Preprints
[1] S. Buchholz, B. Dörich and M. Hochbruck
On averaged exponential integrators for semilinear wave
equations with solutions of low-regularity
CRC 1173-Preprint, no. 2020/8, Karlsruhe Institute of Technology (2020)
Preprint, Paper, BibTex×@techreport{10.5445/IR/1000117802,
author = {S.~Buchholz and B.~D\"orich and M.~Hochbruck},
title = {On averaged exponential integrators for semilinear wave
equations with solutions of low-regularity},
year = {2020},
institution = {Karlsruhe Institute of Technology},
type = {CRC 1173-Preprint},
issn = {2365-662X},
number = {2020/8},
url = {https://www.waves.kit.edu/downloads/CRC1173_Preprint_2020-8.pdf},
}
[2] M. Hochbruck and J. Leibold
Finite element discretization of semilinear acoustic wave
equations with kinetic boundary conditions
CRC 1173-Preprint, no. 2019/26, Karlsruhe Institute of Technology (2020)
Preprint, Paper, BibTex×@techreport{10.5445/IR/1000105549,
author = {M.~Hochbruck and J.~Leibold},
title = {Finite element discretization of semilinear acoustic wave
equations with kinetic boundary conditions},
year = {2020},
institution = {Karlsruhe Institute of Technology},
type = {CRC 1173-Preprint},
issn = {2365-662X},
number = {2019/26},
url = {https://www.waves.kit.edu/downloads/CRC1173_Preprint_2019-26.pdf},
}
[3] C. Carle, M. Hochbruck and A. Sturm
On leapfrog-Chebyshev schemes
CRC 1173-Preprint, no. 2019/19, Karlsruhe Institute of Technology (2019)
Preprint, Paper, BibTex×@techreport{CarHocStu19*Olf-Cs,
author = {C.~Carle and M.~Hochbruck and A.~Sturm},
title = {On leapfrog-{C}hebyshev schemes},
year = {2019},
institution = {Karlsruhe Institute of Technology},
type = {CRC 1173-Preprint},
issn = {2365-662X},
number = {2019/19},
url = {https://www.waves.kit.edu/downloads/CRC1173_Preprint_2019-19.pdf},
}
[4] M. Hochbruck and J. Köhler
Error analysis of discontinuous Galerkin discretizations of a
class of linear wave-type problems
CRC 1173-Preprint, no. 2019/14, Karlsruhe Institute of Technology (2019)
Preprint, Paper, BibTex×@techreport{HocKoe19*,
author = {M.~Hochbruck and J.~K\"ohler},
title = {Error analysis of discontinuous Galerkin discretizations of a
class of linear wave-type problems},
year = {2019},
institution = {Karlsruhe Institute of Technology},
type = {CRC 1173-Preprint},
issn = {2365-662X},
number = {2019/14},
url = {http://www.waves.kit.edu/downloads/CRC1173_Preprint_2019-14.pdf},
}
[5] M. Hochbruck and M. E. Hochstenbach
Subspace extraction for matrix functions
preprint (2005)
Preprint, Paper, BibTex×@techreport{HocH05,
author = {M.~Hochbruck and M.~E.~Hochstenbach},
title = {Subspace extraction for matrix functions},
year = {2005},
institution = {Dept. of Math., Case Western Reserve University},
url = {http://na.math.kit.edu/download/papers/funext.pdf},
}
Papers
[1] M. Hochbruck, J. Leibold and A. Ostermann
On the convergence of Lawson methods for semilinear
stiff problems
Numer. Math., pp. 1—28, online first (2020)
Preprint, Paper, BibTex×@article{10.1007/s00211-020-01120-4,
author = {M.~Hochbruck and J.~Leibold and A.~Ostermann},
title = {On the convergence of {L}awson methods for semilinear
stiff problems},
journal = {Numer. Math.},
fjournal = {Numerische Mathematik},
year = {2020},
pages = {1--28, online first},
issn = {0029-599X},
doi = {10.1007/s00211-020-01120-4},
url = {https://doi.org/10.1007/s00211-020-01120-4},
}
[2] M. Hochbruck, B. Maier and C. Stohrer
Heterogeneous Multiscale Method for Maxwell's Equations
Multiscale Model. Sim., vol. 17, no. 4, pp. 1147—1171 (2019)
Preprint, Paper, BibTex×@article{doi:10.1137/18M1234072,
author = {M.~Hochbruck and B.~Maier and C.~Stohrer},
title = {Heterogeneous Multiscale Method for {M}axwell's Equations},
journal = {Multiscale Model. Sim.},
fjournal = {Multiscale Modeling \& Simulation},
volume = {17},
number = {4},
pages = {1147--1171},
year = {2019},
doi = {10.1137/18M1234072},
url = {https://doi.org/10.1137/18M1234072},
}
[3] M. Hochbruck and A. Sturm
