publications.bib
@article{ErnstEtAl2024,
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk and Chao Zhang},
date-added = {2024-03-11 11:39:10 +0100},
date-modified = {2024-03-11 12:43:52 +0100},
journal = {International Journal on Geomathematics},
volume = {15},
number = {1},
pages = {Article 11},
mvpubtype = {journal},
doi = {10.1007/s13137-024-00250-3},
pdf = {PubArchive/ernstEtAl2024.pdf},
title = {Uncertainty Modeling and Propagation for Groundwater Flow: A Comparative Study of Surrogates},
year = {2024}
}
@article{KurgyisEtAl2024,
author = {Kurgyis, Kata and Achtziger-Zupan{\v c}i{\v c}, Peter and Bjorge, Merle and Boxberg, Marc S. and Broggi, Matteo and Buchwald, J{\"o}rg and Ernst, Oliver G. and Fl{\"u}gge, Judith and Ganopolski, Andrey and Graf, Thomas and Kortenbruck, Philipp and Kowalski, Julia and Kreye, Phillip and Kukla, Peter and Mayr, Sibylle and Miro, Shorash and Nagel, Thomas and Nowak, Wolfgang and Oladyshkin, Sergey and Renz, Alexander and Rien{\"a}cker-Burschil, Julia and R{\"o}hlig, Klaus-J{\"u}rgen and Str{\"a}ter, Oliver and Thiedau, Jan and Wagner, Florian and Wellmann, Florian and Wengler, Marc and Wolf, Jens and R{\"u}haak, Wolfram},
date-added = {2024-03-11 11:34:38 +0100},
date-modified = {2024-03-11 12:37:27 +0100},
doi = {10.1007/s12665-023-11346-8},
journal = {Environmental Earth Sciences},
mvpubtype = {journal},
number = {2},
pages = {82},
pdf = {PubArchive/kurgyisEtAl2024.pdf},
title = {Uncertainties and robustness with regard to the safety of a repository for high-level radioactive waste: introduction of a research initiative},
volume = {83},
year = {2024},
bdsk-url-1 = {https://doi.org/10.1007/s12665-023-11346-8}
}
@article{BlechtaErnst2024,
author = {Jan Blechta and Oliver G. Ernst},
date-added = {2024-03-11 11:34:21 +0100},
date-modified = {2024-03-11 12:44:17 +0100},
journal = {SIAM Journal on Scientific Computing},
volume = {46},
number = {2},
pages = {A1160--A1185},
doi = {10.1137/22M1520591},
mvpubtype = {journal},
pdf = {PubArchive/blechtaErnst2024.pdf},
title = {Efficient Solution of Parameter Identification Problems with {$H^1$} Regularization},
year = {2024}
}
@article{ErnstEtAl2020,
author = {Oliver G. Ernst and Fabio Nobile and Claudia Schillings and Tim Sullivan},
date-added = {2024-03-11 11:34:09 +0100},
date-modified = {2024-03-11 11:34:09 +0100},
doi = {10.4171/OWR/2019/12},
journal = {Oberwolfach Reports},
mvpubtype = {general},
number = {1},
pages = {695--772},
title = {Uncertainty Quantification},
volume = {16},
year = {2020},
bdsk-url-1 = {https://doi.org/10.4171/OWR/2019/12}
}
@article{ErnstEtAl2022,
author = {Oliver G. Ernst and Alois Pichler and Bj{\"o}rn Sprungk},
date-added = {2022-08-17 06:46:01 +0200},
date-modified = {2022-08-17 06:49:43 +0200},
doi = {10.1137/20M1325459},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
mvpubtype = {journal},
number = {3},
pages = {915--948},
pdf = {PubArchive/ernstEtAl2022.pdf},
title = {Wasserstein Sensitivity of Risk and Uncertainty Propagation},
volume = {10},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1137/20M1325459}
}
@incollection{ErnstEtAl2021a,
address = {Cham},
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk and Lorenzo Tamellini},
booktitle = {Sparse Grids and Applications -- Munich 2018},
date-added = {2022-05-03 16:38:06 +0200},
date-modified = {2022-05-03 18:02:32 +0200},
doi = {10.1007/978-3-030-81362-8_1},
editor = {Bungartz, Hans-Joachim and Garcke, Jochen and Pfl{\"u}ger, Dirk},
