2011 - present   I  am head of the  scientific computing project WaveES  supported by the Swedish Institute and by the Swedish Research  Council.

2012 -  2015  PI of the  Project ``Global convergence and adaptivity for coefficient inverse problems for Maxwell equations'' supported by VR, Sweden.  Project includes development of the new mathematical idea  - adaptive finite element method-  to the solution of coefficient inverse problems in subsurface  imaging   using electromagnetic waves.

2011 – 2014     Project  “Globally Convergent Numerical Methods for Inverse Problems of Imaging of Buried Targets”. This is a collaborative project with the PI's of the project  Prof. Michael V. Klibanov,  University of North Carolina at Charlotte, USA, and  Prof. Michael Fiddy,  Optical Center of the  University of North Carolina at Charlotte, USA.  This project  is supported by the  USA  Army    Research Laboratory  grant     W911NF-11-1-0399.   This is the continuation of the collaborative  effort with the PI's of the Project  on the topic of the application of approximately globally convergent numerical methods and adaptivity for the solution of Coefficient Inverse Problems. Both analytical and numerical issues will be studied. The focus will be on extension of the current Beilina-Klibanov technique to Coefficient Inverse Problems for the time dependent Maxwell equations.

2010-2013    PI of the  Project   "Adaptive finite element methods for solutions of inverse problems"  supported by the Swedish Institute, Visby Program. This is the collaborative project between Sweden and Russia.  Project includes development of new mathematical idea - adaptivity technique - to the solution of coefficient inverse problems in imaging using electromagnetic waves as well as in signal reconstruction in scanning electron tomography.

2007-2011    Project ``Globally convergent numerical methods  for   Multidimensional Coefficient Inverse Problems''.  This Project was supported  by the  Army    Research  Office (ARO) grant   W911NF-08-1-0470. PI of the project was  Prof. Michael V. Klibanov,  University of North Carolina at  Charlotte, USA.

2007-2008      The Notur project (THE NORWEGIAN METACENTER FOR COMPUTATIONAL SCIENCE) of High Performance Computing (HPC) at Norwegian University of Science and Technology, NTNU.  I have developed the C++ software in a parallel infrastructure for numerical solutions of some hyperbolic equations with variable coefficients as well as for corresponding MCIPs.

2007-2008          Project  "Information and Communication Technologies" at Norwegian University of Science and Technology, NTNU, in collaboration with the project leader Prof. Harald Krogstad. I  worked on the application of adaptive FEM for solution of an inverse electromagnetic scattering problem.  Some results of this Project are  in the presentation "A posteriori error estimation in computational inverse scattering: application to photonic crystal".

2003-2005     Project "Quantitative sonographic imaging of human hard tissue by mathematical modelling in scanning acoustic microscopy" (QUASIM). This was a collaborative project with the Medical Center of The Frankfurt University (Prof. Dr. Robert Sader), the Institute for Applied Mathematics of the University of Basel (Prof. Marcus Grote), and the Institute of Experimental Surgery and Hospital Management, University Hospital of Basel (Prof. Michael Heberer).

2003-2005     Project "New numerical methods for Maxwell  equations"    at the University of Basel, Switzerland, under the leadership of Prof. Marcus Grote. I worked on the analytical and numerical issues of  the new hybrid  FEM/FDM method for solution of Maxwell  equations and application of it to solution of the MCIP.