Prof. Dr. Gerald Warnecke
Prof. Dr. Gerald Warnecke
Institute of Analysis and Numerics
Research Interests
- Convergence, stability and accuracy of numerical methods, for partial differential equations, analysis and development of numerical methods, finite element methods, finite volume methods, finite difference methods, dicontinuous Galerkin methods, kinetic schemes
- Theoretical and numerical study of systems of conservation and balance, especially in gas dynamics, multi phase mixtures, laser induced gas bubbles
- Riemann problems for systems of hyperbolic conservation laws, resonant waves, phase transitions
- Analytical and numerical methods for population balance equations in chemical and bio process engineering, existence and uniqueness of solutions, cell average method, finite volume schemes, discontinuous Galerkin methods
Current Courses
| SoSe2021 |
Previous Courses
Degrees: | |
|---|---|
| 1981 | Diploma in mathematics, Freie Universität Berlin, Germany |
| 1985 | Dr. rer. nat., Freie Universität Berlin, Advisor: K. Doppel |
| 1992 | Dr. habil., Universität Stuttgart, Germany; Postdoc Advisor: W. Wendland |
Positions: | |
|---|---|
| 04/1981 - 12/1986 | Scientific assistant, Freie Universität Berlin, Germany |
| 01/1987 - 09/1992 | Scientific employee, University Stuttgart |
| 10/1992 - 03/1994 | Oberassistent (C2), University Stuttgart |
| 1994 | Substitute Professor (C3), Technische Universität München |
| 09/1994 - present | Chair for Numerical Mathematics, Otto-von-Guericke Universität Magdeburg |
| 1994 - 2002 | Member and applicant of the Research school "Modeling, Computation and Identification of mechanical systems" |
| 1994 2002, 2005 - | Member of the faculty council |
| 1995 - 1998 | Member of the senate room planning commitee of the university |
| 1995- 2002 | Member of the senate budget planning commitee of the university |
| 1996 - 1999 | Director of the Institute for Analysis and Numerics |
| 1996 - 2003 | Co-ordinator DFG priority research program "Analysis and numerics of conservation laws" Cooperation of researchers in mathematical analysis, numerical mathematics, astrophysics and engineering |
| 1997 - 2003 | Applicant and member of the DFG research group "Dynamics of Boundaries in Structure Formation Processes" in Magdeburg |
| 2000 - 2002 | Vice-dean of the Faculty of Mathematics |
| 2002 - 2019 |
Member and vice-speakerer/speaker of the DFG-Graduate School 828 and 1554 "Micro-Macro-Interactions in Structured Media and Particle Systems" |
| 2002 - 2005 | Member of the university senate |
| 2005 - 2006 | Dean of the Faculty of Mathematics |
| 2006 - 2012 | Vice-dean of the Faculty of Mathematics |
| 2007 - 2013 | Member and vice-speaker of the "International Max-Planck Research School for Analysis, Design and Optimization in Chemical and Biochemical Process Engineering (IMPRS)" |
| 2008 - 2012 |
Member of the university senate |
| since 2009 | Scientific Director of the "Otto-von-Guericke Graduate Academy" |
| since 2013 | Member and vice-speaker of the "Max-Planck Research School (IMPRS) for Advanced Methods in Process and Systems Engineering - IMPRS ProEng Magdeburg" |
| since 04/2022 | retired |
Head:
Prof. Dr. Gerald Warnecke
Secretary:
Stephanie Wernicke
Research assistants: |
|---|
| apl. Prof. Matthias Kunik |
Visiting scientists: | |
|---|---|
| Dr. Imad Barghouti (Jerusalem, DAAD) | (12.07.-12.09.2003) |
| Dr. Qiangchang Ju (P.R. China, DFG) | (27.09.03-31.01.2004) |
| Prof. Dr. Jiequan Li (P. R. China) | (Jan. - Sep. 1999, 29.05.04-25.05.2005, 21.06.-10.07.2008, 26.08.-05.09.2009) |
| Prof. Dr. Hailiang Liu (P. R. China, A. v. Humboldt-Stiftung, DFG) | (1.7.1997 - 31.12.1999, 27.11.-18.12.2014) |
| Prof. Dr. P. Prasad (Indien, A. v. Humboldt-Stiftung) | (30.09.03-29.02.2004) |
| Prof. Dr. Naji Qatanani (Palästina) | (1.6.1999 - 31.8.1999, 1.7.2000 - 31.8.2000, 1.10.2002 - 31.7.2003, 16.12.04-31.01.2005) |
| Dr. Jorge Salazar (Portugal, DFG) | (1.2.2001 - 31.6.2002) |
| Prof. Dr. Subbiah Sundar (Indien, DAAD) | (01.07.-22.07.2003, 05.05.-05.08.2005) |
| Prof. Huazhong Tang (P. R. China, A. v. Humboldt-Stiftung) | (1.10.2002 - 30.9.2003) |
| Prof. Dr. J. Wang (P. R. China, DFG) | (Nov.1996 - Aug.1997, 20.04.1999 - 26.06.1999)(11.10.02-11-11.02) |
| Prof. Dr. Xiaozhong Yang (P. R. China) | (27.11.2005-27.11.2006) |
| Dr. Yousef Zahaykah (Palästina) | (01.04.1998-01.10.2004) |
| Prof. Dr. Hui Zhang (P. R. China, A. v. Humboldt-Stiftung) | (01.11.2007 - 30.04.2008) |
| Dr. Ahmed Bagabir (Jemen, DAAD) | (04.08.-18.08.2009, 01.07.-15.08.2015) |
Former research assistants: |
|---|
| M.Sc. Bolaji Adesokan |
| Dr. Nikolai Andrianov (Schlumberger, Moskau) |
| Dr. Sergey Chernigovski |
| Prof. Dr. Etienne Emmerich |
| Jochen Gilbert |
| Dipl.-Math. Robin Gröpler |
| Dr. Maren Hantke |
| Prof. Dr. Christiane Helzel |
| Dr. Uwe Iben (Robert Bosch AG, Stuttgart) |
| Karin Jaschke |
| Prof. Dr. Jitendra Kumar (IIT Kharagpur) |
| Prof. Dr. Maria Lukácová (ehemals Tschechische Republik, TU Hamburg Harburg, jetzt Univ. Mainz) |
| Dr. Jun Pan, M.Sc. (ehemals P. R. China, jetzt Ames, Iowa, USA) |
| Prof. Dr. Shamsul Qamar (COMSATS of Information Technology, Islamabad, Pakistan) |
| Dipl.-Math. Michael Rother |
