträter, J. Thiedau, F. Wagner, F. Wellmann, M. Wengler,
J. Wolf, and W. Rühaak, “Uncertainties and robustness with regard to the
safety of a repository for high-level radioactive waste: introduction of a
research initiative,” Environmental Earth Sciences, vol. 83, no. 2,
p. 82, 2024.
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[3]
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J. Blechta and O. G. Ernst, “Efficient solution of parameter identification
problems with H1 regularization,” SIAM Journal on Scientific
Computing, vol. 46, no. 2, pp. A1160-A1185, 2024.
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[4]
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O. G. Ernst, A. Pichler, and B. Sprungk, “Wasserstein sensitivity of risk and
uncertainty propagation,” SIAM/ASA Journal on Uncertainty
Quantification, vol. 10, no. 3, pp. 915-948, 2022.
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[5]
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M. Eigel, O. G. Ernst, B. Sprungk, and L. Tamellini, “On the convergence of
adaptive stochastic collocation for elliptic partial differential equations
with affine diffusion,” SIAM Journal on Numerical Analysis, vol. 60,
no. 2, pp. 659-687, 2022.
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[6]
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J. Blechschmidt and O. G. Ernst, “Three ways to solve partial differential
equations with neural networks: a review,” GAMM Mitteilungen, vol. 44,
no. 2, p. e202100006, 2021.
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[7]
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D. Gerth, S. Hannusch, O. G. Ernst, and J. Ihlemann, “Regularization for the
inversion of fibre Bragg grating spectra,” Inverse Problems in
Science and Engineering, vol. 29, no. 13, pp. 2629-2655, 2021.
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[8]
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O. G. Ernst, B. Sprungk, and L. Tamellini, “Convergence of sparse collocation
for functions of countably many Gaussian random variables (with application
to elliptic PDEs),” SIAM Journal on Numerical Analysis, vol. 56,
no. 2, pp. 877-905, 2018.
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[9]
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O. G. Ernst, B. Sprungk, and H.-J. Starkloff, “Analysis of the ensemble and
polynomial chaos Kalman filters in Bayesian inverse problems,”
SIAM/ASA Journal on Uncertainty Quantification, vol. 3, no. 1, pp. 823-851,
2015.
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[10]
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R.-U. Börner, O. G. Ernst, and S. Güttel, “Three-dimensional transient
electromagnetic modelling using rational Krylov methods,” Geophysical
Journal International, vol. 202, pp. 2025-2043, 2015.
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[11]
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M. Ullmann, U. Prüfert, J. Seidel, O. G. Ernst, and C. Hasse, “Application
of proper orthogonal decomposition methods in reactive pore diffusion
simulations,” Canadian Journal of Chemical Engineering, vol. 92,
no. 9, pp. 1552-1560, 2014.
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[12]
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J. Seidel and O. G. Ernst, “Model reduction for cold rolling processes,”
Steel Research, vol. 85, no. 9, pp. 1334-1339, 2014.
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[13]
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H. C. Elman, O. G. Ernst, and E. Ullmann, “Efficient iterative solvers for
stochastic Galerkin discretizations of log-transformed random diffusion
problems,” SIAM Journal on Scientific Computing, vol. 34, no. 2,
pp. A659-A682, 2012.
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[14]
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O. G. Ernst, A. Mugler, H.-J. Starkloff, and E. Ullmann, “On the convergence
of generalized polynomial chaos expansions,” M2AN, vol. 46, no. 2,
pp. 317-339, 2012.
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[15]
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I. Busch, O. G. Ernst, and E. Ullmann, “Expansion of random field gradients
using hierarchical matrices,” PAMM, vol. 11, no. 1, pp. 911-914,
2011.
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[16]
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M. Eiermann, O. G. Ernst, and S. Güttel, “Deflated restarting for matrix
functions,” SIAM Journal on Matrix Analysis and Applications, vol. 32,
no. 2, pp. 621-641, 2011.
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[17]
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O. G. Ernst and E. Ullmann, “Stochastic Galerkin matrices,” SIAM
Journal on Matrix Analysis and Applications, vol. 31, no. 4, pp. 1848-1872,
2010.
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[18]
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O. G. Ernst, C. E. Powell, D. Silvester, and E. Ullmann, “Efficient solvers
for a linear stochastic Galerkin mixed formulation of diffusion problems
with random data,” SIAM Journal on Scientific Computing, vol. 31,
no. 2, pp. 1424-1447, 2009.
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[19]
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M. Afanasjew, M. Eiermann, O. G. Ernst, and S. Güttel, “A generalization
of the steepest descent method for matrix functions,” Electronic
Transactions on Numerical Analysis, vol. 28, pp. 206-222, 2008.
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[20]
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M. Afanasjew, M. Eiermann, O. G. Ernst, and S. Güttel, “Implementation of
a restarted Krylov subspace method for the evaluation of matrix
functions,” Linear Algebra and its Applications, vol. 429, no. 10,
pp. 2293-2314, 2008.