Upwind discontinuous Galerkin space discretization and
locally implicit time integration for linear Maxwell's
equations
Math. Comp., vol. 88, no. 317, pp. 1121—1153 (2019)
Preprint, Paper, BibTex×@article{HocStu19,
author = {M.~Hochbruck and A.~Sturm},
title = {Upwind discontinuous {G}alerkin space discretization and
locally implicit time integration for linear {M}axwell's
equations},
journal = {Math. Comp.},
fjournal = {Mathematics of Computation},
year = {2019},
volume = {88},
number = {317},
pages = {1121--1153},
url = {https://doi.org/10.1090/mcom/3365},
}
[4] M. M. Müller, B. Maier, M. Hochbruck and C. Rockstuhl
Analytical and numerical analysis of linear and nonlinear
properties of an rf-SQUID based metasurface
Phys. Rev. B, vol. 99, no. 7, pp. 075401 (2019)
Preprint, Paper, BibTex×@article{MueMRH19,
author = {M.~M.~M\"uller and B.~Maier and M.~Hochbruck and C.~Rockstuhl},
title = {Analytical and numerical analysis of linear and nonlinear
properties of an rf-{SQUID} based metasurface},
year = {2019},
volume = {99},
number = {7},
pages = {075401},
journal = {Phys. Rev. B},
fjournal = {Physical Review B},
url = {https://doi.org/10.1103/PhysRevB.99.075401},
}
[5] M. Hochbruck, and J. Köhler
On the efficiency of the Peaceman—Rachford ADI-dG method
for wave-type problems
in Numerical Mathematics and Advanced Applications ENUMATH 2017 , edited by Radu, F.A., Kumar, K., Berre, I., Nordbotten, J.M. and
Pop and I.S. , Lecture Notes in Computational Science and Engineering , Springer International Publishing , vol. 126 pp. 135—144 (2019)
Preprint, Paper, BibTex×@inproceedings{HocK17,
author = {M.~Hochbruck and and J.~K\"ohler},
title = {On the efficiency of the {P}eaceman--{R}achford {ADI-dG} method
for wave-type problems},
booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2017},
year = {2019},
editor = {Radu, F.A. and Kumar, K. and Berre, I. and Nordbotten, J.M. and
Pop, I.S.},
volume = {126},
series = {Lecture Notes in Computational Science and Engineering},
pages = {135--144},
publisher = {Springer International Publishing},
url = {https://doi.org/10.1007/978-3-319-96415-7},
doi = {10.1007/978-3-319-96415-7},
}
[6] S. Buchholz, L. Gauckler, V. Grimm, M. Hochbruck and T. Jahnke
Closing the gap between trigonometric integrators and
splitting methods for highly oscillatory differential equations
IMA J. Numer. Anal., vol. 38, no. 1, pp. 57—74 (2018)
Preprint, Paper, BibTex×@article{BucGGHJ17,
author = {S.~Buchholz and L.~Gauckler and V.~Grimm and M.~Hochbruck and T.~Jahnke},
title = {Closing the gap between trigonometric integrators and
splitting methods for highly oscillatory differential equations},
year = {2018},
journal = {IMA J. Numer. Anal.},
fjournal = {IMA Journal of Numerical Analysis},
volume = {38},
number = {1},
pages = {57--74},
doi = {10.1093/imanum/drx007},
url = {https://doi.org/10.1093/imanum/drx007},
}
[7] D. Hipp, M. Hochbruck and C. Stohrer
Unified error analysis for non-conforming space discretizations of wave-type equations
IMA Journal of Numerical Analysis, pp. 1—40, online first (2018)
Preprint, Paper, BibTex×@article{HipHocSto18*Ueafn-csdow-te,
author = {D.~Hipp and M.~Hochbruck and C.~Stohrer},
title = {Unified error analysis for non-conforming space discretizations of wave-type equations},
journal = {IMA Journal of Numerical Analysis},
year = {2018},
pages = {1--40, online first},
doi = {10.1093/imanum/dry036},
url = {https://doi.org/10.1093/imanum/dry036},
}
[8] M. Hochbruck, T. Pažur and R. Schnaubelt
Error analysis of implicit Runge-Kutta methods for
quasilinear hyperbolic evolution equations
Numerische Mathematik, vol. 138, no. 3, pp. 557—579 (2018)
Preprint, Paper, BibTex×@article{HocPS18,
author = {M.~Hochbruck and T.~Pa\v{z}ur and R.~Schnaubelt},
title = {Error analysis of implicit {R}unge-{K}utta methods for
quasilinear hyperbolic evolution equations},
journal = {Numerische Mathematik},
volume = {138},
number = {3},
