Team > Univ.-Prof. Dr. Vadym Aizinger

Faculty of mathematics, physics & computer science
Chair of Scientific Computing

Univ.-Prof. Dr. Vadym Aizinger

Career path

Education

Faculty of mathematics, physics & computer science
Chair of Scientific Computing

Main fields of research

• Numerical methods for partial differential equations
• High performance computing
  
• Modeling of climate and its compartments
  

Topics and methods

The main focus of my work is the development, analysis, and application of numerical algorithms and discretization schemes for simulation of physical, chemical, and biological processes in environmental and climate applications. The systems being simulated are usually characterized by very large domains with complex geometry; the spatial and temporal scales are highly heterogenious: the simulated phenomena can have sizes between meters and thousands of kilometers and durations from fractions of a second to centuries. These considerations set a very high bar for mathematical modeling skill, efficiency of the numerical methods, and high performance computing (HPC) proficiency.

The discontinuous Galerkin (DG) finite element methods offer many desirable properties that make them an attractive choice for environmental and climate models. These include:

• robustness for low-regularity problems such as those with shocks and discontinuities;
  
• guaranteed local conservation of all unknowns;
• natural support for arbitrary order approximation spaces;
• non-conforming meshes and hanging nodes present no difficulty;
• easy accommodation of h- and p-refinement;
• local approximation stencils highly suitable for parallel computing.

A relatively high computational cost of DG discretizations compared to the classical finite elements or finite volumes of the same order can be partially offset by superior parallel scaling of DG schemes. In addition, a number of strategies appear to hold promise with regard to increasing method’s efficiency and accuracy

• mesh adaptivity allows to efficiently utilize computational resources and obtain a more accurate solution in the areas of interest;
• locality of DG approximation stencils improves parallel scalability on HPC clusters and hybrid computational architectures;
• approximation space adaptivity permits very high accuracy without excessive computational cost in parts of the computational domain, where the analytical solution is smooth, and relies on low-order approximations otherwise — all this without violating the local conservation properties of the scheme.
  

Faculty of mathematics, physics & computer science
Chair of Scientific Computing

Publications

2024

Journal articles

Pouyan Ahmadi, Franz Dichgans, Lisa Jagau, Christian Schmidt, Vadym Aizinger, Benjamin Silas Gilfedder, Jan Fleckenstein: Systematic CFD-based evaluation of physical factors influencing the spatiotemporal distribution patterns of microplastic particles in lakes. In: Science of the Total Environment, 917 (2024). - .
doi:10.1016/j.scitotenv.2024.170218

Book sections and proceedings

Markus Büttner, Christoph Alt, Tobias Kenter, Harald Köstler, Christian Plessl, Vadym Aizinger: Enabling Performance Portability for Shallow Water Equations on CPUs, GPUs, and FPGAs with SYCL. In: Proceedings of the Platform for Advanced Scientific Computing Conference. - New York, NY : 2024.
doi:10.1145/3659914.3659925

2023

Journal articles

Sara Faghih-Naini, Sebastian Kuckuk, Daniel Zint, Samuel Kemmler, Harald Köstler, Vadym Aizinger: Discontinuous Galerkin method for the shallow water equations on complex domains using masked block-structured grids. In: Advances in Water Resources, (2023). - .
doi:10.1016/j.advwatres.2023.104584

Markus Musch, Andreas Rupp, Vadym Aizinger, Peter Knabner: Hybridizable discontinuous Galerkin method with mixed-order spaces for non-linear diffusion equations with internal jumps. In: GEM : International Journal on Geomathematics, 14 (2023). - .
doi:10.1007/s13137-023-00228-7

Book sections and proceedings

Christoph Alt, Tobias Kenter, Sara Faghih-Naini, Jennifer Faj, Jan-Oliver Opdenhövel, Christian Plessl, Vadym Aizinger, Jan Hönig, Harald Köstler: Shallow Water DG Simulations on FPGAs : Design and Comparison of a Novel Code Generation Pipeline. In: Abhinav Bhatele, Jeff Hammond, Marc Baboulin, Carola Kruse (Hrsg.): High Performance Computing : Proceedings. - Cham : Springer, 2023. - S. 86-105.
doi:10.1007/978-3-031-32041-5_5

Jennifer Faj, Tobias Kenter, Sara Faghih-Naini, Christian Plessl, Vadym Aizinger: Scalable Multi-FPGA Design of a Discontinuous Galerkin Shallow-Water Model on Unstructured Meshes. In: Proceedings of the Platform for Advanced Scientific Computing Conference. - New York, NY : Association for Computing Machinery, 2023.
doi:10.1145/3592979.3593407

