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IACM’s long tradition in Numerical Analysis and Scientific Computing research is focused on both fundamental research as well as on applied, industrial applications. Our aim is the development, implementation, evaluation and analysis of numerical methods for the accurate and efficient simulation of challenging continuum and stochastic mathematical models. Our expertise spans on a variety of computational methods and alternative methodologies. Specific applications the team is actively involved with are: computational fluid dynamics, numerical simulation of crack propagation, methods for conservation laws, dispersive wave propagation, viscous flow through heterogeneous media, large scale convective flows, and drift-diffusion systems with applications in solar cells, to name a few.

A considerable effort will be made to pitch as many as current fundamental research projects as possible into potentially interested industrial partners in Greece and abroad, aiming to expand their applicability and to facilitate their transition from enquiry-driven research into technological innovation. 

Scientific Computing : We develop algorithms and software for the numerical modelling of complex systems and phenomena. Specific applications group members are actively involved with are: computational fluid dynamics, numerical simulation of crack propagation, methods for conservation laws, dispersive wave propagation, viscous flow through heterogeneous media.

Some recent activities:

  

• Development of space-time adaptive algorithms for capturing singular phenomena such as: shocks, shear bands, localized solutions of nonlinear evolutionary PDEs. The development of next-generation space-time adaptive algorithms for the numerical approximation of solutions of nonlinear PDEs exhibiting singular behavior. Although adaptive algorithms are increasingly becoming a sought-after computational complexity reduction device in industrial, large scale simulators in various disciplines (aeronautics, material science, structural dynamics, geosciences), their mathematical foundations are still largely unexplored in the more challenging contexts of locally singular phenomena.
• The development and study of novel, rigorous, structure-preserving numerical methods for the accurate and efficient simulation of challenging kinetic equations with highly complex collision kernels, following exciting recent paradigm-shift developments in the mathematical analysis of such kinetic models. Moreover, notwithstanding the important fundamental research implications, the development of new high-order, structure-preserving numerical simulation capabilities for Boltzmann, Landau or Vlasov-type equations is deemed to enhance the potential of collaboration between IACM and other institutes’ research directions, especially in the context of statistical physics.

• The simulation and prediction of past and possible future tsunamis in the Aegean and neighbouring seas, and the estimation of tsunami hazard along Greek coasts. Tsunamis are long surface waves of small amplitude and their propagation in the open sea is efficiently modelled by the Shallow Water (SW) equations over variable bottom topography. 

• The development of novel multiscale numerical methods for flows through heterogeneous materials with specific applications arising in geo-engineering and oil-reservoir/petroleum modelling. The recent development of numerical methods on general polytopic cells/elements (by IACM members), in conjunction with respective modern numerical upscaling techniques has the potential of achieving unprecedented computational complexity reduction in realistic geological porous media flow scenarios.
• We have considerable expertise on coupling models across scales.  Multiscale models are devised utilising solid numerical analysis methodologies and satisfy certain structure-preserving criteria. The reliability of the approaches taken are checked using mathematical analysis tools. Key applications include atomistic-continuum coupling in the modelling of crack propagation in materials as well as kinetic-continuum coupled models.
• Rigorous theory for a variety of numerical methods, including a posteriori error bounds for time-dependent problems, fundamental questions for time stepping schemes, analysis of approximation for dispersive problems, finite volume and virtual element methods,  positivity preserving schemes, error analysis for PDE control problems.
• The development of a general framework for numerical methods on polygonal and polyhedral elements with arbitrary shapes and number of faces based on discontinuous Galerkin approaches, paving the way for next generation computational model reduction approaches.
• Novel methods for energy minimisation problems, including appropriate discontinuous Galerkin formulations, convergence  analysis towards minimisers, stabilisation mechanisms as solution selection criteria.

Education and Training: The group contributes to the education and training of undergraduate, graduate and post-graduate students as well as of PhD candidates and Postdoctoral researchers.

RESEARCHERS

• Georgios Akrivis
• Panagiotis Chatzipantelidis
• Konstantinos Chrysafinos
• Vassilios A. Dougalis
• Evangelia Flouri
• Emmanuil Georgoulis
• Evangelia Kalligianaki
• Theodoros Katsaounis
• Charalambos Makridakis
• Michael Plexousakis
• Nikolaos Rekatsinas

For any information regarding the Group, please contact:

Scientific Computing and Software Development Group
Institute of Applied and Computational Mathematics
Foundation for Research and Technology - Hellas
Nikolaou Plastira 100, Vassilika Vouton,
GR 700 13 Heraklion, Crete
GREECE

Tel: +30 2810 391800
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. (Mrs. Maria Papadaki)

Tel.: +30 2810 391805
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. (Mrs. Yiota Rigopoulou)