year = {2018},
pages = {557--579},
issn = {0945-3245},
doi = {10.1007/s00211-017-0914-6},
url = {https://doi.org/10.1007/s00211-017-0914-6},
}
[9] L. Fath, M. Hochbruck and C.V. Singh
A fast mollified impulse method for biomolecular atomistic simulations
J. Comp. Phys., vol. 333, pp. 180—198 (2017)
Preprint, Paper, BibTex×@article{FatHS16,
author = {L.~Fath and M.~Hochbruck and C.V.~Singh},
title = {A fast mollified impulse method for biomolecular atomistic simulations},
year = {2017},
pages = {180--198},
journal = {J. Comp. Phys.},
fjournal = {Journal of Computational Physics},
volume = {333},
issn = {0021-9991},
doi = {10.1016/j.jcp.2016.12.024},
url = {http://dx.doi.org/10.1016/j.jcp.2016.12.024},
}
[10] M. Hochbruck and T. Pažur
Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations
Numerische Mathematik, vol. 135, no. 2, pp. 547—569 (2017)
Preprint, Paper, BibTex×@article{HocP17,
author = {M.~Hochbruck and T.~Pa\v{z}ur},
title = {Error analysis of implicit {E}uler methods for quasilinear hyperbolic evolution equations},
year = {2017},
journal = {Numerische Mathematik},
volume = {135},
number = {2},
pages = {547--569},
issn = {0945-3245},
doi = {10.1007/s00211-016-0810-5},
url = {http://dx.doi.org/10.1007/s00211-016-0810-5},
}
[11] J. Deppler, B. Braun, A. Fidlin and M. Hochbruck
Convergence of viscoelastic constraints to nonholonomic idealization
European Journal of Mechanics - A/Solids, vol. 58, pp. 140—147 (2016)
Preprint, Paper, BibTex×@article{DepBFH16,
author = {J.~Deppler and B.~Braun and A.~Fidlin and M.~Hochbruck},
title = {Convergence of viscoelastic constraints to nonholonomic idealization},
year = {2016},
pages = {140--147},
journal = {European Journal of Mechanics - A/Solids},
volume = {58},
issn = {0997-7538},
doi = {10.1016/j.euromechsol.2016.01.003},
url = {http://www.sciencedirect.com/science/article/pii/S0997753816000048},
}
[12] M. Hochbruck and C. Stohrer
Finite element heterogeneous multiscale method for time-dependent
Maxwell's equations
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 (978-3-319-65870-4), pp. 269-281, online first (2016)
Preprint, Paper, BibTex×@article{HocSto16*fehmmftdmq,
author = {M.~Hochbruck and C.~Stohrer},
title = {Finite element heterogeneous multiscale method for time-dependent
{M}axwell's equations},
year = {2016},
pages = {269-281, online first},
journal = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 (978-3-319-65870-4)},
url = {https://doi.org/10.1007/978-3-319-65870-4_18},
}
[13] M. Hochbruck and A. Sturm
Error analysis of a second-order locally implicit method for
linear Maxwell's equations
SIAM J. Numer. Anal., vol. 54, no. 5, pp. 3167-3191 (2016)
Preprint, Paper, BibTex×@article{doi:10.1137/15M1038037,
author = {M.~Hochbruck and A.~Sturm},
title = {Error analysis of a second-order locally implicit method for
linear {M}axwell's equations},
journal = {SIAM J. Numer. Anal.},
volume = {54},
number = {5},
pages = {3167-3191},
year = {2016},
institution = {Karlsruhe Institute of Technology},
doi = {10.1137/15M1038037},
url = {http://dx.doi.org/10.1137/15M1038037},
}
[14] A. Demirel, J. Niegemann, K. Busch and M. Hochbruck
Efficient Multiple Time-Stepping Algorithms of Higher Order
J. Comp. Phys., vol. 285, pp. 133—148 (2015)
Preprint, Paper, BibTex×@article{DemNBH14,
author = {A.~Demirel and J.~Niegemann and K.~Busch and M.~Hochbruck},
title = {Efficient Multiple Time-Stepping Algorithms of Higher Order},
year = {2015},
journal = {J. Comp. Phys.},
volume = {285},
pages = {133--148},
url = {http://dx.doi.org/10.1016/j.jcp.2015.01.018},
}
[15] M. Hochbruck, T. Jahnke and R. Schnaubelt
Convergence of an ADI splitting for Maxwell's equations
Numerische Mathematik, vol. 129, pp. 535—561 (2015)
Preprint, Paper, BibTex×@article{HocJS15,
author = {M.~Hochbruck and T.~Jahnke and R.~Schnaubelt},
title = {Convergence of an {ADI} splitting for {Maxwell}'s equations},
year = {2015},
volume = {129},
pages = {535--561},