2022

Journal articles

Sara Faghih-Naini, Vadym Aizinger: p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator. In: GEM : International Journal on Geomathematics, 13 (2022). - .
doi:10.1007/s13137-022-00208-3

Yannic Fischler, Martin Rückamp, Christian Bischof, Vadym Aizinger, Mathieu Morlighem, Angelika Humbert: A scalability study of the Ice-sheet and Sea-level System Model (ISSM, version 4.18). In: Geoscientific Model Development, 15 (2022). - S. 3753-3771.
doi:10.5194/gmd-15-3753-2022

Book sections and proceedings

Daniel Zint, Roberto Grosso, Vadym Aizinger, Sara Faghih-Naini, Sebastian Kuckuk, Harald Köstler: Automatic Generation of Load-Balancing-Aware Block-Structured Grids for Complex Ocean Domains. In: Trevor Robinson, David Moxey, Vladimir Z. Tomov (Hrsg.): Proceedings of the 2022 SIAM International Meshing Roundtable. - Virtual Conference : Zenodo, 2022.
doi:10.5281/zenodo.6562440

2021

Journal articles

Fei Xu, Qingang Xiong, Vadym Aizinger, Guillaume Ducrozet: Development and Application of Open-Source Software for Problems with Numerical PDEs. In: Computers & Mathematics with Applications, 81 (2021). - S. 1-2.
doi:10.1016/j.camwa.2020.12.002

Balthasar Reuter, Hennes Hajduk, Andreas Rupp, Florian Frank, Vadym Aizinger, Peter Knabner: FESTUNG 1.0 : Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods. In: Computers & Mathematics with Applications, 81 (2021). - S. 3-41.
doi:10.1016/j.camwa.2020.08.018

Andreas Rupp, Moritz Hauck, Vadym Aizinger: A subcell-enriched Galerkin method for advection problems. In: Computers & Mathematics with Applications, 93 (2021). - S. 120-129.
doi:10.1016/j.camwa.2021.04.010

Book sections and proceedings

Tobias Kenter, Adesh Shambhu, Sara Faghih-Naini, Vadym Aizinger: Algorithm-hardware co-design of a discontinuous Galerkin shallow-water model for a dataflow architecture on FPGA. In: Proceedings of the Platform for Advanced Scientific Computing Conference. - Geneva : 2021. - S. 1-11.
doi:10.1145/3468267.3470617

2020

Journal articles

Moritz Hauck, Vadym Aizinger, Florian Frank, Hennes Hajduk, Andreas Rupp: Enriched Galerkin method for the shallow-water equations. In: GEM : International Journal on Geomathematics, 11 (2020). - .
doi:10.1007/s13137-020-00167-7

Balthasar Reuter, Andreas Rupp, Vadym Aizinger, Florian Frank, Peter Knabner: FESTUNG: A MATLAB / GNU Octave Toolbox for the Discontinuous Galerkin Method. Part IV. Generic Problem Framework and Model-Coupling Interface. In: Communications in Computational Physics, 28 (2020). - S. 827-876.
doi:10.4208/cicp.OA-2019-0132

Sara Faghih-Naini, Vadym Aizinger, Sebastian Kuckuk, Daniel Zint, Roberto Grosso, Harald Köstler: Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes. In: Advances in Water Resources, 138 (2020). - .
doi:10.1016/j.advwatres.2020.103552

Book sections and proceedings

Hennes Hajduk, Dmitri Kuzmin, Vadym Aizinger: Bathymetry Reconstruction Using Inverse ShallowWater Models : Finite Element Discretization and Regularization. In: Harald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza (Hrsg.): Numerical Methods for Flows : FEF 2017 Selected Contributions. - Cham : Springer, 2020. - S. 223-230.
doi:10.1007/978-3-030-30705-9_20

2019

Journal articles

Balthasar Reuter, Andreas Rupp, Vadym Aizinger, Peter Knabner: Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems. In: Computers & Mathematics with Applications, 77 (2019). - S. 2291-2309.
doi:10.1016/j.camwa.2018.12.020

Daniel Zint, Roberto Grosso, Vadym Aizinger, Harald Köstler: Generation of Block Structured Grids on Complex Domains for High Performance Simulation. In: Computational Mathematics and Mathematical Physics, 59 (2019). - S. 2108-2123.
doi:10.1134/S0965542519120182

Hennes Hajduk, Dmitri Kuzmin, Vadym Aizinger: New directional vector limiters for discontinuous Galerkin methods. In: Journal of Computational Physics, 384 (2019). - S. 308-325.
doi:10.1016/j.jcp.2019.01.032