| M.Sc. Shaohua Yu |
Former doctoral students: | |
|---|---|
| Prof. Dr. Christiane Helzel | "Numerical Approximation of Conservation Laws with Stiff Source Term for the Modelling of Detonation Waves" 2000 |
| Dr. Jun Pan, MSc | 2000 |
| Dr. Yousef Zahaykah | 2002 |
| Dr. Nikolai Andrianov | "Analytical and numerical investigation of two-phase flows" 2003 |
| Prof. Dr. Shamsul Qamar | "Kinetic Schemes for the Relativistic Hydrodynamics" 2003 |
| Dr. Qurrat-Ul-Ain | "Multidimensional Schemes for Hyperbolic Conservation Laws on Triangular Meshes" 2005 |
| Dr. Wolfram Heineken | "Adaptive Verfahren zur numerischen Berechnung von Reaktions-Diffusions-Systemen" 2005 |
| Dr. Rüdiger Müller | "Numerische Simulation dendritischen Kristallwachstums" 2005 |
| Prof. Dr. Jitendra Kumar | "Numerical approximations of population balance equations in particulate systems" 2006 |
| Dr. Suresh Nadupuri | "Numerical study of drying in porous media" 2007 |
| Dr. Nagaiah Chamakuri | "Adaptive numerical simulation of reaction-diffusion systems" 2007 |
| Dr. Narni Nageswara Rao | "Simulations for Modelling of Population Balance Equations of Particulate Processes using the Discrete Particle Model (DPM)"" 2008 |
| Dr. Ankik Kumar Giri | "Mathematical and numerical analysis of coagulation-fragmentation equations" 2010 |
| Dr. Ali Zein | "Numerical methods for multiphase mixture conservation laws with phase transition" 2010 |
| Dr. Rajesh Kumar | "Numerical analysis of finite volume schemes for population balance equations" 2011 |
| Dr. Vincent Ssemaganda | "The Dynamics of the Becker-Döring Model of Nucleation" 2011 |
| Dr. Shumaila Javeed | "Analysis and Numerical Investigation of Dynamic Models for Liquid Chromotography" 201 |
| Dr. Ee Han | "Exact Riemann solutions to two selected resonant hyperbolic systems" 2013 |
| Dr. Carlos Cueto Camejo | "The Singular Coagulation and Coagulation-Fragmentation Equations" 2013 |
| Dr. Yaser Al-Kurdi | "Numerical Simulation Schemes for Inhomogeneous Convection-Diffusion Systems Modelin Fluidized Beds" 2017 |
| Dr. Jared Okiro | "Analytical and Numerical Investigation of an Intracellular Calcium Dynamics Model" 2017 |
| Dr. Abdulatif Badenjki | "The PNPM schemes for the one dimensional hyperbolic conservation laws" 2018 |
| Dr. Sebastian Bannasch | "Die Zeitseparationstechnik - eine effiziente modellbasierte Rekonstruktionstechnik für die computertomographische Perfusionsbildgebung " 2019 |
| Dr. Taj Munir | "Analysis of coupling interface problems for bi-domain diffusion equations" 2020 |
| M.Sc. Adnan Hayat | |
| M.Sc. Ahmad Al Mhamad |
Diploma and master theses: |
|---|
| Steffen Leutgeb (1993) |
| Martin Mittnacht (1993) |
| Jochen Gilbert (1994) |
| Karin Jaschke (1994) |
| Thomas Casper (1998) |
| Nico Krzebek (1998) |
| Kathrin Schmidt (2000) |
| Dipl.- Ing. Jan Blumschein (2002) |
| Thilo Moshagen (2004) |
| Nadine Aden (2007) |
| Matthias Würkner (2008) |
| Robin Gröpler (2010) |
| Michael Rother (2010) |
| Conrad Küchler (2011) |
| Stefanie Kabelitz (2012) |
| Steffen Heuer (2013) |
| Sebastian Bannasch (2013) |
| Constantin Kwiatkowski (2014) |
organized Conferences since 2000
| February 28 - March 03, 2000 | Conference "Eighth International Conference on Hyperbolic Problems",Magdeburg | with H. Freistühler (Aachen) |
| June 25 - 28, 2000 | "Symposium on Entropy", Dresden | withA. Greven (Erlangen) and G.Keller (Erlangen) |
| September 16 - 21, 2000 | 5th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with D. Kröner (Freiburg) |
| January 31 - February 2, 2001 | Colloquium for the Contuniation for the DFG-Program "Analysis und numerics of conservation laws" (ANumE), Magdeburg | |
| February 03 - 06, 2001 | "Continuum Physics and Nonlinear Partial Differential Equations" a conference in honour of Constantine M. Dafermos, Heidelberg | with J. Ball, H. Freistühler, W. Jäger, S. Müller, D. Serre, A. Tzavaras |
| September 15 - 21, 2002 | "6th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with D. Kröner (Freiburg) |
| September 30 - October 03, 2002 | "Analysis of Linear and Nonlinear Hyperbolic Systems of Partial Differential Equations", Potsdam | with J. Härterich (Berlin), B.-W. Schulze (Potsdam) |
| October 07 - 11, 2002 | "German-Chinese Workshop on Partial Differential Equations", Potsdam, | with C. Hua (Wuhan), B.-W. Schulze (Potsdam), C. Shuxing (Shanghai), I. Witt (Potsdam) |
| September 03 - 05, 2003 | "Abschlusskolloquium des DFG-Schwerpunktprogramms (ANumE)", Magdeburg | |
| March 01 - 04, 2004 | Workshop "Schemes for multidimensional wave structures in hyperbolic systems", Hamburg | with M. Lukacova (Hamburg), S. Noelle (Aachen) Workshop |
| August 08 - September 04, 2004 | "7th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with D. Kröner (Freiburg) |
| March 07 - 09, 2005 | Workshop on "Methods for the efficient resolution of NAVIER-STOKES and HYPERBOLIC SYSTEMS with source terms", Magdeburg | with L. Tobiska (Magdeburg) |
| June 06, 2006 | Mini-Workshop on "Methods for the efficient resolution of NAVIER-STOKES and HYPERBOLIC SYSTEMS with source terms", Magdeburg | |
| September 09 - 15, 2007 | "8th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke (Magdeburg) |