mvpubtype = {bookchapter},
pages = {1--31},
pdf = {PubArchive/ernstEtAl2021a.pdf},
publisher = {Springer International Publishing},
series = {LNCSE},
title = {On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic {PDE}s},
volume = {144},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1007/978-3-030-81362-8_1}
}
@article{BlechschmidtErnst2021,
author = {Jan Blechschmidt and Oliver G. Ernst},
date-added = {2022-05-03 16:29:00 +0200},
date-modified = {2022-05-03 16:50:11 +0200},
doi = {10.1002/gamm.202100006},
journal = {GAMM Mitteilungen},
mvpubtype = {journal},
number = {2},
pages = {e202100006},
pdf = {PubArchive/blechschmidtErnst2021.pdf},
title = {Three ways to solve partial differential equations with neural networks: a review},
volume = {44},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1002/gamm.202100006}
}
@article{EiglEtAl2022,
author = {Martin Eigel and Oliver G. Ernst and Bj{\"o}rn Sprungk and Lorenzo Tamellini},
date-added = {2022-05-03 16:21:52 +0200},
date-modified = {2024-03-11 13:07:23 +0100},
doi = {10.1137/20M1364722},
journal = {SIAM Journal on Numerical Analysis},
mvpubtype = {journal},
number = {2},
pages = {659--687},
pdf = {PubArchive/eiglEtAl2022.pdf},
title = {On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion},
volume = {60},
year = {2022},
bdsk-url-1 = {https://doi.org/10.1137/20M1364722}
}
@article{GerthEtAl2021,
author = {Daniel Gerth and Susann Hannusch and Oliver G. Ernst and J{\"o}rn Ihlemann},
date-added = {2022-05-03 16:14:32 +0200},
date-modified = {2022-05-03 20:03:11 +0200},
doi = {10.1080/17415977.2021.1943383},
journal = {Inverse Problems in Science and Engineering},
mvpubtype = {journal},
number = {13},
pages = {2629--2655},
pdf = {PubArchive/gerthEtAl2021.pdf},
title = {Regularization for the inversion of fibre {B}ragg grating spectra},
volume = {29},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1080/17415977.2021.1943383}
}
@article{Ernst2017,
author = {Oliver G. Ernst},
date-added = {2018-04-15 16:57:30 +0000},
date-modified = {2018-04-15 17:14:26 +0000},
journal = {GAMM Rundbrief},
mvpubtype = {general},
pages = {4--9},
pdf = {PubArchive/ernst2017},
title = {Quantifizierung von {U}nsicherheit: {P}ropagation und {I}nferenz},
volume = {2},
year = {2017}
}
@article{ErnstEtAl2018,
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk and Lorenzo Tamellini},
date-added = {2018-04-15 16:05:45 +0000},
date-modified = {2018-04-15 16:28:30 +0000},
doi = {10.1137/17M1123079},
journal = {SIAM Journal on Numerical Analysis},
mvpubtype = {journal},
number = {2},
pages = {877--905},
pdf = {PubArchive/ernstEtAl2018.pdf},
title = {Convergence of Sparse Collocation for Functions of Countably Many {G}aussian Random Variables (with Application to Elliptic {PDE}s)},
volume = {56},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1137/17M1123079}
}
@article{ErnstEtAl2015,
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk and Hans-J{\"o}rg Starkloff},
date-added = {2015-10-24 21:45:56 +0000},
date-modified = {2015-10-25 07:19:03 +0000},
doi = {10.1137/140981319},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
mvpubtype = {journal},
number = {1},
pages = {823--851},
pdf = {PubArchive/ernstEtAl2015.pdf},
title = {Analysis of the Ensemble and Polynomial Chaos {K}alman Filters in {B}ayesian Inverse Problems},
volume = {3},
year = {2015},
bdsk-url-1 = {http://dx.doi.org/10.1137/140981319}
}
@article{BoernerEtAl2015,