N. V. Koldunov, Vadym Aizinger, N. Rakowsky, P. Scholz, D. Sidorenko, S. Danilov, Thomas Jung: Scalability and some optimization of the Finite-volumE Sea ice--Ocean Model, Version 2.0 (FESOM2). In: Geoscientific Model Development, 12 (2019). - S. 3991-4012.
doi:10.5194/gmd-12-3991-2019

Book sections and proceedings

Daniel Zint, Roberto Grosso, Vadym Aizinger, Harald Köstler: Generation of Block Structured Grids on Complex Domains for High Performance Simulation. In: Vladimir A. Garanzha, Lennard Kamenski, Hang Si (Hrsg.): Numerical Geometry, Grid Generation and Scientific Computing : Proceedings of the 9th International Conference, NUMGRID 2018. - Cham : Springer International Publishing, 2019. - S. 87-99.
doi:10.1007/978-3-030-23436-2_6

2018

Journal articles

Vadym Aizinger, Andreas Rupp, Jochen Schütz, Peter Knabner: Analysis of a mixed discontinuous Galerkin method for instationary Darcy flow. In: Computational Geosciences, 22 (2018). - S. 179-194.
doi:10.1007/s10596-017-9682-8

Vadym Aizinger, Leon Bungert, Michael Fried: Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem. In: Computing and Visualization in Science, 18 (2018). - S. 193-202.
doi:10.1007/s00791-018-0291-4

Sebastian Beyer, Thomas Kleiner, Vadym Aizinger, Martin Rückamp, Angelika Humbert: A confined-unconfined aquifer model for subglacial hydrology and its application to the Northeast Greenland Ice Stream. In: The Cryosphere, 12 (2018). - S. 3931-3947.
doi:10.5194/tc-12-3931-2018

Alexander Jaust, Balthasar Reuter, Vadym Aizinger, Jochen Schütz, Peter Knabner: FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III. Hybridized discontinuous Galerkin (HDG) formulation. In: Computers & Mathematics with Applications, 75 (2018). - S. 4505-4533.
doi:10.1016/j.camwa.2018.03.045

Anne Marx, Marcus Conrad, Vadym Aizinger, Alexander Prechtel, Robert van Geldern, Johannes A. C. Barth: Groundwater data improve modelling of headwater stream CO₂ outgassing with a stable DIC isotope approach. In: Biogeosciences, 15 (2018). - S. 3093-3106.
doi:10.5194/bg-15-3093-2018

Hennes Hajduk, Ben R. Hodges, Vadym Aizinger, Balthasar Reuter: Locally Filtered Transport for computational efficiency in multi-component advection-reaction models. In: Environmental Modelling & Software, 102 (2018). - S. 185-198.
doi:10.1016/j.envsoft.2018.01.003

2017

Journal articles

Vadym Aizinger, Adam Kosík, Dmitri Kuzmin, Balthasar Reuter: Anisotropic slope limiting for discontinuous Galerkin methods. In: International Journal for Numerical Methods in Fluids, 84 (2017). - S. 543-565.
doi:10.1002/fld.4360

Leon Bungert, Vadym Aizinger, Michael Fried: A Discontinuous Galerkin Method for the Subjective Surfaces Problem. In: Journal of Mathematical Imaging and Vision, 58 (2017). - S. 147-161.
doi:10.1007/s10851-016-0695-z

Jochen Schütz, Vadym Aizinger: A hierarchical scale separation approach for the hybridized discontinuous Galerkin method. In: Journal of Computational and Applied Mathematics, 317 (2017). - S. 500-509.
doi:10.1016/j.cam.2016.12.018

Book sections and proceedings

Alexander Ditter, Dominik Schönwetter, Anton Kuzmin, Dietmar Fey, Vadym Aizinger: Memory Analysis and Performance Modeling for HPC Applications on Embedded Hardware via Instruction Accurate Simulation. In: Jan Janech, Jozef Kostolny, Tomasz Gratkowski (Hrsg.): Proceedings of the 2015 Federated Conference on Software Development and Object Technologies. - Cham : Springer International Publishing, 2017. - S. 19-34.
doi:10.1007/978-3-319-46535-7_2

2016

Journal articles

Alexander Jaust, Jochen Schütz, Vadym Aizinger: An efficient linear solver for the hybridized discontinuous Galerkin method. In: Proceedings in Applied Mathematics and Mechanics, 16 (2016). - S. 845-846.
doi:10.1002/pamm.201610411