| September 06 - 09, 2009 | "9th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke (Magdeburg) |
| September 06- 12, 2011 | "10th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke (Magdeburg) |
| September 08 - 09, 2013 | "11th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke (Magdeburg) |
| September 13 - 19, 2015 | "12th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke and F. Thein (Magdeburg) |
| September 17 - 23, 2017 | "13th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke and F. Thein (Magdeburg) |
| September 08 - 14, 2019 | "14th Hirschegg Workshop on Conservation Laws", Hirschegg, Kleinwalsertal | with M. Hantke (Halle) and F. Thein (Magdeburg) |
2023
Hantke, Maren; Matern, Christoph; Warnecke, Gerald
A new method to discretize a model for isothermal flow with a multi-component equation of state.
In: Journal of Computational and Applied Mathematics 422 (2023) 114876.
2021
Kunik, Matthias; Warnecke, Gerald
Radially symmetric solutions of the ultra-relativistic Euler equations
In: Methods and Applications of Analysis, Volume 28 (2021), Number 4
2020
Warnecke, Gerald
Ein Brief von C.F. Gauß an C.L. Gerling - kleinste Fehlerquadrate und das Gauß-Seidel-Verfahren
In: Mathematische Semesterberichte - Berlin: Springer, Bd. 67.2020, S. 57-84
2019
Theoretical analysis of forced segmented temperature gradients in liquid chromatography
In: Processes - Basel: MDPI, Volume 7 (2019), 1, Artikel 846
Theoretical and numerical studies of the PNPM DG schemes in one space dimension
In: Applications of mathematics - Dordrecht [u.a.]: Springer Science + Business Media B.V, Bd. 64.2019, 6, S. 599-635
Book contribution
Zahl oder Menge - über grundlegende Formen der Mathematik
In: Ästhetik & Artikulation - Münster: Waxmann, S. 191-204, 2019 - (Dialog der Wissenschaften; 3)
2018
Noise reduction in perfusion imaging using data-driven prior knowledge
In: Clinical neuroradiology - München: Urban & Vogel, Vol. 28.2018, Suppl. 1, Abstr. 288, S. S100-S101
Multiscale modeling and numerical simulation of calcium cycling in cardiac myocytes
In: Multiscale modeling & simulation - Philadelphia, Pa: SIAM, Bd. 16.2018, 3, S. 1115-1145
Time separation technique - accurate solution for 4D C-Arm-CT perfusion imaging using a temporal decomposition model
In: Medical physics - Hoboken, NJ: Wiley, Bd. 45.2018, 3, S. 1080-1092
Buchbeitrag
Numerical solutions for a weakly hyperbolic dispersed two-phase flow model
In: Theory, Numerics and Applications of Hyperbolic Problems I: Aachen, Germany, August 2016 - Cham: Springer International Publishing, S. 665-675, 2018 - (Springer Proceedings in Mathematics & Statistics; 236)
2017
Dynamische Perfusionsbildgebung mit C-Arm-System
In: Clinical neuroradiology: official publication of the German, Austrian and Swiss societies of neuroradiology - München: Urban & Vogel, Vol. 27.2017, Suppl. 1, Art. 311, S. S46
Robust computation of perfusion maps for spatiotemporal model-based CT reconstructionsons
In: Recent progress and developments: 3rd Conference on Image-Guided Interventions & Focus Neuroradiologie, November 6 and 7, 2017, Magdeburg, Germany : abstract book - Magdeburg, 2017, Art. ID47, S. 31 ; [Konferenz: 3rd Conference on Image-Guided Interventions & Focus Neuroradiologie, Magdeburg, Germany, November 6 and 7, 2017]
Hallak, Bassem; Specht, Eckehard; Herz, Fabian; Gröpler, Robin; Warnecke, Gerald
Influence of particle size distribution on the limestone decomposition in single shaft kilns
In: Energy procedia - Amsterdam [u.a.]: Elsevier, Bd. 120.2017, S. 604-611
2016
A compaqct algorithm for a model-based perfusion reconstruction technique
In: IMA Conference on Numerical Linear Algebra und Optimization: Wednesday 7 - Friday 9 September 2016, University of Birmingham ; abstracts book and delegate list - Birmingham: Institut of Mathematics & its Applications, S. 36-37 ; [Kongress: 5th IMA Conference on Numerical Linear Algebra und Optimization, Birmingham, UK, 7-9 September, 2016]
Simulation of limestone calcination in normal shaft kilns, Part 3: Influence of particle size distribution and type of limestone
In: Cement, lime, gypsum - Gütersloh: Bauverl. BV, Bd. 69.2016, 3, S. 64-68
2015
Acceleration of a regularized Algebraic Reconstruction Technique evaluated with a simulation of computed tomography
In: IMA Conference on Numerical Methods for Simulation: Tuesday 1 - Friday 4 September 2015, Mathematical Institute, University of Oxford ; abstracts book and delegate list - Oxford: Univ., S. 17
Koeffizientenbasierte Algebraische Rekonstruktions-Technik für modellbasierte Perfusionsbildgebung
In: IGIC 2015: 2. Image-Guided Interventions Conference, 2. - 3. November 2015, Mannheim ; Abstractband - Vorträge - Mannheim, S. 19 ; [Beitrag auf USB-Stick]
An optimal relaxation of the algebraic reconstruction technique for CT imaging
In: Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine: proceedings - Newport, 2015, 2015, Art. Th21, S. 622-625
Simulation of the limestone calcination in normal shaft kilns
In: 10th European Conference on Industrial Furnaces and Boilers: INFUB ; Gaia (Porto), Hotel Holiday Inn Gaia, Portugal, 7 - 10 April 2015 - Gaia (Porto), insges. 10 S.