author = {Ralph-Uwe B{\"o}rner and Oliver G. Ernst and Stefan G{\"u}ttel},
date-added = {2015-10-24 21:30:59 +0000},
date-modified = {2015-10-25 07:55:47 +0000},
doi = {10.1093/gji/ggv224},
journal = {Geophysical Journal International},
mvpubtype = {journal},
pages = {2025--2043},
pdf = {PubArchive/boernerEtAl2015.pdf},
title = {Three-dimensional transient electromagnetic modelling using rational {K}rylov methods},
volume = {202},
year = {2015},
bdsk-url-1 = {http://dx.doi.org/10.1093/gji/ggv224}
}
@incollection{ErnstEtAl2014,
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk and Hans-J{\"o}rg Starkloff},
booktitle = {Extraction of Quantifiable Information from Complex Systems},
date-added = {2014-11-25 12:19:48 +0000},
date-modified = {2022-05-03 18:02:49 +0200},
doi = {10.1007/978-3-319-08159-5_7},
editor = {Dahlke, Stephan et al.},
mvpubtype = {bookchapter},
pages = {133--159},
pdf = {PubArchive/ernstEtAl2014.pdf},
publisher = {Springer-Verlag},
series = {Lecture Notes in Computational Science and Engineering},
title = {Bayesian Inverse Problems and {K}alman Filters},
volume = {102},
year = {2014},
bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-319-08159-5_7}
}
@article{UllmannEtAl2014,
author = {Martin Ullmann and Uwe Pr{\"u}fert and Jens Seidel and Oliver G. Ernst and Christian Hasse},
date-added = {2014-11-25 10:42:56 +0000},
date-modified = {2014-11-25 12:03:57 +0000},
doi = {10.1002/cjce.22018},
journal = {Canadian Journal of Chemical Engineering},
mvpubtype = {journal},
number = {9},
pages = {1552--1560},
pdf = {PubArchive/ullmannEtAl2014.pdf},
title = {Application of Proper Orthogonal Decomposition Methods in Reactive Pore DIffusion Simulations},
volume = {92},
year = {2014},
bdsk-url-1 = {http://dx.doi.org/10.1002/cjce.22018}
}
@article{SeidelErnst2014,
author = {Jens Seidel and Oliver G. Ernst},
date-added = {2014-11-25 10:42:52 +0000},
date-modified = {2014-11-25 12:04:31 +0000},
doi = {10.1002/srin.201300220},
journal = {Steel Research},
mvpubtype = {journal},
number = {9},
pages = {1334--1339},
pdf = {PubArchive/seidelErnst2014.pdf},
title = {Model Reduction for Cold Rolling Processes},
volume = {85},
year = {2014},
bdsk-url-1 = {http://dx.doi.org/10.1002/srin.201300220}
}
@article{ErnstCliffe2012,
author = {Oliver G. Ernst and K. Andrew Cliffe},
date-modified = {2018-04-15 17:14:04 +0000},
journal = {SIAM News},
month = {October},
mvpubtype = {general},
number = {8},
title = {Uncertainty {Q}uantification 2012: {P}robabilistic {UQ} for {PDE}s with {R}andom {D}ata: {A} {C}ase {S}tudy},
volume = {45},
year = {2012}
}
@incollection{ErnstSprungk2014,
annote = {Convergence analysis of sparse grid stochastic collocation for diffusion equations with lognormal coefficient.},
author = {Oliver G. Ernst and Bj{\"o}rn Sprungk},
booktitle = {Sparse Grids and Applications - Munich 2012},
date-modified = {2015-10-25 08:13:10 +0000},
doi = {10.1007/978-3-319-04537-5_2},
editor = {Jochen Garcke and Dirk Pfl{\"u}ger},
mvpubtype = {bookchapter},
pages = {29--53},
pdf = {PubArchive/ernstSprungk2014.pdf},
publisher = {Springer-Verlag},
series = {Lecture Notes in Computational Science and Engineering},
title = {Stochastic Collocation for Elliptic {PDE}s with Random Data - the Lognormal Case},
volume = {97},
year = {2014},
bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-319-04537-5_2}
}
@unpublished{Ernst1989,
author = {Oliver G. Ernst},
mvpubtype = {theses},
note = {Diplomarbeit, Institut f{\"u}r Praktische Mathematik, Universit{\"a}t Karlsruhe},
