# zbMATH — the first resource for mathematics

## Grimm, Volker

Compute Distance To:
 Author ID: grimm.volker Published as: Grimm, Volker; Grimm, V. Homepage: http://na.math.kit.edu/grimm/?lang=en External Links: MGP
 Documents Indexed: 22 Publications since 2003, including 1 Book
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#### Co-Authors

 5 single-authored 4 Göckler, Tanja 4 Hochbruck, Marlis 4 Quispel, Gilles Reinout Willem 2 Gugat, Martin 2 McLachlan, Robert I. 2 McLaren, David I. 1 Botchev, Mike A. 1 Buchholz, Simone 1 Celledoni, Elena 1 Gauckler, Ludwig J. 1 Henn, Stefan 1 Jahnke, Tobias 1 O’Neale, Dion R. J. 1 Owren, Brynjulf 1 Railsback, Steven F. 1 Scherer, Rudolf 1 Schönlieb, Carola-Bibiane 1 Witsch, Kristian
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#### Serials

 4 BIT 3 SIAM Journal on Numerical Analysis 2 Numerische Mathematik 1 IMA Journal of Numerical Analysis 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Physics A: Mathematical and General 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 Numerical Linear Algebra with Applications 1 Journal of Physics A: Mathematical and Theoretical
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#### Fields

 19 Numerical analysis (65-XX) 7 Ordinary differential equations (34-XX) 5 Partial differential equations (35-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Information and communication theory, circuits (94-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

20 Publications have been cited 347 times in 273 Documents Cited by Year
Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184
Celledoni, E.; Grimm, V.; McLachlan, R. I.; McLaren, D. I.; O’Neale, D.; Owren, B.; Quispel, G. R. W.
2012
Individual-based modeling and ecology. Zbl 1085.92043
Grimm, Volker; Railsback, Steven F.
2005
Error analysis of exponential integrators for oscillatory second-order differential equations. Zbl 1093.65078
Grimm, Volker; Hochbruck, Marlis
2006
On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations. Zbl 1074.65097
Grimm, Volker
2005
Residual, restarting, and Richardson iteration for the matrix exponential. Zbl 1278.65052
Botchev, Mike A.; Grimm, Volker; Hochbruck, Marlis
2013
A note on the Gautschi-type method for oscillatory second-order differential equations. Zbl 1082.65080
Grimm, Volker
2005
Resolvent Krylov subspace approximation to operator functions. Zbl 1258.65052
Grimm, Volker
2012
Rational approximation to trigonometric operators. Zbl 1148.65075
Grimm, V.; Hochbruck, M.
2008
Geometric integration methods that preserve Lyapunov functions. Zbl 1094.65070
Grimm, V.; Quispel, G. R. W.
2005
Uniform approximation of $$\varphi$$-functions in exponential integrators by a rational Krylov subspace method with simple poles. Zbl 1416.65192
Göckler, Tanja; Grimm, Volker
2014
Convergence analysis of an extended Krylov subspace method for the approximation of operator functions in exponential integrators. Zbl 1278.65076
Göckler, Tanja; Grimm, Volker
2013
On the use of the Gautschi-type exponential integrator for wave equations. Zbl 1119.65353
Grimm, Volker
2006
Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052
Grimm, Volker; Gugat, Martin
2010
Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146
Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B.
2017
Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023
Gugat, Martin; Grimm, Volker
2011
A generalized $$W$$-transformation for constructing symplectic partitioned Runge-Kutta methods. Zbl 1024.65123
Grimm, V.; Scherer, R.
2003
Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations. Zbl 1404.65056
Buchholz, Simone; Gauckler, Ludwig; Grimm, Volker; Hochbruck, Marlis; Jahnke, Tobias
2018
A higher-order PDE-based image registration approach. Zbl 1174.94305
Grimm, Volker; Henn, Stefan; Witsch, Kristian
2006
Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $$C_0$$-semigroups. Zbl 1367.65070
Grimm, Volker; Göckler, Tanja
2017
Acceleration of contour integration techniques by rational Krylov subspace methods. Zbl 1372.65139
Göckler, T.; Grimm, V.
2017
Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations. Zbl 1404.65056
Buchholz, Simone; Gauckler, Ludwig; Grimm, Volker; Hochbruck, Marlis; Jahnke, Tobias
2018
Discrete gradient methods for solving variational image regularisation models. Zbl 1371.94146
Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B.
2017
Automatic smoothness detection of the resolvent Krylov subspace method for the approximation of $$C_0$$-semigroups. Zbl 1367.65070
Grimm, Volker; Göckler, Tanja
2017
Acceleration of contour integration techniques by rational Krylov subspace methods. Zbl 1372.65139
Göckler, T.; Grimm, V.
2017
Uniform approximation of $$\varphi$$-functions in exponential integrators by a rational Krylov subspace method with simple poles. Zbl 1416.65192
Göckler, Tanja; Grimm, Volker
2014
Residual, restarting, and Richardson iteration for the matrix exponential. Zbl 1278.65052
Botchev, Mike A.; Grimm, Volker; Hochbruck, Marlis
2013
Convergence analysis of an extended Krylov subspace method for the approximation of operator functions in exponential integrators. Zbl 1278.65076
Göckler, Tanja; Grimm, Volker
2013
Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method. Zbl 1284.65184
Celledoni, E.; Grimm, V.; McLachlan, R. I.; McLaren, D. I.; O&rsquo;Neale, D.; Owren, B.; Quispel, G. R. W.
2012
Resolvent Krylov subspace approximation to operator functions. Zbl 1258.65052
Grimm, Volker
2012
Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023
Gugat, Martin; Grimm, Volker
2011
Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052
Grimm, Volker; Gugat, Martin
2010
Rational approximation to trigonometric operators. Zbl 1148.65075
Grimm, V.; Hochbruck, M.
2008
Error analysis of exponential integrators for oscillatory second-order differential equations. Zbl 1093.65078
Grimm, Volker; Hochbruck, Marlis
2006
On the use of the Gautschi-type exponential integrator for wave equations. Zbl 1119.65353
Grimm, Volker
2006
A higher-order PDE-based image registration approach. Zbl 1174.94305
Grimm, Volker; Henn, Stefan; Witsch, Kristian
2006
Individual-based modeling and ecology. Zbl 1085.92043
Grimm, Volker; Railsback, Steven F.
2005
On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations. Zbl 1074.65097
Grimm, Volker
2005
A note on the Gautschi-type method for oscillatory second-order differential equations. Zbl 1082.65080
Grimm, Volker
2005
Geometric integration methods that preserve Lyapunov functions. Zbl 1094.65070
Grimm, V.; Quispel, G. R. W.
2005
A generalized $$W$$-transformation for constructing symplectic partitioned Runge-Kutta methods. Zbl 1024.65123
Grimm, V.; Scherer, R.
2003
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#### Cited by 419 Authors