M. Geveler, B. Reuter, Vadym Aizinger, D. Göddeke, S. Turek: Energy efficiency of the simulation of three-dimensional coastal ocean circulation on modern commodity and mobile processors. In: Computer Science : Research + Development, 31 (2016). - S. 225-234.
doi:10.1007/s00450-016-0324-5

B. Reuter, Vadym Aizinger, Manuel Wieland, F. Frank, P. Knabner: FESTUNG : A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting. In: Computers & Mathematics with Applications, 72 (2016). - S. 1896-1925.
doi:10.1016/j.camwa.2016.08.006

Book sections and proceedings

Dominik Schönwetter, A. Ditter, Vadym Aizinger, B. Reuter, D. Fey: Cache Aware Instruction Accurate Simulation of a 3-D Coastal Ocean Model on Low Power Hardware. In: Yuri Merkuryev (Hrsg.): SIMULTECH 2016 : Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. Volume 1. - Setúbal : SCITEPRESS, 2016. - S. 129-137.
doi:10.5220/0006006501290137

Dominik Schönwetter, Alexander Ditter, Bruno Kleinert, Arne Hendricks, Vadym Aizinger, Dietmar Fey: Virtualization Guided Tsunami and Storm Surge Simulations for Low Power Architectures. In: Mohammad S. Obaidat, Janusz Kacprzyk, Tuncer Ören, Joaquim Filipe (Hrsg.): Simulation and Modeling Methodologies, Technologies and Applications. - Cham : Springer International Publishing, 2016. - S. 99-114.
doi:10.1007/978-3-319-31295-8_7

2015

Journal articles

Chris Mirabito, Clint Dawson, Vadym Aizinger: An a priori error estimate for the local discontinuous Galerkin method applied to two-dimensional shallow water and morphodynamic flow. In: Numerical Methods for Partial Differential Equations, 31 (2015). - S. 397-421.
doi:10.1002/num.21914

F. Frank, B. Reuter, Vadym Aizinger, P. Knabner: FESTUNG : A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator. In: Computers & Mathematics with Applications, 70 (2015). - S. 11-46.
doi:10.1016/j.camwa.2015.04.013

Vadym Aizinger, Peter Korn, Marco Giorgetta, Sebastian Reich: Large-scale turbulence modelling via α-regularisation for atmospheric simulations. In: Journal of Turbulence, 16 (2015). - S. 367-391.
doi:10.1080/14685248.2014.991443

Balthasar Reuter, Vadym Aizinger, Harald Köstler: A multi-platform scaling study for an OpenMP parallelization of a discontinuous Galerkin ocean model. In: Computers & Fluids, 117 (2015). - S. 325-335.
doi:10.1016/j.compfluid.2015.05.020

N. Shokina, Vadym Aizinger: On numerical modelling of impulse water waves generated by submarine landslides. In: Environmental Earth Sciences, 74 (2015). - S. 7387-7405.
doi:10.1007/s12665-015-4746-3

Reinhard Hinkelmann, Q. Liang, Vadym Aizinger, Clint Dawson: Robust shallow water models. In: Environmental Earth Sciences, 74 (2015). - S. 7273-7274.
doi:10.1007/s12665-015-4764-1

Vadym Aizinger, D. Kuzmin, L. Korous: Scale separation in fast hierarchical solvers for discontinuous Galerkin methods. In: Applied Mathematics and Computation, 266 (2015). - S. 838-849.
doi:10.1016/j.amc.2015.05.047

Book sections and proceedings

Jan Oetjen, Max Engel, Christoph Effkemann, Simon M. May, Shiva P. Pudasaini, Theide Wöffler, Vadym Aizinger, Holger Schüttrumpf, Helmut Brückner: Numerical modelling of tsunami scenarios for the island of Bonaire (Leeward Antilles). In: Abstract of the 4th International Tsunami Field Symposium. - s.l. : 2015. - S. 81-85.

Dominik Schönwetter, A. Ditter, B. Kleinert, Arne Hendricks, Vadym Aizinger, H. Koestler, D. Fey: Tsunami and Storm Surge Simulation Using Low Power Architectures : Concept and Evaluation. In: Mohammad S. Obaidat (Hrsg.): SIMULTECH 2015 : Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. Volume 1. - Setúbal : SCITEPRESS, 2015. - S. 377-382.
doi:10.5220/0005566603770382

2013

Journal articles

Vadym Aizinger, J. Proft, Clint Dawson, D. Pothina, S. Negusse: A three-dimensional discontinuous Galerkin model applied to the baroclinic simulation of Corpus Christi Bay. In: Ocean Dynamics, 63 (2013). - S. 89-113.
doi:10.1007/s10236-012-0579-8