title = {{\"U}ber einige {A}nwendungen komplexer {O}rthogonalpolynome in der {N}umerik},
year = {1989}
}
@incollection{ErnstGander2013,
address = {Berlin/Boston},
annote = {Our attempt at constructing a wave-number robust multigrid V-cycle for Helmholtz problems in 1D.},
author = {Oliver G. Ernst and Martin J. Gander},
booktitle = {Direct and Inverse Problems in Wave Propagation and Applications},
date-modified = {2015-10-25 08:02:42 +0000},
editor = {Ivan G. Graham and Ulrich Langer and Jens M. Melenk and Mourad Sini},
mvpubtype = {bookchapter},
pdf = {PubArchive/ernstGander2013TR.pdf},
publisher = {Walter de Gruyter GmbH},
series = {Radon Series on Computational and Applied Mathematics},
title = {Multigrid Methods for {H}elmholtz Problems: A Convergent Scheme in 1{D} Using Standard Components},
volume = {14},
year = {2013}
}
@article{ElmanEtAl2011,
annote = {We show how to reformulate a diffusion problem with lognormal random field as a convection-diffusion problem with a random convection term, turning a stochastically nonlinear problem into one which is stochastically linear.},
author = {Howard C. Elman and Oliver G. Ernst and Elisabeth Ullmann},
doi = {http://dx.doi.org/10.1137/110836675},
journal = {SIAM Journal on Scientific Computing},
mvpubtype = {journal},
number = {2},
pages = {A659--A682},
pdf = {PubArchive/diffStochCD.pdf},
title = {Efficient Iterative Solvers for Stochastic {G}alerkin Discretizations of log-Transformed Random Diffusion Problems},
volume = {34},
year = {2012},
bdsk-url-1 = {http://dx.doi.org/10.1137/110836675}
}
@article{BuschEtAl2011,
annote = {A short note describing how to compute the KL expansion of the gradient of a random field.},
author = {Ingolf Busch and Oliver G. Ernst and Elisabeth Ullmann},
date-added = {2011-07-28 18:11:34 +0200},
date-modified = {2016-06-09 04:20:23 +0000},
journal = {PAMM},
mvpubtype = {journal},
number = {1},
pages = {911--914},
pdf = {PubArchive/rfGradients.pdf},
title = {Expansion of random field gradients using hierarchical matrices},
volume = {11},
year = {2011}
}
@inproceedings{ErnstGander2012,
address = {Berlin Heidelberg},
annote = {A survey article on iterative solvers for discrete Helmholtz problems, written in connection with the 2010 London Mathematical Society Symposium in Durham (UK).},
author = {Oliver G. Ernst and Martin J. Gander},
booktitle = {Numerical Analysis of Multiscale Problems},
date-added = {2011-01-03 21:20:22 +0100},
date-modified = {2015-10-27 19:54:43 +0000},
doi = {10.1007/978-3-642-22061-6_10},
editor = {I. Graham and T. Hou and O. Lakkis and R. Scheichl},
mvpubtype = {bookchapter},
pages = {325--361},
pdf = {PubArchive/ernstGander2012.pdf},
publisher = {Springer-Verlag},
series = {Lecture Notes in Computational Science and Engineering},
title = {Why it is Difficult to Solve {H}elmholtz Problems with Classical Iterative Methods},
volume = {83},
year = {2012},
bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-642-03344-5_2}
}
@article{ErnstEtAl2012,
annote = {Answers the question when second-order random variables can be expanded in mean-square convergent generalized polynomial chaos expansions.},
author = {Oliver G. Ernst and Antje Mugler and Hans-J{\"o}rg Starkloff and Elisabeth Ullmann},
date-added = {2010-06-30 23:20:24 +0200},
date-modified = {2014-03-13 09:52:08 +0000},
doi = {http://dx.doi.org/10.1051/m2an/2011045},
journal = {M2AN},
mvpubtype = {journal},
number = {2},