journal = {Numerische Mathematik},
doi = {10.1007/s00211-014-0642-0},
url = {http://dx.doi.org/10.1007/s00211-014-0642-0},
}
[16] M. Hochbruck and T. Pažur
Implicit Runge—Kutta methods and discontinuous Galerkin discretizations for linear Maxwell's equations
SIAM J. Numer. Anal., vol. 53, no. 1, pp. 485—507 (2015)
Preprint, Paper, BibTex×@article{HocP15,
author = {M.~Hochbruck and T.~Pa\v{z}ur},
title = {Implicit {R}unge--{K}utta methods and discontinuous {G}alerkin discretizations for linear {M}axwell's equations},
year = {2015},
journal = {SIAM J. Numer. Anal.},
volume = {53},
number = {1},
pages = {485--507},
url = {http://dx.doi.org/10.1137/130944114},
}
[17] M. Hochbruck, T. Pažur, A. Schulz, E. Thawinan and C. Wieners
Efficient time integration for discontinuous Galerkin
approximations of linear wave equations
ZAMM, vol. 95, no. 3, pp. 237—259 (2015)
Preprint, Paper, BibTex×@article{HocPSTW15,
author = {M.~Hochbruck and T.~Pa\v{z}ur and A.~Schulz and E.~Thawinan and C.~Wieners},
title = {Efficient time integration for discontinuous {Galerkin}
approximations of linear wave equations},
journal = {ZAMM},
volume = {95},
year = {2015},
number = {3},
pages = {237--259},
url = {http://dx.doi.org/10.1002/zamm.201300306},
}
[18] D. Hipp and M. Hochbruck
A preconditioned Krylov method for an exponential
integrator for non-autonomous parabolic systems
Oberwolfach Reports, vol. 11, no. 1, pp. 822—824 (2014)
Preprint, Paper, BibTex×@article{HipH14,
author = {D.~Hipp and M.~Hochbruck},
title = {A preconditioned {K}rylov method for an exponential
integrator for non-autonomous parabolic systems},
journal = {Oberwolfach Reports},
volume = {11},
year = {2014},
number = {1},
pages = {822--824},
url = {http://dx.doi.org/10.4171/OWR/2014/14},
}
[19] D. Hipp, M. Hochbruck and A. Ostermann
An exponential integrator for non-autonomous parabolic problems
ETNA, vol. 41, pp. 497—511 (2014)
Preprint, Paper, BibTex×@article{HipHO14,
author = {D.~Hipp and M.~Hochbruck and A.~Ostermann},
title = {An exponential integrator for non-autonomous parabolic problems},
year = {2014},
journal = {ETNA},
volume = {41},
pages = {497--511},
url = {http://etna.mcs.kent.edu/volumes/2011-2020/vol41/abstract.php?vol=41&pages=497-511},
}
[20] M. A. Botchev, V. Grimm and M. Hochbruck
Residual, restarting and Richardson iteration for the
matrix exponential
SIAM J. Sci. Comput., vol. 35, no. 3, pp. A1376-A1397 (2013)
Preprint, Paper, BibTex×@article{BotGH13,
author = {M.~A.~Botchev and V.~Grimm and M.~Hochbruck},
title = {Residual, restarting and Richardson iteration for the
matrix exponential},
year = {2013},
journal = {SIAM J. Sci. Comput.},
volume = {35},
number = {3},
pages = {A1376-A1397},
doi = {10.1137/110820191},
url = {http://dx.doi.org/10.1137/110820191},
}
[21] D. Hipp, M. Hochbruck and A. Ostermann
Exponential integrators for parabolic problems with time
dependent coefficients
Oberwolfach Reports, vol. 9, no. 4, pp. 3602—3606 (2012)
Preprint, Paper, BibTex×@article{HipHO12,
author = {D.~Hipp and M.~Hochbruck and A.~Ostermann},
title = {Exponential integrators for parabolic problems with time
dependent coefficients},
journal = {Oberwolfach Reports},
volume = {9},
year = {2012},
number = {4},
pages = {3602--3606},
url = {http://dx.doi.org/10.4171/OWR/2012/60},
}
[22] M. Hochbruck and A. Ostermann
Exponential multistep methods of Adams-type
BIT, vol. 51, pp. 889-908 (2011)
Preprint, Paper, BibTex×@article{number = 4,
author = {M.~Hochbruck and A.~Ostermann},
title = {Exponential multistep methods of Adams-type},
journal = {BIT},
volume = {51},
pages = {889-908},
year = {2011},
doi = {10.1007/s10543-011-0332-6},
url = {http://www.springerlink.com/content/y7663431k7573224/},
}
[23] M. Hochbruck and D. Löchel
A multilevel Jacobi-Davidson method for polynomial PDE eigenvalue problems arising in plasma physics
SIAM Journal on Scientific Computing, vol. 32, no. 6, pp. 3151—3169 (2010)