2012

Journal articles

P. D. Düben, P. Korn, Vadym Aizinger: A discontinuous/continuous low order finite element shallow water model on the sphere. In: Journal of Computational Physics, 231 (2012). - S. 2396-2413.
doi:10.1016/j.jcp.2011.11.018

2011

Book sections and proceedings

Vadym Aizinger: A geometry independent slope limiter for the discontinuous Galerkin method. In: Egon Krause, Yurii Shokin, Michael Resch, Dietmar Kröner, Nina Shokina (Hrsg.): Computational Science and High Performance Computing IV. - Berlin : Springer, 2011. - S. 207-217.
doi:10.1007/978-3-642-17770-5_16

2010

Book sections and proceedings

Vadym Aizinger, Andreas Hauser, Gabriele Wittum: Simulation of Flow and Transport in a Static Mixer Using Adaptive and Higher Order Numerical Methods. In: Henning Bockhorn, D. Mewes, W. Peukert, H.-J. Warnecke (Hrsg.): Micro and Macro Mixing : analysis, simulation and numerical calculation. - Berlin ; Heidelberg : Springer, 2010. - S. 245-262.
doi:10.1007/978-3-642-04549-3_14

2007

Journal articles

Vadym Aizinger, Clint Dawson: The local discontinuous Galerkin method for three-dimensional shallow water flow. In: Computer Methods in Applied Mechanics and Engineering, 196 (2007). - S. 734-746.
doi:10.1016/j.cma.2006.04.010

2005

Journal articles

Clint Dawson, Vadym Aizinger: A discontinuous Galerkin method for three-dimensional shallow water equations. In: Journal of Scientific Computing, 22 (2005). - S. 245-267.
doi:10.1007/s10915-004-4139-3

2004

Book sections and proceedings

Vadym Aizinger, Clint Dawson: A discontinuous Galerkin method for three-dimensional shallow water flows with free surface. In: Cass T. Miller, M. W. Farthing, W. G. Gray, G. F. Pinder (Hrsg.): Computational Methods in Water Resources. Volume 2. Proceedings of the XVth International Conference on Computational Methods in Water Resources. - Amsterdam : Elsevier, 2004. - S. 1691-1702.
doi:10.1016/S0167-5648(04)80177-1

2002

Journal articles

Vadym Aizinger, Clint Dawson: A discontinuous Galerkin method for two-dimensional flow and transport in shallow water. In: Advances in Water Resources, 25 (2002). - S. 67-84.
doi:10.1016/S0309-1708(01)00019-7

Book sections and proceedings

Clint Dawson, Vadym Aizinger: Discontinuous Galerkin methods for shallow water flow and transport. In: S. Majid Hassanizadeh, R. J. Schotting, W.G. Gray, G. F. Pinder (Hrsg.): Computational Methods in Water Resources. Volume 2. Proceedings of the XIV International Conference on Computational Methods in Water Resources. - Amsterdam : Elsevier, 2002. - S. 915-922.

Clint Dawson, Vadym Aizinger: The local discontinuous Galerkin method for advection-diffusion equations arising in groundwater and surface water applications. In: John Chadam, Al Cunningham, Richard E. Ewing, Peter Ortoleva, Mary F. Wheeler (Hrsg.): Resource Recovery, Confinement, and Remediation of Environmental Hazards. - New York : Springer, 2002. - S. 231-245.
doi:10.1007/978-1-4613-0037-3_13

2000

Journal articles

Vadym Aizinger, Clint Dawson, Bernardo Cockburn, Paul Castillo: The local discontinuous Galerkin method for contaminant transport. In: Advances in Water Resources, 24 (2000). - S. 73-87.
doi:10.1016/S0309-1708(00)00022-1

Book sections and proceedings

Clint Dawson, Vadym Aizinger, Bernardo Cockburn: The Local Discontinuous Galerkin Method for Contaminant Transport Problems. In: Bernardo Cockburn, G. E. Karniadakis, C.-W. Shu (Hrsg.): Discontinuous Galerkin Methods : Theory, Computation and Applications. - Berlin ; Heidelberg : Springer, 2000. - S. 309-314.
doi:10.1007/978-3-642-59721-3_26

1999

Journal articles

Clint Dawson, Vadym Aizinger: Upwind-mixed methods for transport equations. In: Computational Geosciences, 3 (1999). - S. 93-110.
doi:10.1023/A:1011531109949

Faculty of mathematics, physics & computer science
Chair of Scientific Computing

Univ.-Prof. Dr. Vadym Aizinger
Professor

Office: NW III, 2.32

Phone: +49-921-55 7873
E-mail: vadym.aizinger@uni-bayreuth.de
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ORCID: link
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