Regular solutions to the coagulation equations with singular kernels
In: Mathematical methods in the applied sciences - Chichester, West Sussex: Wiley, Bd. 38.2015, 11, S. 2171-2184
Simulation of limestone calcination in normal shaft kilns - Part 1 - mathematical model
In: Cement, lime, gypsum - Gütersloh: Bauverl. BV, 9, S. 66-71, 2015
Simulation of limestone calcination in normal shaft kilns - Part 2: influence of process parameters
In: Cement, lime, gypsum - Gütersloh: Bauverl. BV, 10, S. 46-50, 2015
The singular kernel coagulation equation with multifragmentation
In: Mathematical methods in the applied sciences - Chichester, West Sussex: Wiley, Bd. 38.2015, 14, S. 2953-2973
Simulation of limestone calcination in normal shaft kilns - mathematical model
In: ZKG international: Bundesverband der Deutschen Zementindustrie ; Bundesverband der Deutschen Kalkindustrie ; Bundesverband der Gips- und Gipsbauplattenindustrie - Walluf: Bauverl, Bd. 68.2015, 9, S. 66-71
2014
An implicit optimization approach for the Kaczmarz method applied to algebraic reconstruction techniques for computed tomography
In: 4th IMA Confernece on Numerical Linear Algebra and Optimisation - Birmingham: Univ., S. 10, 2014 ; Kongress: IMA Confernece on Numerical Linear Algebra and Optimisation 4 (Birmingham : 2014.09.03-05)
Optimale Relaxation der algebraischen Rekonstruktionstechnik für CT
In: IGIC 2014 - Abstractband: 1st Conference on Image-Guided Interventions, 13. - 14. Oktober 2014, Magdeburg ; [1. Tagung \"Image-Guided Interventions\"] - Magdeburg: Univ., S. 25-26 ; Kongress: Conference on Image-Guided Interventions 1 (Magdeburg) ; 2014.10.13-14
A note on existence and uniqueness of solutions for a thermodynamically consistent Becker-Döring model
In: Methods and applications of analysis. - Somerville, Mass : International Press, Bd. 21.2014, 2, S. 177-200
Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations
In: Kinetic and related models: KRM - Springfield, Mo: AIMS, Bd. 7.2014, 4, S. 713-737
Exact Riemann solutions to shallow water equations
In: Quarterly of applied mathematics. - Providence, RI : Brown Univ, insges. 47 S., 2014
Modeling of aggregation kernels for fluidized beds using discrete particle model simulations
In: Particuology - Amsterdam: Elsevier, Bd. 13.2014, S. 134-144
2013
Analysis and numerical investigation of two dynamic models for liquid chromatography
In: Chemical engineering science. - Amsterdam [u.a.] : Elsevier Science, Bd. 90.2013, S. 17-31
Bubbles in liquids with phase transition. Part 2: On balance laws for mixture theories of disperse vapor bubbles in liquid with phase change
In: Continuum mechanics and thermodynamics: analysis of complex materials and judicious evaluation of the environment - Berlin: Springer, insges. 29 S., 2013
Criteria for nonuniqueness of Riemann solutions to compressible duct flows
In: ZAMM: journal of applied mathematics and mechanics - Berlin: Wiley-VCH, 2013
Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition
In: Quarterly of applied mathematics - Providence, RI: Brown University, Division of Applied Mathematics, Bd. 71.2013, S. 509-540
Moment preserving finite volume schemes for solving population balance equations incorporating aggregation, breakage, growth and source terms
In: Mathematical models and methods in applied sciences (M 3 AS). - Singapore [u.a.] : World Scientific, Bd. 23.2013, 7
On the modeling and simulation of a laser-induced cavitation bubble
In: International journal for numerical methods in fluids - Chichester: Wiley, Bd. 73.2013, 2, S. 172-203
Parallel and high resolution numerical solution of concentration and temperature distributions in fluidized beds
In: Computers & chemical engineering. - Amsterdam [u.a.] : Elsevier Science, Bd. 52.2013, S. 122-133
Bannasch, Sebastian; Rose, Georg; Warnecke, Gerald
Iterative solution of system matrices from computer tomography using discrete time flow methods
In: Magdeburg, Univ., Fak. für Mathematik, 2013, 12 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,11)
2012
Bubbles in liquids with phase transition. Part 1: On phase change of a single vapor bubble in liquid water
In: Continuum mechanics and thermodynamics: analysis of complex materials and judicious evaluation of the environment - Berlin: Springer, Bd. 24.2012, 4/6, S. 461-483
Exact Riemann solutions to compressible Euler equations in ducts with discontinuous cross-section
In: Journal of hyperbolic differential equations. - London [u.a.] : World Scientific, Bd. 9.2012, 3, S. 403-449
Nagaiah, Ch.; Rüdiger, S.; Warnecke, Gerald; Falcke, M.
