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Arbeitsgruppe Numerik

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 3.002 (3. OG)

Adresse
Karlsruher Institut für Technologie
Institut für Angewandte und Numerische Mathematik 1
Englerstr. 2
76131 Karlsruhe

Öffnungszeiten:
Montag bis Freitag 10-11 Uhr

Kontakt:
Telefon:0721 608-42061
Fax:0721 608-43767
E-Mail:na-sek@math.kit.edu

Forschung

Seiteninhalt

Forschungsgebiete

  • Matrixfunktionen
  • (Rationale) Krylov-Unterraum-Verfahren
  • Trigonometrische Integratoren
  • Diskrete-Gradienten-Verfahren
  • Bildverarbeitung
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Preprints

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Artikel

[1] S. Buchholz, L. Gauckler, V. Grimm, M. Hochbruck und T. Jahnke
Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations
IMA J. Numer. Anal., pp. 1—18 (online first) (2017)
Preprint, Paper, BibTex

[2] T. Göckler und V. Grimm
Acceleration of contour integration techniques by rational Krylov subspace methods
J. Comp. Appl. Math., vol. 316, pp. 133—142 (2017)
Preprint, Paper, BibTex

[3] V. Grimm
Implementation of digcrete gradient methods for dissipative PDEs in image processing on GPUs
Proceedings of Geometric Numerical Integration and its Applications, MI Lecture Note Series, Kyushu University, Japan, vol. 74, pp. 69—71 (2017)
Preprint, Paper, BibTex

[4] V. Grimm und T. Göckler
Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $C_0$-semigroups
SIAM Journal on Numerical Analysis, vol. 55, no. 3, pp. 1483—1504 (2017)
Preprint, Paper, BibTex

[5] V. Grimm, R. I. McLachlan, D. I. McLaren, G. R. W. Quispel und C.-B. Schönlieb
Discrete gradient methods for solving variational image regularisation models
Journal of Physics. A. Mathematical and Theoretical, vol. 50, no. 29, pp. 0—21 (online first) (2017)
Preprint, Paper, BibTex

[6] T. Göckler und V. Grimm
Uniform approximation of $\varphi$-functions in exponential integrators by a rational Krylov subspace method with simple poles
SIAM J. Matrix Anal. Appl., vol. 35, no. 4, pp. 1467—1489 (2014)
Preprint, Paper, BibTex

[7] M. A. Botchev, V. Grimm und 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

[8] T. Göckler und V. Grimm
Convergence analysis of an extended Krylov subspace method for the approximation of operator functions in exponential integrators
SIAM Journal on Numerical Analysis, vol. 51, no. 4, pp. 2189—2213 (2013)
Preprint, Paper, BibTex

[9] E. Celledoni, V. Grimm, R. I. McLachlan, D. I. McLaren, D. O'Neale, B. Owren und G. R. W. Quispel
Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field'' method
J. Comput. Phys., vol. 231, pp. 6670—6789 (2012)
Preprint, Paper, BibTex

[10] V. Grimm
Resolvent Krylov subspace approximation to operator functions
BIT Numerical Mathematics, vol. 52, pp. 639—659 (2012)
Preprint, Paper, BibTex

[11] M. Gugat und V. Grimm
Optimal boundary control of the wave equation with pointwise control constraints
Comput. Optim. Appl., no. 1, pp. 123—147 (2011)
Preprint, Paper, BibTex

[12] V. Grimm und M. Gugat
Approximation of semigroups and related operator functions by resolvent series
SIAM Journal on Numerical Analysis, vol. 48, no. 5, pp. 1826—1845 (2010)
Preprint, Paper, BibTex

[13] V. Grimm und M. Hochbruck
Rational approximation to trigonometric operators
BIT, vol. 48, no. 2, pp. 215—229 (2008)
Preprint, Paper, BibTex

[14] V. Grimm und G. R. W. Quispel
Geometric integration methods that unconditionally contract volume
Appl. Num. Math., vol. 58, no. 8, pp. 1103—1112 (2008)
Preprint, Paper, BibTex

[15] 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

[16] V. Grimm und 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

[17] V. Grimm, S. Henn und K. Witsch
A higher-order PDE-based image registration approach
Numer. Linear Algebra Appl., vol. 13, pp. 339—417 (2006)
Preprint, Paper, BibTex

[18] Volker Grimm
A note on the Gautschi-type method for oscillatory second-order differential equations
Numer. Math., vol. 102, no. 1, pp. 61—66 (2005)
Preprint, Paper, BibTex

[19] Volker Grimm
On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
Numer. Math., vol. 100, no. 1, pp. 71—89 (2005)
Preprint, Paper, BibTex

[20] Volker Grimm
On the Use of the Gautschi-Type Exponential Integrator for Wave Equations
Springer-Verlag, Berlin Heidelberg, Numerical Mathematics and Advanced Applications, ENUMATH 2005, pp. 557—563 (2005)
Preprint, Paper, BibTex

[21] Volker Grimm und G. Reinout W. Quispel
Geometric integration methods that preserve Lyapunov functions
BIT, vol. 45, no. 4, pp. 709—723 (2005)
Preprint, Paper, BibTex

[22] Volker Grimm und Rudolf Scherer
A generalized W-transformation for constructing symplectic partitioned Runge-Kutta methods
BIT, vol. 43, no. 5, pp. 57—66 (2003)
Preprint, Paper, BibTex

[23] Volker Grimm
(Dissertation) Exponentielle Integratoren als Lange-Zeitschritt-Verfahren für oszillatorische Differentialgleichungen zweiter Ordnung
Heinrich-Heine Universität Düsseldorf, Lehrstuhl für Angewandte Mathematik (Juli 2002)
Preprint, Paper, BibTex