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[21]
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R.-U. Börner, O. G. Ernst, and K. Spitzer, “Fast 3d simulation of
transient electromagnetic fields by model reduction in the frequency domain
using Krylov subspace projection,” Geophysical Journal
International, vol. 173, pp. 766-780, 2008.
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[22]
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M. Eiermann, O. G. Ernst, and E. Ullmann, “Computational aspects of the
stochastic finite element method,” Computing and Visualization in
Science, vol. 10, no. 1, pp. 3-15, 2007.
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[23]
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M. Eiermann and O. G. Ernst, “A restarted Krylov subspace method for the
evaluation of matrix functions,” SIAM Journal on Numerical Analysis,
vol. 44, no. 6, pp. 2481-2504, 2006.
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[24]
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H. C. Elman, O. G. Ernst, D. P. O'Leary, and M. Stewart, “Efficient iterative
algorithms for the stochastic finite element method with applications to
acoustic scattering,” Computer Methods in Applied Mechanics and
Engineering, vol. 194, pp. 1037-1055, 2005.
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[25]
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H. C. Elman, O. G. Ernst, and D. P. O'Leary, “A multigrid method enhanced by
Krylov subspace iteration for discrete Helmholtz equations,” SIAM
Journal on Scientific Computing, vol. 23, no. 4, pp. 1290-1314, 2001.
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[26]
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M. Eiermann and O. G. Ernst, “Geometric aspects of the theory of Krylov
subspace methods,” Acta Numerica, vol. 10, pp. 251-312, 2001.
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[27]
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O. G. Ernst, “Equivalent iterative methods for p-cyclic matrices,”
Numerical Algorithms, vol. 25, pp. 161-180, 2000.
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[28]
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M. Eiermann, O. G. Ernst, and O. Schneider, “Analysis of acceleration
strategies for restarted minimal residual methods,” Journal of
Computational and Applied Mathematics, vol. 123, pp. 262-292, 2000.
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[29]
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O. G. Ernst, “Residual-minimizing Krylov subspace methods for stabilized
discretizations of convection-diffusion equations,” SIAM Journal on
Matrix Analysis and Applications, vol. 21, no. 4, pp. 1079-1101, 2000.
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[30]
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O. G. Ernst, “A finite element capacitance matrix method for exterior
Helmholtz problems,” Numerische Mathematik, vol. 75, no. 2,
pp. 175-204, 1996.
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[1]
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O. G. Ernst, B. Sprungk, and L. Tamellini, “On expansions and nodes for sparse
grid collocation of lognormal elliptic PDEs,” in Sparse Grids and
Applications - Munich 2018 (H.-J. Bungartz, J. Garcke, and D. Pflüger,
eds.), vol. 144 of LNCSE, pp. 1-31, Cham: Springer International
Publishing, 2021.
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[2]
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O. G. Ernst, B. Sprungk, and H.-J. Starkloff, “Bayesian inverse problems and
Kalman filters,” in Extraction of Quantifiable Information from
Complex Systems (S. e. a. Dahlke, ed.), vol. 102 of Lecture Notes in
Computational Science and Engineering, pp. 133-159, Springer-Verlag, 2014.
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[3]
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O. G. Ernst and B. Sprungk, “Stochastic collocation for elliptic PDEs with
random data - the lognormal case,” in Sparse Grids and Applications -
Munich 2012 (J. Garcke and D. Pflüger, eds.), vol. 97 of Lecture
Notes in Computational Science and Engineering, pp. 29-53, Springer-Verlag,
2014.
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[4]
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O. G. Ernst and M. J. Gander, “Multigrid methods for Helmholtz problems: A
convergent scheme in 1D using standard components,” in Direct and
Inverse Problems in Wave Propagation and Applications (I. G. Graham,
U. Langer, J. M. Melenk, and M. Sini, eds.), vol. 14 of Radon Series on
Computational and Applied Mathematics, Berlin/Boston: Walter de Gruyter
GmbH, 2013.
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[5]
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O. G. Ernst and M. J. Gander, “Why it is difficult to solve Helmholtz
problems with classical iterative methods,” in Numerical Analysis of
Multiscale Problems (I. Graham, T. Hou, O. Lakkis, and R. Scheichl, eds.),
vol. 83 of Lecture Notes in Computational Science and Engineering,
(Berlin Heidelberg), pp. 325-361, Springer-Verlag, 2012.
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[6]
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H. C. Elman and O. G. Ernst, “Numerical experiences with a Krylov-enhanced
multigrid solver for exterior Helmholtz problems,” in Proceedings of
the Fifth International Conference on Mathematical and Numerical Aspects of
Wave Propagation, Waves 2000 (Santiago de Compostela) (A. Bermúdez,
D. Gómez, C. Hazard, P. Joly, and J. E. Roberts, eds.), (Philadelphia),
SIAM, 2000.
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[7]
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O. G. Ernst and G. H. Golub, A Domain Decomposition Approach to Solving
the Helmholtz Equation with a Radiation Boundary Condition, vol. 157 of
Contemporary Mathematics.
AMS, 1992.
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