Preprint, Paper, BibTex×@article{HocL10,
author = {M.~Hochbruck and D.~L\"ochel},
title = {A multilevel {J}acobi-{D}avidson method for polynomial PDE eigenvalue problems arising in plasma physics},
year = {2010},
journal = {SIAM Journal on Scientific Computing},
volume = {32},
number = {6},
pages = {3151--3169},
keywords = {Polynomial eigenvalue problem, pde eigenvalue problem, Jacobi-Davidson method, multilevel method, parameter dependent problem, optimal scaling, drift instabilities},
doi = {10.1137/090774604},
url = {http://link.aip.org/link/?SCE/32/3151},
}
[24] M. Hochbruck and A. Ostermann
Exponential integrators
Acta Numerica, vol. 19, pp. 209-286 (2010)
Preprint (© Cambridge University Press), Paper, BibTex×@article{HocO10,
author = {M.~Hochbruck and A.~Ostermann},
title = {Exponential integrators},
journal = {Acta Numerica},
volume = {19},
pages = {209-286},
year = {2010},
doi = {10.1017/S0962492910000048},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7701740&fulltextType=RA&fileId=S0962492910000048},
copyright = {Cambridge University Press},
}
[25] M. Hochbruck and M. Hönig
On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems
Numerische Mathematik, vol. 115, no. 1, pp. 71—79 (2010)
Preprint, Paper, BibTex×@article{HocH10,
author = {M.~Hochbruck and M.~H\"onig},
title = {On the convergence of a regularizing {L}evenberg-{M}arquardt scheme for nonlinear ill-posed problems},
year = {2010},
journal = {Numerische Mathematik},
volume = {115},
number = {1},
pages = {71--79},
doi = {10.1007/s00211-009-0268-9},
url = {http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00211-009-0268-9},
}
[26] T. Tückmantel, A. Pukhov, J. Liljo and M. Hochbruck
Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator
IEEE Transactions on Plasma Science, vol. 38, no. 9, pp. 2383-2389 (2010)
Preprint, Paper, BibTex×@article{TuePLH10,
author = {T. T\"uckmantel and A. Pukhov and J. Liljo and M. Hochbruck},
title = {Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator},
year = {2010},
journal = {IEEE Transactions on Plasma Science},
volume = {38},
number = {9},
pages = {2383-2389},
doi = {10.1109/TPS.2010.2056706},
url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5535138},
}
[27] D. Löchel, M. Tokar, M. Hochbruck and D. Reiser
Effect of poloidal inhomogeneity in plasma parameters on edge anomalous transport
IOP, Physics of Plasmas, vol. 16, no. 4 (April 2009)
Preprint, Paper, BibTex×@article{LoeTHR0904,
author = {D.~L\"ochel and M.~Tokar and M.~Hochbruck and D.~Reiser},
title = {Effect of poloidal inhomogeneity in plasma parameters on edge anomalous transport},
publisher = {IOP},
year = {2009},
month = {04},
journal = {Physics of Plasmas},
volume = {16},
number = {4},
url = {http://link.aip.org/link/?PHP/16/044508},
doi = {10.1063/1.3121222},
}
[28] M. Hochbruck, M. Hönig and A. Ostermann
A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems
Inverse Problems, vol. 25 (2009)
Preprint, Paper, BibTex×@article{HocHO09b,
author = {M.~Hochbruck and M.~H\"onig and A.~Ostermann},
title = {A convergence analysis of the exponential {E}uler iteration for nonlinear ill-posed problems},
year = {2009},
journal = {Inverse Problems},
volume = {25},
url = {http://stacks.iop.org/0266-5611/25/075009},
doi = {075009},
}
[29] M. Hochbruck, M. Hönig and A. Ostermann
Regularization of nonlinear ill-posed problems by exponential integrators
M2NA, vol. 43, pp. 709-720 (2009)
Preprint, Paper, BibTex×@article{HocHO09a,
author = {M.~Hochbruck and M.~H\"onig and A.~Ostermann},
title = {Regularization of nonlinear ill-posed problems by exponential integrators},
year = {2009},
journal = {M2NA},
volume = {43},
pages = {709-720},
url = {http://dx.doi.org/10.1051/m2an/2009021},
}
[30] M. Hochbruck, A. Ostermann and J. Schweitzer
Exponential Rosenbrock-type methods
SIAM J. Numer. Anal., vol. 47, no. 1, pp. 786—803 (2009)
Preprint, Paper, BibTex×@article{HocOS09,
author = {M.~Hochbruck and A.~Ostermann and J.~Schweitzer},