Adaptive space and time numerical simulation of reaction-diffusion models for intracellular calcium dynamics
In: Applied mathematics and computation. - Amsterdam [u.a.] : Elsevier, Bd. 218.2012, 20, S. 10194-10210
In: Chemical engineering journal - Amsterdam: Elsevier, Bd. 191.2012, S. 426-440
Robust a posteriori error estimates for subgrid stabilization of non-stationary convection dominated diffusive transport
In: Applied mathematics and computation. - Amsterdam [u.a.] : Elsevier, Bd. 218.2012, 9, S. 5276-5291
Weak solutions to the continuous coagulation equation with multiple fragmentation
In: Nonlinear analysis. - Oxford : Pergamon, Elsevier Science, Bd. 75.2012, 4, S. 2199-2208
2011
Numerical methods for solving two-dimensional aggregation population balance equations
In: Computers & chemical engineering. - Amsterdam [u.a.] : Elsevier Science, Bd. 35.2011, 6, S. 999-1009
Javeed, Shumaila; Qamar, Shamsul; Seidel-Morgenstern, Andreas; Warnecke, Gerald
A discontinuous Galerkin method to solve chromatographic models
In: Journal of chromatography. - Amsterdam [u.a.] : ElsevierJournal of chromatography / A, Bd. 1218.2011, 40, S. 7137-7146
Uniqueness for the coagulation-fragmentation equation with strong fragmentation
In: Zeitschrift für angewandte Mathematik und Physik. - Basel [u.a.] : Birkhäuser, Bd. 62.2011, 6, S. 1047-1063
Uniqueness of steady-state solutions for thermodynamically consistent Becker-Döring models
In: Journal of mathematical physics. - Melville, NY : American Institute of Physics, Bd. 52.2011, 8, insges. 28 S.
Weak solutions to the continuous coagulation equation with multiple fragmentation
In: Nonlinear analysis. - Amsterdam [u.a.] : Elsevier, Pergamon PressNonlinear analysis / Theory, methods and applications, 2011
2010
A note on moment preservation of finite volume schemes for solving growth and aggregation population balance equations
In: Society for Industrial and Applied Mathematics : SIAM journal on scientific computing . - Philadelphia, Pa. : SIAM, Bd. 32.2010, 2, S. 703-713
Calcium domains around single and clustered IP 3 receptors and their modulation by buffers
In: Biophysical journal . - Bethesda, Md. : Biophysical Soc., Bd. 99.2010, 1, S. 3-12
Efficient and accurate numerical simulation of nonlinear chromatographic processes
In: Computers & chemical engineering: CACE ; an international journal - Amsterdam [u.a.]: Elsevier, Bd. 35.2011, 11, S. 2294-2305, 2010
Modeling phase transition for compressible two-phase flows applied to metastable liquids
In: Journal of computational physics - Amsterdam: Elsevier, Bd. 229.2010, 8, S. 2964-2998
Steady states of the 1D Doi-Onsager model in the strong shear flow
In: Communications in mathematical sciences . - Somerville, Mass. : International Press, Bd. 8.2010, 3, S. 721-734
The continuous coagulation equation with multiple fragmentation
In: Journal of mathematical analysis and applications . - Amsterdam [u.a.] : Elsevier, ISSN 0022-247x, Bd. 374.2010, 1, S. 71-87
2009
"Alles was zählt!" - der mathematische Blick
In: Magdeburg: Univ., Fak. für Mathematik, 2009; Getr. Zählung: Ill.; 29 cm - (Technical Report / Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2009,2)
Disintegration process of surface stabilized sol-gel TiO 2 nanoparticles by population balances
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 64.2009, 24, S. 5302-5307
Local oscillations in finite difference solutions of hyperbolic conservation laws
In: Mathematics of computation . - Providence, RI : Soc., Bd. 78.2009, 268, S. 1997-2018
Modeling of the modulation by buffers of Ca 2+ release through clusters of IP 3 receptors
In: Biophysical journal . - Bethesda, Md. : Biophysical Soc., Bd. 97.2009, 4, S. 992-1002
Numerical approximations of a population balance model for coupled batch preferential crystallizers
In: , Bd. 59.2009, 3/4, S. 739-753
On the solution of population balances for nucleation, growth, aggregation and breakage processes
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 64.2009, 9, S. 2088-2095
2008
A laplace transformation based technique for reconstructing crystal size distributions regarding size independent growth
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 63.2008, 8, S. 2233-2240
Adaptive numerical simulation of intracellular calcium dynamics using domain decomposition methods
In: Applied numerical mathematics . - Amsterdam [u.a.] : North-Holland Publ. Co., Bd. 58.2008, 11, S. 1658-1674
An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation
In: Powder technology . - Amsterdam [u.a.] : Elsevier, Bd. 182.2008, 1, S. 81-104
Analytical and numerical investigations of a batch crystallization model
In: Journal of computational and applied mathematics . - Amsterdam [u.a.] : North-Holland, Bd. 222.2008, 2, S. 715-731
Convergence analysis of sectional methods for solving breakage population balance equations-I - the fixed pivot technique