pages = {317--339},
pdf = {PubArchive/genpc_m2an.pdf},
title = {On the Convergence of Generalized Polynomial Chaos Expansions},
volume = {46},
year = {2012},
bdsk-url-1 = {http://dx.doi.org/10.1051/m2an/2011045}
}
@article{EiermannEtAl2011,
annote = {Here we show how Ron Morgan-style deflation for accelerated restarting with Krylov subspace methods can be generalized from linear systems to general matrix functions.},
author = {Michael Eiermann and Oliver G. Ernst and Stefan G{\"u}ttel},
date-added = {2009-10-23 09:02:46 +0200},
date-modified = {2014-03-13 09:54:33 +0000},
doi = {http://dx.doi.org/10.1137/090774665},
journal = {SIAM Journal on Matrix Analysis and Applications},
mvpubtype = {journal},
number = {2},
pages = {621--641},
pdf = {PubArchive/thick.pdf},
title = {Deflated Restarting for Matrix Functions},
volume = {32},
year = {2011},
bdsk-url-1 = {http://dx.doi.org/10.1137/090774665}
}
@article{ErnstUllmann2010,
annote = {This is a collection of results on the properties of matrices arising in stochastic Galerkin discretization.},
author = {Oliver G. Ernst and Elisabeth Ullmann},
date-added = {2009-02-25 09:55:00 +0100},
date-modified = {2014-03-13 09:59:10 +0000},
doi = {http://dx.doi.org/10.1137/080742282},
journal = {SIAM Journal on Matrix Analysis and Applications},
mvpubtype = {journal},
number = {4},
pages = {1848--1872},
pdf = {PubArchive/sgMatricesPublished.pdf},
title = {Stochastic {G}alerkin Matrices},
volume = {31},
year = {2010},
bdsk-url-1 = {http://dx.doi.org/10.1137/080742282}
}
@article{ErnstEtAl2009,
annote = {Here we discuss mean-based preconditioning for the mixed discretization of second-order elliptic problems with random coefficients in the stochatically linear case.},
author = {Oliver G. Ernst and Catherine E. Powell and David Silvester and Elisabeth Ullmann},
date-added = {2007-10-22 11:34:54 +0200},
date-modified = {2014-11-25 12:04:46 +0000},
doi = {http://dx.doi.org/10.1137/070705817},
journal = {SIAM Journal on Scientific Computing},
mvpubtype = {journal},
number = {2},
pages = {1424--1447},
pdf = {PubArchive/ernstEtAl2009.pdf},
title = {Efficient Solvers for a Linear Stochastic {G}alerkin Mixed Formulation of Diffusion Problems with Random Data},
volume = {31},
year = {2009},
bdsk-url-1 = {http://dx.doi.org/10.1137/070705817}
}
@article{AfanasjewEtAl2008a,
annote = {An analysis of our restarted Krylov subspace approximation for matrix functions in the special case of restart length one.},
author = {Martin Afanasjew and Michael Eiermann and Oliver G. Ernst and Stefan G{\"u}ttel},
date-added = {2007-10-14 23:01:24 +0200},
date-modified = {2009-02-25 10:13:43 +0100},
journal = {Electronic Transactions on Numerical Analysis},
mvpubtype = {journal},
pages = {206--222},
pdf = {PubArchive/steepestETNA.pdf},
title = {A Generalization of the Steepest Descent Method for Matrix Functions},
volume = {28},
year = {2008}
}
@article{AfanasjewEtAl2008b,
annote = {Presents a stable implementation of our restarted Krylov subspace method for matrix function which now has constant work per restart cycle. Also includes an a posteriori error estimator and applications to time dependent problems from heat conduction, the quasi-static Maxwell equations and convection diffusion. },
author = {Martin Afanasjew and Michael Eiermann and Oliver G. Ernst and Stefan G{\"u}ttel},
date-added = {2007-10-14 10:55:00 +0200},
date-modified = {2014-03-13 10:04:11 +0000},
doi = {http://dx.doi.org/10.1016/j.laa.2008.06.029},