title = {Exponential {R}osenbrock-type methods},
year = {2009},
journal = {SIAM J. Numer. Anal.},
volume = {47},
number = {1},
pages = {786--803},
url = {http://epubs.siam.org/doi/abs/10.1137/080717717},
doi = {10.1137/080717717},
}
[31] V. Grimm and M. Hochbruck
Rational approximation to trigonometric operators
BIT, vol. 48, no. 2, pp. 215—229 (2008)
Preprint, Paper, BibTex×@article{GriH08,
author = {V.~Grimm and M.~Hochbruck},
title = {Rational approximation to trigonometric operators},
year = {2008},
journal = {BIT},
volume = {48},
number = {2},
pages = {215--229},
url = {http://dx.doi.org/10.1007/s10543-008-0185-9},
}
[32] M. Hochbruck and J. Niehoff
Approximation of matrix operators applied to multiple vectors
Math. Comput. Simul., vol. 79, no. 4, pp. 1270—1283 (2008)
Preprint, Paper, BibTex×@article{HocN08,
author = {M.~Hochbruck and J.~Niehoff},
title = {Approximation of matrix operators applied to multiple vectors},
year = {2008},
journal = {Math. Comput. Simul.},
volume = {79},
number = {4},
pages = {1270--1283},
url = {http://dx.doi.org/10.1016/j.matcom.2008.03.016},
}
[33] C. Karle, J. Schweitzer, M. Hochbruck and K. H. Spatschek
A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems
J. Comp. Phys., vol. 227, pp. 7701—7719 (2008)
Preprint, Paper, BibTex×@article{KarSHS08,
author = {C.~Karle and J.~Schweitzer and M.~Hochbruck and K.~H.~Spatschek},
title = {A parallel implementation of a two-dimensional fluid laser-plasma integrator for stratified plasma-vacuum systems},
year = {2008},
journal = {J. Comp. Phys.},
volume = {227},
pages = {7701--7719},
url = {http://dx.doi.org/10.1016/j.jcp.2008.04.024},
}
[34] J. Liljo, A. Karmakar, A. Pukhov and M. Hochbruck
One dimensional electromagnetic relativistic PIC-hydrodynamic hybrid simulation code H-VLPL (Hybrid Virtual Laser Plasma Lab)
Computer Physics Communication, vol. 179, no. 6, pp. 371—379 (2008)
Preprint, Paper, BibTex×@article{LilKPH08,
author = {J.~Liljo and A.~Karmakar and A.~Pukhov and M.~Hochbruck},
title = {One dimensional electromagnetic relativistic {PIC}-hydrodynamic hybrid simulation code {H-VLPL} ({H}ybrid {V}irtual {L}aser {P}lasma {L}ab)},
year = {2008},
journal = {Computer Physics Communication},
volume = {179},
number = {6},
pages = {371--379},
url = {http://dx.doi.org/10.1016/j.cpc.2008.03.008},
}
[35] V. Grimm (joint work with M. Hochbruck)
Exponential integrators for highly oscillatory differential equations
Oberwolfach Reports, vol. 3, no. 1, pp. 868—869 (2006)
Preprint, Paper, BibTex×@article{Gri06,
author = {V.~Grimm (joint work with M.~Hochbruck)},
title = {Exponential integrators for highly oscillatory differential equations},
year = {2006},
journal = {Oberwolfach Reports},
volume = {3},
number = {1},
pages = {868--869},
}
[36] V. Grimm and M. Hochbruck
Error analysis of exponential integrators for oscillatory second-order differential equations
J. Phys. A: Math. Gen., vol. 39, pp. 5495—5507 (2006)
Preprint, Paper, BibTex×@article{GriH06,
author = {V.~Grimm and M.~Hochbruck},
title = {Error analysis of exponential integrators for oscillatory second-order differential equations},
year = {2006},
journal = {J. Phys. A: Math. Gen.},
volume = {39},
pages = {5495--5507},
url = {http://dx.doi.org/10.1088/0305-4470/39/19/S10},
}
[37] C. Karle, J. Schweitzer, M. Hochbruck, E. W. Laedke and K. H. Spatschek
Numerical solution of nonlinear wave equations in stratified dispersive media
J. Comp. Phys., vol. 216, pp. 138—152 (2006)
Preprint, Paper, BibTex×@article{KarSHLS06,
author = {C.~Karle and J.~Schweitzer and M.~Hochbruck and E.~W.~Laedke and K.~H.~Spatschek},
title = {Numerical solution of nonlinear wave equations in stratified dispersive media},
year = {2006},
journal = {J. Comp. Phys.},
volume = {216},
pages = {138--152},
url = {http://dx.doi.org/10.1016/j.jcp.2005.11.024},
}
[38] Marlis Hochbruck and Alexander Ostermann
Explicit integrators of Rosenbrock-type