In: Numerische Mathematik . - Berlin : Springer, Bd. 111.2008, 1, S. 81-108
Convergence analysis of sectional methods for solving breakage population balance equations-II - the cell average technique
In: Numerische Mathematik . - Berlin : Springer, Bd. 110.2008, 4, S. 539-559
Numerical solutions of population balance models in preferential crystallization
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 63.2008, 5, S. 1342-1352
The cell average technique for solving multi-dimensional aggregation population balance equations
In: Computers & chemical engineering . - Amsterdam [u.a.] : Elsevier, Bd. 32.2008, 8, S. 1810-1830
Three-dimensional numerical study of heat and mass transfer in fluidized beds with spray nozzle
In: Computers & chemical engineering . - Amsterdam [u.a.] : Elsevier, Bd. 32.2008, 12, S. 2877-2890
Book contribution
A note on sectional and finite volume methods for solving population balance equations
In: Micro-macro-interactions . - Berlin [u.a.] : Springer, ISBN 978-3-540-85714-3, S. 285-297
Population balance modelling for agglomeration and disintegration of nanoparticles
In: Micro-macro-interactions . - Berlin [u.a.] : Springer, ISBN 978-3-540-85714-3, S. 299-309
Warnecke, Gerald
Predigt beim Akademischen Gottesdienst am 23. Januar 2005 in der Wallonerkirche zu Magdeburg
In: Predigten der Magdeburger Akademischen Gottesdienste 2001 bis 2007 . - Magdeburg : Univ., Evangel. Hochschulpfarramt, S. 167-176, 2008
2007
A high-resolution space-time conservative method for non-linear hyperbolic conservation laws
In: International journal of computational methods: IJCM - Singapore [u.a.]: World Scientific Publishing, Bd. 4.2007, 2, S. 223-247
Adaptive high-resolution schemes for multidimensional population balances in crystallization processes
In: Computers & chemical engineering: CACE : an international journal - Amsterdam [u.a.]: Elsevier, Bd. 31.2007, 10, S. 1296-1311
An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation
In: Powder technology: an international journal on the science and technology of wet and dry particulate systems - Amsterdam [u.a.]: Elsevier, Bd. 179.2007, S. 205-228
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
In: Applied numerical mathematics: transactions of IMACS - Amsterdam [u.a.]: North-Holland Publ. Co, Bd. 57.2007, 9, S. 1050-1064
Hybrid stochastic and deterministic simulations of calcium blips
In: Biophysical journal: BJ - Bethesda, Md: Biophysical Soc, Bd. 93.2007, 6, S. 1847-1857
Numerical solution of population balance equations for nucleation, growth and aggregation processes
In: Computers & chemical engineering: CACE : an international journal - Amsterdam [u.a.]: Elsevier, Bd. 31.2007, 12, S. 1576-1589
On convergence of a domain decomposition method for a scalar convervation law
In: SIAM journal on numerical analysis . - Philadelphia, Pa. : SIAM, Bd. 45.2007, 4, S. 1453-1471
On the stability of evolution Galerkin schemes applied to a two-dimensional wave equation system
In: SIAM journal on numerical analysis: a publication of the Society for Industrial and Applied Mathematics - Philadelphia, Pa: SIAM, Bd. 44.2007, 4, S. 1556-1583
Study on a cross diffusion parabolic system
In: Acta mathematicae applicatae sinica / English series - Berlin: Springer, Bd. 23.2007, 1, S. 9-28
Book contribution
Numerical methods on population balances
In: Computational tools at different scales - Weinheim: Wiley-VCH, S. 209-260, 2007
2006
Application of space-time CE/SE method to shallow water magnetohydrodynamic equations
In: Journal of computational and applied mathematics . - Amsterdam [u.a.] : North-Holland, Bd. 196.2006, 1, S. 132-149
A comparative study of high resolution schemes for solving population balances in crystallization
In: Computers & chemical engineering . - Amsterdam [u.a.] : Elsevier Science, Bd. 30.2006, 6/7, S. 1119-1131
A direct Eulerian GRP scheme for compressible fluid flows
In: Journal of computational physics . - Orlando, Fla. : Academic Press, Bd. 218.2006, 1, S. 19-43
A discretized model for tracer population balance equation - improved accuracy and convergence
In: Computers & chemical engineering . - Amsterdam [u.a.] : Elsevier Science, Bd. 30.2006, 8, S. 1278-1292
A generic population balance model for simultaneous agglomeration and drying in fluidized beds
In: Chemical engineering science: journal internat. de génie chimique - Amsterdam: Elsevier, Bd. 62.2007, 1/2, S. 513-532, 2006
A new technique to determine rate constants for growth and agglomeration with size- and time-dependent nuclei formation
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 61.2006, 1, S. 282-292
A space-time conservative method for hyperbolic systems with stiff and non stiff source terms
In: Communications in computational physics . - Wanchai : Global Science Press, Bd. 1.2006, 3, S. 451-480
An improved discretized tracer mass distribution of Hounslow et al.