 20 Wu, Xinyuan 12 Wang, Yushun 10 Wang, Bin 9 Miyatake, Yuto 7 Grimm, Volker 7 Karasözen, Bülent 7 Liu, Changying 7 Matsuo, Takayasu 6 Gong, Yuezheng 6 Uzunca, Murat 6 Zhao, Xiaofei 5 Bao, Weizhu 5 Cai, Jiaxiang 5 Güttel, Stefan 5 Li, Haochen 5 Owren, Brynjulf 5 Su, Chunmei 4 Celledoni, Elena 4 Dong, Xuanchun 4 Eidnes, Sølve 4 Hashimoto, Yuka 4 Hochbruck, Marlis 4 Jiang, Chaolong 4 McLachlan, Robert I. 4 Moret, Igor 4 Quispel, Gilles Reinout Willem 4 Sato, Shun 4 Shi, Wei 3 Calvo, Manuel 3 Cano, Begoña 3 Furihata, Daisuke 3 Ketcheson, David I. 3 Laburta, María Pilar 3 Li, Lu 3 Li, Yuwen 3 Liu, Hailiang 3 Montijano, Juan Ignacio 3 Nodera, Takashi 3 Petrovskii, Sergei V. 3 Qian, Xu 3 Rández, Luis 3 Ringholm, Torbjørn 3 Sogabe, Tomohiro 3 Song, Songhe 3 Sun, Zhengjie 3 Zhang, Shao-Liang 2 Al-Mohy, Awad H. 2 Anazawa, Masahiro 2 Berljafa, Mario 2 Botchev, Mike A. 2 Cai, Wenjun 2 Druskin, Vladimir 2 Ellis, John Richard 2 Ferrer, Jordi 2 Gauckler, Ludwig J. 2 Geurts, Bernard J. 2 Ginovart, Marta 2 Göckler, Tanja 2 Gugat, Martin 2 Higham, Nicholas J. 2 Hou, Baohui 2 Iserles, Arieh 2 Johnson, Leah R. 2 Kim, Pilwon 2 Kooij, Gijs L. 2 Lane, W. D. 2 Le Bris, Claude 2 Legoll, Frédéric 2 Liang, Dong 2 Lv, Zhongquan 2 Martin-Vergara, Francisca 2 McLaren, David I. 2 Meron, Ehud 2 Michels, Dominik Ludewig 2 Moore, Brian E. 2 Moreta, María Jesús 2 O’Neale, Dion R. J. 2 Ostermann, Alexander 2 Petrovskaya, Natalia B. 2 Prats, Clara 2 Ranocha, Hendrik 2 Remis, Rob F. 2 Ruan, Shigui 2 Rus, Francisco 2 Sarıaydın-Filibelioğlu, Ayşe 2 Schönlieb, Carola-Bibiane 2 Schweitzer, Julia 2 Song, Yongzhong 2 Tyson, Rebecca C. 2 Villatoro, Francisco R. 2 Wang, Qi 2 Wang, Yang 2 Wei, Guowei 2 Wilson, James B. 2 Wu, Gang 2 Xia, Jianlin 2 Yaguchi, Takaharu 2 Yan, JingYe 2 Yang, Siyang 2 Yang, Zhiguo ...and 319 more Authors
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#### Cited in 81 Serials