Oberwolfach Reports, vol. 3, no. 2, pp. 1107—1110 (2006)
Preprint, Paper, BibTex×@article{HocO06,
author = {Marlis Hochbruck and Alexander Ostermann},
title = {Explicit integrators of {R}osenbrock-type},
year = {2006},
journal = {Oberwolfach Reports},
volume = {3},
number = {2},
pages = {1107--1110},
url = {http://www.ems-ph.org/journals/show_pdf.php?issn=1660-8933&vol=3&iss=2&rank=4},
}
[39] J. van den Eshof and M. Hochbruck
Preconditioning Lanczos approximations to the matrix exponential
SIAM J. Sci. Comp., vol. 27, no. 4, pp. 1438—1457 (2006)
Preprint, Paper, BibTex×@article{vdEshH06,
author = {J.~van den Eshof and M.~Hochbruck},
title = {Preconditioning {L}anczos approximations to the matrix exponential},
year = {2006},
journal = {SIAM J. Sci. Comp.},
volume = {27},
number = {4},
pages = {1438--1457},
url = {http://dx.doi.org/10.1137/040605461},
}
[40] Marlis Hochbruck and Alexander Ostermann
Explicit exponential Runge-Kutta methods for semilinear parabolic problems
SIAM J. Numer. Anal., vol. 43, no. 3, pp. 1069—1090 (2005)
Preprint, Paper, BibTex×@article{HocO05b,
author = {Marlis Hochbruck and Alexander Ostermann},
title = {Explicit exponential {R}unge-{K}utta methods for semilinear parabolic problems},
year = {2005},
journal = {SIAM J. Numer. Anal.},
volume = {43},
number = {3},
pages = {1069--1090},
url = {http://dx.doi.org/10.1137/040611434},
}
[41] Marlis Hochbruck and Alexander Ostermann
Exponential Runge-Kutta methods for parabolic problems
Appl. Numer. Math., vol. 53, no. 2—4, pp. 323—339 (2005)
Preprint, Paper, BibTex×@article{HocO05a,
author = {Marlis Hochbruck and Alexander Ostermann},
title = {Exponential {R}unge-{K}utta methods for parabolic problems},
year = {2005},
journal = {Appl. Numer. Math.},
volume = {53},
number = {2--4},
pages = {323--339},
url = {http://authors.elsevier.com/sd/article/S0168927404001400},
}
[42] Marlis Hochbruck and Christian Lubich
On Magnus integrators for time-dependent Schrödinger equations
SIAM J. Numer. Anal., vol. 41, no. 3, pp. 945—963 (2003)
Preprint, Paper, BibTex×@article{HocL03,
author = {Marlis Hochbruck and Christian Lubich},
title = {On Magnus integrators for time-dependent {S}chr\"odinger equations},
year = {2003},
journal = {SIAM J. Numer. Anal.},
volume = {41},
number = {3},
pages = {945--963},
url = {http://dx.doi.org/10.1137/S0036142902403875},
}
[43] Marlis Hochbruck and Jörg-M. Sautter
Mathematik fürs Leben am Beispiel der Computertomographie
Mathematische Semesterberichte, vol. 49, no. 1, pp. 95—113 (2002)
Preprint, Paper, BibTex×@article{HocS02,
author = {Marlis Hochbruck and J\"org-M. Sautter},
title = {Mathematik f\"urs {L}eben am {B}eispiel der {C}omputertomographie},
year = {2002},
journal = {Mathematische Semesterberichte},
volume = {49},
number = {1},
pages = {95--113},
url = {http://dx.doi.org/10.1007/s005910200042},
}
[44] Marlis Hochbruck and Christian Lubich
A Gautschi-type method for oscillatory second-order differential equations
Numer. Math., vol. 83, no. 3, pp. 403—426 (1999)
Preprint, Paper, BibTex×@article{HocL99a,
author = {Marlis Hochbruck and Christian Lubich},
title = {A {G}autschi-type method for oscillatory second-order differential equations},
year = {1999},
journal = {Numer. Math.},
volume = {83},
number = {3},
pages = {403--426},
url = {http://dx.doi.org/10.1007/s002110050456},
}
[45] Marlis Hochbruck and Christian Lubich
Exponential integrators for quantum-classical molecular dynamics
BIT, vol. 39, no. 4, pp. 620—645 (1999)
Preprint, Paper, BibTex×@article{HocL99b,
author = {Marlis Hochbruck and Christian Lubich},
title = {Exponential integrators for quantum-classical molecular dynamics},
year = {1999},
journal = {BIT},
volume = {39},
number = {4},
pages = {620--645},
url = {http://dx.doi.org/10.1023/A:1022335122807},
}
[46] M. Hochbruck and Ch. Lubich
A bunch of time integrators for quantum/classical molecular dynamics