In: AIChE journal - Hoboken, NJ: Wiley, Bd. 52.2006, 4, S. 1326-1332
High resolution schemes for conservation laws and convection-diffusion equations with varying time and space grids
In: Journal of computational mathematics . - Beijing : Chinese Acad. of Mathematics and System Sciences, Bd. 24.2006, 2, S. 121-140
Improved accuracy and convergence of discretized population balance for aggregation - the cell average technique
In: Chemical engineering science: journal internat. de génie chimique - Amsterdam: Elsevier, Bd. 61.2006, 10, S. 3327-3342
Numerical simulation of dendritic crystal growth
In: Proceedings in applied mathematics and mechanics. - Weinheim [u.a.] : Wiley-VCH, Bd. 6.2006, 1, S. 751-752
Numerical simulation of temperature and concentration distributions in fluidized beds with liquid injection
In: Chemical engineering science: journal internat. de génie chimique - Amsterdam: Elsevier, Bd. 62.2007, 6, S. 1567-1590, 2006
Partioning methods for reaction-diffusion problems
In: Applied numerical mathematics . - Amsterdam [u.a.] : North-Holland Publ. Co., Bd. 56.2006, 7, S. 981-1000
Solving population balance equations for two-component aggregation by a finite volume scheme
In: Chemical engineering science . - Amsterdam : Elsevier, Bd. 62.2007, 3, S. 679-693
Book contribution
A high order gas kinetic method for the relativistic Euler equations
In: Hyperbolic problems: theory, numerics and applications; Vol. 2: . - Yokohoma : Yokohama Publ., ISBN 4-946552-22-7, S. 141-148, 2006 ; Kongress: Hyp2004; 10 (Osaka) : 2004.09.13-17 ; International Conference on Hyperbolic Problems; 10 (Osaka) : 2004.09.13-17
Peglow, Mirko; Kumar, Jitendra; Tsotsas, Evangelos; Heinrich, Stefan; Warnecke, Gerald; Mörl, Lothar
A population balance model for simulationeous drying and agglomeration
In: Drying 2006 - Gödöllő: Univ., S. 219-226 ; Kongress: International Drying Symposium 15 (Budapest, Hungary : 2006.08.20-23
2005
High resolution schemes for solving population balances in crystallization.
In: L\'Ôcole Nationale de l\'Industrie Minérale (Veranst.): D\'Analyse numerique et optimisation, JAN 08(8. journées, Rabat, 14 au 16 Decembre, 2005). - actes. Rabat, 2005, S. 442 - 447
Kunik, Matthias; Qamar, Shamsul; Warnecke, Gerald
A BGK-type flux-vector splitting scheme for the ultrarelativistic euler equations.
In: SIAM journal on scientific computing [Philadelphia, Pa.] 26(2004), Nr. 1, S. 196 - 223
A Runge-Kutta discontinuous galerkin method for the euler equations.
In: Computers & fluids : an international journal [New York, NY] 34(2005), S. 375 - 398
A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying time and space grids.
In: SIAM journal on scientific computing [Philadelphia, Pa.] 26(2005), Nr. 4, S. 1415 - 1431
A high order kinetic Flux-splitting method for the special relativistic hydrodynamics.
In: International journal of computational methods [Singapore] 2(2005), Nr. 1, S. 49 - 74
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics.
In: Journal of computational physics [Orlando, Fl.] 205(2005), S. 182 - 204
A reduction of the Boltzmann-Peierls equation.
In: International journal of computational methods [Singapore] 2(2005), Nr. 2, S. 213 - 229
Book contribution
Ain, Qurrat-Ul; Qamar, Shamsul; Warnecke, Gerald
A space-time conservative finite volume scheme for hyperbolic conservation laws.
In: Benkhaldoun, Fayssal (Hrsg.) ; Quazar, Driss (Hrsg.) ; Raghay, Said (Hrsg.): Finite volumes for complex applications IV. London [u.a.] : Hermes Science Publ., 2005, S. 459 - 470
2004
A note on (2K+1)-point conservative monotone schemes.
In: Mathematical modelling and numerical analysis [Les Ulis] 38(2004), Nr. 2, S. 345 - 357
A note on (2k + 1)-point conservative monotone schemes.
In: RAIRO /AFCET, Mathematical modelling and numerical analysis [Paris] 38(2004), Nr. 2, S. 345 - 357
Asymptotic stability of traveling waves for viscous consservation laws with dispersion.
In: Advances in differential equations [Athens, Ohio] 9(2004), Nr. 9/10, S. 1167 - 1184
Finite volume evolution Galerkin methods for hyperbolic systems.
In: SIAM journal on scientific computing [Philadelphia, Pa.] 26(2004), Nr. 1, S. 1 - 30
Kinetic schemes for the relativistic gas dynamics.
In: Numerische Mathematik [Berlin] 97(2004), S. 159 - 191
On evolution galerkin methods for the maxwell and the linearized Euler equations.
In: Applications of mathematics [Praha] 49(2004), Nr. 5, S. 415 - 439
On the boundary conditions for EG methods applied to the two-dimensional wave equation system.
In: Zeitschrift für angewandte Mathematik und Mechanik : ZAMM [Berlin] 84(2004), Nr. 4, S. 237 - 251
On the solution to the Riemann problem for the compressible duct flow.
In: Siam journal on applied mathematics [Philadelphia] 64(2004), Nr. 3, S. 878 - 901
Simulation of multicomponent flows using high order central schemes.
In: Applied numerical mathematics [Amsterdam] 50(2004), S. 183 - 201
The Riemann problem for the Baer-Nunziato two-phase flow model.
In: Journal of computational physics [Orlando, Fl.] 195(2004), S. 434 - 464
2003
A simple method for compressible multiphase mixtures and interfaces.
In: International journal for numerical methods in fluids [Chichester] 41(2003), S. 109 - 131
Evolution Galerkin schemes applied to two-dimensional Riemann problems for the wave equation system.