journal = {Linear Algebra and its Applications},
mvpubtype = {journal},
number = {10},
pages = {2293--2314},
pdf = {PubArchive/restartStableLAA.pdf},
title = {Implementation of a Restarted {K}rylov Subspace Method for the Evaluation of Matrix Functions},
volume = {429},
year = {2008},
bdsk-url-1 = {http://dx.doi.org/10.1016/j.laa.2008.06.029}
}
@article{BoernerEtAl2008,
annote = {Krylov subspace model reduction applied to a geophysical electromagnetic diffusion problem based on N{\'e}d{\'e}lec element discretization.},
author = {Ralph-Uwe B{\"o}rner and Oliver G. Ernst and Klaus Spitzer},
date-added = {2007-10-14 11:00:38 +0200},
date-modified = {2014-03-13 10:06:52 +0000},
doi = {http://dx.doi.org/10.1111/j.1365-246X.2008.03750.x},
journal = {Geophysical Journal International},
mvpubtype = {journal},
pages = {766--780},
pdf = {PubArchive/temFreq.pdf},
title = {Fast 3D simulation of transient electromagnetic fields by model reduction in the frequency domain using {K}rylov subspace projection},
volume = {173},
year = {2008},
bdsk-url-1 = {http://dx.doi.org/10.1111/j.1365-246X.2008.03750.x}
}
@article{EiermannEtAl2007,
annote = {My invited presentation for the Algoritmy 2005 conference. },
author = {Michael Eiermann and Oliver G. Ernst and Elisabeth Ullmann},
date-added = {2007-10-14 11:09:08 +0200},
date-modified = {2014-03-13 10:08:34 +0000},
doi = {http://dx.doi.org/10.1007/s00791-006-0047-4},
journal = {Computing and Visualization in Science},
mvpubtype = {journal},
number = {1},
pages = {3--15},
pdf = {PubArchive/algoritmy2005.pdf},
title = {Computational Aspects of the Stochastic Finite Element Method},
volume = {10},
year = {2007},
bdsk-url-1 = {http://dx.doi.org/10.1007/s00791-006-0047-4}
}
@article{EiermannErnst2006,
annote = {We present a method of restarting Krylov subspace approximations to functions of a matrix times a vector.},
author = {Michael Eiermann and Oliver G. Ernst},
date-added = {2007-10-14 07:59:53 +0200},
date-modified = {2014-03-13 10:09:45 +0000},
doi = {http://dx.doi.org/10.1137/050633846},
journal = {SIAM Journal on Numerical Analysis},
mvpubtype = {journal},
number = {6},
pages = {2481--2504},
pdf = {PubArchive/eiermannErnstKrylovExp.pdf},
title = {A Restarted {K}rylov Subspace Method for the Evaluation of Matrix Functions},
volume = {44},
year = {2006},
bdsk-url-1 = {http://dx.doi.org/10.1137/050633846}
}
@article{ElmanEtAl2005,
annote = {This paper discusses efficient solution strategies for the linear systems of equations arising from the stochastic finite element method applied to acoustic scattering as well as some post processing for involving the stochastic properties of the solution.},
author = {Howard C. Elman and Oliver G. Ernst and Dianne P. O'Leary and Michael Stewart},
date-added = {2007-10-14 08:03:25 +0200},
date-modified = {2014-03-13 10:10:25 +0000},
doi = {http://dx.doi.org/10.1016/j.cma.2004.06.028},
journal = {Computer Methods in Applied Mechanics and Engineering},
mvpubtype = {journal},
pages = {1037--1055},
pdf = {PubArchive/sfemHelmholtz.pdf},
title = {Efficient Iterative Algorithms for the Stochastic Finite Element Method with Applications to Acoustic Scattering},
volume = {194},
year = {2005},
bdsk-url-1 = {http://dx.doi.org/10.1016/j.cma.2004.06.028}
}
@article{ElmanEtAl2001,
annote = {This paper describes a new multigrid method which uses GMRES as a smoother on meshes too coarse to resolve the waves as well as an outer FGMRES acceleration.},
