New numerical and computational methods for the solution of differential equations with applications in environmental issues

Research Program EPEAEK - Archimedes III

financed by The European Union The Ministry of Education, Lifelong Learning and Religious Affairs of Greece(12/2011 - 08/2014)

Project goals

The proposed project has as main target the development and use of new models and computational methods for the optimization of the prediction of meteorological parameters. More precisely, an integrated approach will be adopted aiming at the development of:

1. A new methodology for the estimation of the distance between data sets or distributions emerging in meteorological and renewable energy forecasting procedures.
2. New computational methods for the solution of the problems/equations that arise.
3. Novel statistical methods for the optimization of the prediction of meteorological parameters with emphasis in the local adaptation of the results.

These goals-objectives will be pursuit based on advanced scientific tools combined with the development of new techniques promoting the cooperation between the research members of our scientific team and proposing new, more effective and widely applicable techniques.

State of the art and the new perspective

The need of accurate local predictions of environmental parameters has increased significantly in recent years as a result of the large number of social and commercial activities that are directly affected. The validity of such data is particularly important in terms of renewable energy for the safe assessment of available energy resources in wind farms and off shore platforms.

On European level, the previous requirements have led to the activation of numerous research and operational centers that develop high quality scientific tools able to provide reliable environmental predictions. In Greece, the available forecasts, although satisfactorily describe the overall picture in large or moderate scale, pose considerable problems to local weather information. These difficulties are magnified in areas of complex orography and coastline - characteristics of the Greek region.

To address these problems, the use of optimization techniques will be employed based on a relatively new branch of mathematics the Information Geometry. The latter implements techniques from the non-Euclidean Geometry in Statistics, targeting to the optimization of the solution of nonlinear problems.

One of the key issues is the appropriate estimation of the distance between two distributions or data sets. The classical treatment of such problems is usually based on regression techniques least squares methods. However, such an approach carries the assumption that the data processed belongs to an Euclidian - finite dimensional space.

Main Research Team:

• Ioannis Th. Famelis, Department of Mathematics, School of Technological Applications, TEI of Athens, Greece
• Georgios Galanis, Atmospheric Modeling and Weather Forecasting Group, Department of Physics, University of Athens, Greece
• Georgios Kallos, Atmospheric Modeling and Weather Forecasting Group, Department of Physics, University of Athens, Greece
• Georgios Smyrlis, Department of Mathematics, TEI of Athens, Greece
• Charalambos Tsitouras, Department of Applied Sciences, TEI of Chalkis, Greece
• Matthias Ehrhardt, Applied Mathematics and Numerical Analysis, University of Wuppertal, Germany

External Collaborators:

• Dimitrios Triandafyllou , Greece