pp. 421—432 in Algorithms for Macromolecular Modelling , edited by P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich and R.D. Skeel , Lecture Notes in Computational Science and Engineering , Springer (1999)
Preprint, Paper, BibTex×@incollection{HocL99LN,
author = {M. Hochbruck and Ch. Lubich},
title = {A bunch of time integrators for quantum/classical molecular dynamics},
booktitle = {Algorithms for Macromolecular Modelling},
editor = {P. Deuflhard and J. Hermans and B. Leimkuhler and A. Mark and S. Reich and R.D. Skeel},
series = {Lecture Notes in Computational Science and Engineering},
publisher = {Springer},
pages = {421--432},
year = {1999},
url = {http://na.math.kit.edu/download/papers/bunch.pdf},
}
[47] Marlis Hochbruck
A numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems
in Special issue on "High Performance Algorithms for Structured Linear Systems". Volume II in the series "Advances in the Theory of Computation and Computational Mathematics" edited by P. Arbenz,
M. Paprzycki, and A. Sameh., vol. 2 (1998)
Preprint, Paper, BibTex×@article{Hoc98,
author = {Marlis Hochbruck},
title = {A numerical comparison of look-ahead {L}evinson and {S}chur algorithms for non-{H}ermitian {T}oeplitz systems},
year = {1998},
journal = {in Special issue on \"High Performance Algorithms for Structured Linear Systems\". Volume II in the series "Advances in the Theory of Computation and Computational Mathematics" edited by P. Arbenz,
M. Paprzycki, and A. Sameh.},
volume = {2},
url = {http://na.math.kit.edu/download/papers/num_toeplitz.pdf},
}
[48] Marlis Hochbruck and Christian Lubich
Error analysis of Krylov methods in a nutshell
SIAM J. Sci. Comput., vol. 19, no. 2, pp. 695—701 (1998)
Preprint, Paper, BibTex×@article{HocL98a,
author = {Marlis Hochbruck and Christian Lubich},
title = {Error analysis of {K}rylov methods in a nutshell},
year = {1998},
journal = {SIAM J. Sci. Comput.},
volume = {19},
number = {2},
pages = {695--701},
url = {http://dx.doi.org/10.1137/S1064827595290450},
}
[49] Marlis Hochbruck, Christian Lubich and Hubert Selhofer
Exponential integrators for large systems of differential equations
SIAM J. Sci. Comp., vol. 19, no. 5, pp. 1552—1574 (1998)
Preprint, Paper, BibTex×@article{HocLS98,
author = {Marlis Hochbruck and Christian Lubich and Hubert Selhofer},
title = {Exponential integrators for large systems of differential equations},
year = {1998},
journal = {SIAM J. Sci. Comp.},
volume = {19},
number = {5},
pages = {1552--1574},
url = {http://dx.doi.org/10.1137/S1064827595295337},
}
[50] Marlis Hochbruck
Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
J. Comp. Appl. Math., vol. 86, no. 1, pp. 219—236 (1997)
Preprint, Paper, BibTex×@article{Hoc97,
author = {Marlis Hochbruck},
title = {Further optimized look-ahead recurrences for adjacent rows in the {P}ad\'e table and {T}oeplitz matrix factorizations},
year = {1997},
journal = {J. Comp. Appl. Math.},
volume = {86},
number = {1},
pages = {219--236},
url = {http://dx.doi.org/10.1016/S0377-0427(97)00157-X},
}
[51] Marlis Hochbruck and Christian Lubich
On Krylov subspace approximations to the matrix exponential operator
SIAM J. Numer. Anal., vol. 34, no. 5, pp. 1911—1925 (1997)
Preprint, Paper, BibTex×@article{HocL97,
author = {Marlis Hochbruck and Christian Lubich},
title = {On {K}rylov subspace approximations to the matrix exponential operator},
year = {1997},
journal = {SIAM J. Numer. Anal.},
volume = {34},
number = {5},
pages = {1911--1925},
url = {http://dx.doi.org/10.1137/S0036142995280572},
}
[52] Martin H. Gutknecht and Marlis Hochbruck
Optimized look-ahead recurrences for adjacent rows in the Padé table
BIT, vol. 36, no. 2, pp. 264—286 (1996)
Preprint, Paper, BibTex×@article{% FEHLT!!!,
author = {Martin H. Gutknecht and Marlis Hochbruck},
title = {Optimized look-ahead recurrences for adjacent rows in the {P}ad\'e table},
year = {1996},
journal = {BIT},
volume = {36},
number = {2},
pages = {264--286},
url = {http://dx.doi.org/10.1007/BF01731983},
}