author = {Howard C. Elman and Oliver G. Ernst and Dianne P. O'Leary},
date-added = {2007-10-14 22:19:14 +0200},
date-modified = {2014-03-13 10:11:14 +0000},
doi = {http://dx.doi.org/10.1137/S1064827501357190},
journal = {SIAM Journal on Scientific Computing},
mvpubtype = {journal},
number = {4},
pages = {1290--1314},
pdf = {PubArchive/elmanErnstOleary.pdf},
title = {A Multigrid Method Enhanced by {K}rylov Subspace Iteration for Discrete {H}elmholtz Equations},
volume = {23},
year = {2001},
bdsk-url-1 = {http://dx.doi.org/10.1137/S1064827501357190}
}
@article{EiermannErnst2001,
annote = { A sort of 'grand-unifying theory' for Krylov subspace algorithms based on an abstract orthogonal and oblique projection in a Hilbert space and involving the angles between certain subspaces. },
author = {Michael Eiermann and Oliver G. Ernst},
date-added = {2007-10-14 22:26:46 +0200},
date-modified = {2014-03-13 10:12:14 +0000},
doi = {http://dx.doi.org/10.1017/S0962492901000046},
journal = {Acta Numerica},
mvpubtype = {journal},
pages = {251--312},
pdf = {PubArchiv/eiermann.ps.gz},
title = {Geometric Aspects of the Theory of {K}rylov Subspace Methods},
volume = {10},
year = {2001},
bdsk-url-1 = {http://dx.doi.org/10.1017/S0962492901000046}
}
@unpublished{Ernst2001,
annote = {My habilitation thesis. This presents a framework for MR and OR methods beginning with abstract projections, then applying these to equation-solving and finally to Krylov subspace methods.},
author = {Oliver G. Ernst},
date-added = {2007-10-14 22:56:08 +0200},
date-modified = {2007-10-14 23:00:00 +0200},
mvpubtype = {theses},
note = {Habilitation Thesis, TU Bergakademie Freiberg},
pdf = {PubArchive/habil.pdf},
title = {Minimal and Orthogonal Residual Methods and their Generalizations for Solving Linear Operator Equations},
year = {2001}
}
@inproceedings{ElmanErnst2000,
address = {Philadelphia},
annote = {Our contribution to the Waves 2000 Meeting in Santiago de Compostela, Spain, July 2000. This contains some further numerical results obtained with our muiltigrid enhanced Krylov solver applied to acoustic scattering by obstacles and an inhomogeneous medium. },
author = {Howard C. Elman and Oliver G. Ernst},
booktitle = {Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Waves 2000 (Santiago de Compostela)},
date-added = {2007-10-14 21:42:57 +0200},
date-modified = {2007-10-14 21:52:27 +0200},
editor = {A. Berm{\'u}dez and D. G{\'o}mez and C. Hazard and P. Joly and J. E. Roberts},
mvpubtype = {bookchapter},
publisher = {SIAM},
title = {Numerical Experiences with a {K}rylov-enhanced Multigrid Solver for Exterior {H}elmholtz Problems},
year = {2000}
}
@article{Ernst2000,
annote = {My contribution to the meeting in honor of Richard Varga's 70th birthday in Kent, March 1999. Contains an overview of how various iterative methods simplify when applied to p-cyclic matrices by resorting to the reduced system.},
author = {Oliver G. Ernst},
date-added = {2007-10-14 22:04:23 +0200},
date-modified = {2014-03-13 10:13:05 +0000},
doi = {http://dx.doi.org/10.1023/A:1016666622895},
journal = {Numerical Algorithms},
mvpubtype = {journal},
pages = {161--180},
pdf = {PubArchive/cyclicRev.ps.gz},
title = {Equivalent Iterative Methods for p-Cyclic Matrices},
volume = {25},
year = {2000},
bdsk-url-1 = {http://dx.doi.org/10.1023/A:1016666622895}
}
@article{EiermannEtAl2000,