In: Discrete and continuous dynamical systems [Springfield, Mo.] 9(2003), Nr. 3, S. 559 - 576
Existence and uniqueness of solutions for a non-uniformly parabolic equation.
In: Journal of differential equations [Orlando, Florida] 189(2003), S. 1 - 16
Generalized characteristics and the uniqueness of entropy solutions to zero-pressure gas dynamics.
In: Advances in differential equations [Athens, Ohio] 8(2003), Nr. 8, S. 961 - 1004
Kinetic schemes for the ultra-relativistic Euler equations.
In: Journal of computational physics [Orlando, Fl.] 187(2003), S. 572 - 596
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations. , S. 695 - 726
In: Journal of computational physics [Orlando, Fl.] 192(2003)
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system.
In: Journal of numerical mathematics [Utrecht] 11(2003), Nr. 3, S. 235 - 251
Book contribution
Introduction.
In: Greven, Andreas (Hrsg.) ; Keller, Gerhard (Hrsg.) ; Warnecke, Gerald (Hrsg.): Entropy. Princeton [u.a.] : Princeton Univ. Press, 2003, S. 1 - 16 (Princeton series in applied mathematics)
Andrianov, Nikolai; Saurel, Richard (ext.); Warnecke, Gerald
The Riemann problem for a two-phase model.
In: Hou, Thomas Y. (Hrsg.) ; Tadmor, Eitan (Hrsg.): Hyperbolic problems : theory, numerics, applications (9th international conference Pasadena, Calif. March 25-29 2002). - proceedings. Berlin [u.a.] : Springer, 2003, S. 275 - 284
2002
Error bounds for the large time step Glimm scheme applied to scalar conservation laws.
In: Numerische Mathematik [Berlin] 91(2002), S. 13 - 34
Finite volume evolution Galerkin methods for Euler equations of gas dynamics.
In: International journal for numerical methods in fluids [Chichester] 40(2002), S. 425 - 434
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems.
In: Journal of computational physics [Orlando, Fl.] 183(2002), S. 533 - 562
On measure solutions to the zero-pressure gas model and their uniqueness.
In: Mathematica bohemica [Praha] 127(2002), Nr. 2, S. 265 - 273
2001
Adaption and reliability of numerical methods for stiff and nonstiff problems in CFD.
In: Computational fluid dynamics journal [Tokyo] 9(2001), Nr. 1, S. 540 - 548
Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation.
In: Journal of computational and applied mathematics [Amsterdam] 134(2001), S. 343 - 367
Convergence rates to discrete shocks for nonconvex conservation laws.
In: Numerische Mathematik [Berlin] 88(2001), Nr. 3, S. 513 - 541
Book contribution
Finite volume evolution galerkin methods for multidimensional hyperbolic systems.
In: Toro, E. F. (Hrsg.): Godunov Methods : theory and applications. New York : Kluwer Academic, 2001, S. 571 - 576
Helzel, Christiane (ext.); Warnecke, Gerald
Unconditionally stable explicit schemes for the approximation of conservation laws.
In: Fiedler, Bernold (Hrsg.): Ergodic theory, analysis, and efficient simulation of dynamical systems. Berlin : Springer, 2001, S. 775 - 803
2000
Numerical schemes based on bicharacteristics for hyperbolic systems.
In: CIMASI\' 2000 (Third international conference on applied mathematics and engineering sciences Casablanca, Marocco October 23- 24 -24, 2000). Casablanca, 2000, Beitrag auf CD- ROM, [6 S.]
Convergence rates for relaxation schemes approximating conservation laws.
In: SIAM journal on numerical analysis [Philadelphia] 37(2000), Nr. 4, S. 1316 - 1337
Evolution galerkin methods for hyperbolic systems in two space dimensions.
In: Mathematics of computation [Washington, DC] 69(2000), Nr. 232, S. 1355 - 1384
Lax-Wendroff type second order evolution Galerkin methods for multidimensional hyperbolic systems.
In: East-west journal of numerical mathematics [Zeist] 8(2000), Nr. 2, S. 127 - 152
Liu, Hailiang (ext.); Wang, Jinghua (ext.); Warnecke, Gerald The LIP+ - stability and error estimates for a relaxation scheme.
In: SIAM journal on numerical analysis [Philadelphia] 38(2000), Nr. 4, S. 1154 - 1170
Book contribution
Adaptive numerics for the simulation of magneto-plasmadynamic rocket thrusters.
In: Neittaanmäki, Pekka (Hrsg.) ; ... (Hrsg.): Numerical mathematics and advanced applications, ENUMATH \'99 (3rd European conference Jyväskylä 26. - 30.07, 1999). - proceedings. River Edge, NJ : World Scientific, 2000, S. 121 - 130
Evolution Galerkin methods for multidimensional hyperbolic systems.
In: Computational methods in applied sciences and engineering, ECCOMAS 2000 (European congress Barcelona, 11-14 September 2000). - proceedings. Barcelona : CIMNE, 2000, [14 S.]
High-resolution finite volume evolution Galerkin schemes for multidimensional hyperbolic conservation laws.
In: Neittaanmäki, Pekka (Hrsg.) ; ... (Hrsg.): Numerical mathematics and advanced applications, ENUMATH \'99 (3rd European conference Jyväskylä 26. - 30.07, 1999). - proceedings. River Edge, NJ : World Scientific, 2000, S. 633 - 640
Initial effects and convergence rates for relaxation methods.
In: Fiedler, Bernold (Hrsg.) ; ... (Hrsg.): EQUADIFF \'99 (international conference on Differential Equations, Berlin 1. - 7. August 1999). vol. 1. - proceedings. Singapore : World Scientific, 2000, S. 301 - 307