 21 Journal of Computational and Applied Mathematics 18 Journal of Computational Physics 17 BIT 15 SIAM Journal on Scientific Computing 12 Applied Mathematics and Computation 12 Applied Numerical Mathematics 12 Journal of Theoretical Biology 11 SIAM Journal on Numerical Analysis 11 Journal of Scientific Computing 9 Numerical Algorithms 8 Numerische Mathematik 6 Advances in Computational Mathematics 5 Computers & Mathematics with Applications 5 Bulletin of Mathematical Biology 5 Theoretical Population Biology 5 Japan Journal of Industrial and Applied Mathematics 4 Calcolo 4 Applied Mathematics Letters 3 Mathematical Biosciences 3 Mathematics of Computation 3 Discrete and Continuous Dynamical Systems 3 Natural Resource Modeling 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Computer Physics Communications 2 Mathematics and Computers in Simulation 2 Numerical Functional Analysis and Optimization 2 SIAM Journal on Matrix Analysis and Applications 2 Computational Mathematics and Mathematical Physics 2 Applied Mathematical Modelling 2 Linear Algebra and its Applications 2 Numerical Linear Algebra with Applications 2 ETNA. Electronic Transactions on Numerical Analysis 2 Engineering Analysis with Boundary Elements 2 Mathematical and Computer Modelling of Dynamical Systems 2 Communications in Nonlinear Science and Numerical Simulation 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Multiscale Modeling & Simulation 2 Journal of Agricultural, Biological, and Environmental Statistics 2 Journal of Computational Dynamics 1 Applicable Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Physics Letters. A 1 Applied Mathematics and Optimization 1 International Journal for Numerical Methods in Engineering 1 Journal of Approximation Theory 1 Physica D 1 ACM Transactions on Graphics 1 Numerical Methods for Partial Differential Equations 1 Journal of Economic Dynamics & Control 1 Annals of Operations Research 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Stochastic Processes and their Applications 1 Journal of Mathematical Imaging and Vision 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Electronic Journal of Probability 1 Mathematical Problems in Engineering 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications 1 Journal of Machine Learning Research (JMLR) 1 International Journal of Computational Methods 1 GAMM-Mitteilungen 1 Mathematical Modelling of Natural Phenomena 1 SIAM Journal on Imaging Sciences 1 Advances in Mathematical Physics 1 International Journal for Numerical Methods in Biomedical Engineering 1 Statistics and Computing 1 Arabian Journal of Mathematics 1 Journal of Applied Analysis and Computation 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 JSIAM Letters 1 SN Partial Differential Equations and Applications
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#### Cited in 34 Fields

 216 Numerical analysis (65-XX) 97 Partial differential equations (35-XX) 45 Dynamical systems and ergodic theory (37-XX) 42 Biology and other natural sciences (92-XX) 23 Ordinary differential equations (34-XX) 17 Fluid mechanics (76-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 12 Computer science (68-XX) 10 Probability theory and stochastic processes (60-XX) 10 Optics, electromagnetic theory (78-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Mechanics of particles and systems (70-XX) 8 Systems theory; control (93-XX) 7 Approximations and expansions (41-XX) 7 Operator theory (47-XX) 7 Statistical mechanics, structure of matter (82-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Statistics (62-XX) 6 Mechanics of deformable solids (74-XX) 5 Operations research, mathematical programming (90-XX) 5 Information and communication theory, circuits (94-XX) 4 Quantum theory (81-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)