annote = {Another theoretical paper on Krylov subspace methods and their generalizations to arbitrary correction spaces, this time focussing on augmented correction spaces, preconditioners that invert on a subspace and de Sturler's optimal truncation scheme. Also contains new simple derivations of how the implicitly restarted Arnoldi method can be used for augmented Krylov subspace methods.},
author = {Michael Eiermann and Oliver G. Ernst and Olaf Schneider},
date-added = {2007-10-14 22:11:23 +0200},
date-modified = {2014-03-13 10:13:53 +0000},
doi = {http://dx.doi.org/10.1016/S0377-0427(00)00398-8},
journal = {Journal of Computational and Applied Mathematics},
mvpubtype = {journal},
pages = {262--292},
pdf = {PubArchive/restart.pdf},
title = {Analysis of Acceleration Strategies for Restarted Minimal Residual Methods},
volume = {123},
year = {2000},
bdsk-url-1 = {http://dx.doi.org/10.1016/S0377-0427(00)00398-8}
}
@article{Ernst2000a,
annote = {This paper discusses the behavior of (unpreconditioned) GMRES on stabilized discrete convection-diffusion problems.},
author = {Oliver G. Ernst},
date-added = {2007-10-14 22:33:34 +0200},
date-modified = {2015-10-25 07:20:33 +0000},
doi = {http://dx.doi.org/10.1137/S0895479897325761},
journal = {SIAM Journal on Matrix Analysis and Applications},
mvpubtype = {journal},
number = {4},
pages = {1079--1101},
pdf = {PubArchive/scd.pdf},
title = {Residual-Minimizing {K}rylov Subspace Methods for Stabilized Discretizations of Convection-Diffusion Equations},
volume = {21},
year = {2000},
bdsk-url-1 = {http://dx.doi.org/10.1137/S0895479897325761}
}
@inproceedings{EiermannEtAl1996,
author = {Michael Eiermann and Oliver G. Ernst and Werner Queck},
booktitle = {Simulationstechniken in der Materialwissenschaft},
date-added = {2011-10-07 09:17:34 +0200},
date-modified = {2011-10-07 09:20:21 +0200},
editor = {Peter Klimanek and Wolfgang Pantleon},
mvpubtype = {general},
pages = {17--40},
publisher = {TU Bergakademie Freiberg},
series = {Freiberger Forschungshefte},
title = {A Very Short Finite Element Tutorial},
volume = {B 279},
year = {1996}
}
@article{Ernst1996,
annote = {This is more or less one chapter of my thesis: the finite element iterative imbedding algorithm.},
author = {Oliver G. Ernst},
date-added = {2007-10-14 22:38:20 +0200},
date-modified = {2014-03-13 10:15:26 +0000},
doi = {http://dx.doi.org/10.1007/s002110050236},
journal = {Numerische Mathematik},
mvpubtype = {journal},
number = {2},
pages = {175--204},
pdf = {PubArchive/paperfecmm.ps},
title = {A Finite Element Capacitance Matrix Method for Exterior {H}elmholtz Problems},
volume = {75},
year = {1996},
bdsk-url-1 = {http://dx.doi.org/10.1007/s002110050236}
}
@unpublished{Ernst1994,
annote = {My dissertation.},
author = {Oliver G. Ernst},
date-added = {2007-10-14 22:43:15 +0200},
date-modified = {2007-10-22 11:34:46 +0200},
mvpubtype = {theses},
note = {PhD thesis, Stanford University},
pdf = {PubArchive/thesis.ps.gz},
title = {Fast Numerical Solution of Exterior {H}elmholtz Problems with Radiation Boundary Condition by Imbedding},
year = {1994}
}
@inbook{ErnstGolub1992,
author = {Oliver G. Ernst and Gene H. Golub},
date-added = {2007-10-14 22:48:18 +0200},
date-modified = {2007-10-14 22:53:37 +0200},
editor = {A. Quarteroni},
journal = {Contemporary Mathematics},
mvpubtype = {bookchapter},
pdf = {PubArchive/ernst_golub.ps},
publisher = {AMS},
series = {Contemporary Mathematics},
title = {A Domain Decomposition Approach to Solving the {H}elmholtz Equation with a Radiation Boundary Condition},
volume = {157},
year = {1992}
}