Research Interests

Partial Differential Equations. Linear and non-linear elliptic equations, coupled problems for elliptic-parabolic equations. Fluid-structure interaction. Optimization theory. Shape and topology optimization of problems governed by partial differential equations. Numerical Analysis. Finite element method for partial differential equations and related shape and topology optimization problems.

Chapters in books

Topological derivative and Levelset method in shape optimization
P. Fulmanski, A. Laurain, J.-F. Scheid, J. Sokolowski, K. Szulc
Electrical Capacitance Tomography. Theoretical Basis and Applications, Dominik Sankowski and Jan Sikora, Eds, Wydawnictwo Ksiazkowe Instytutu Elektrotechniki, Warsaw, 2010, ISBN 978-83-61956-00-6 p.12-67

Reviewed Journal Articles

Shape and topological sensitivity analysis in domains with cracks
A. Khludnev, J. Sokolowski, K. Szulc
Applications of Mathematics, 2010, Vol.55, No.6, pp.433-469.

Topological derivative for semilinear elliptic problems
M. Iguernane, S.A. Nazarov, J.R. Roche, J. Sokolowski, K. Szulc
Internation Jurnal of Applied Mathematics and Computer Science (AMCS), 2009, Vol.19, No.2, pp.191-205.

Conferece Papers

Application of topological derivative to accelerate genetic algorithm in shape optimization of coupled models
A.A. Novotny, K. Szulc, A. Zochowski
IEEE-MMAR 2012, 17th International Conference on Methods and Models in Automation and Robotics, pp.131-135.

A numerical method for shape and topology optimization for semilinear elliptic equation
J.-F. Scheid, J. Sokolowski, K. Szulc
IEEE-MMAR 2010, 15th International Conference on Methods and Models in Automation and Robotics (MMAR), pp.290-295.

Application of topological derivative and neural networks for inverse problem
M. Grzanek, K. Szulc
System Modeling and Optimization, IFIP Advances in Information and communication Technology, Springer Boston, Vol. 312/2009, p.268-281

Using self-adjoint extensions in shape opimization
A. Laurain, K. Szulc
System Modeling and Optimization, IFIP Advances in Information and communication Technology, Springer Boston, Vol. 312/2009, p.331-349

Numerical algorithms for an inverse problem in shape optimization
M. Grzanek, A. Laurain, K. Szulc
6th International Conference on Inverse Problems in Engineering: Theory and Practice, Journal of Physics: Conference series, Vol. 135, 2008, 012047.

Reports

Topological derivative for semilinear elliptic problems
M. Iguernane, S.A. Nazarov, J.R. Roche, J. Sokolowski, K. Szulc
Pré-publication de l'Institut Elie Cartan, Universite Nancy I, 2008/n°38

Shape and topological sensitivity analysis in domains with cracks
A. Khludnev, J. Sokolowski, K. Szulc
Pré-publication de l'Institut Elie Cartan, Universite Nancy I, 2008/n°36

Topological derivative in nonsmooth domain
Autorzy: Zakaria Belhachmi, Jean-Marc Sac-Epee, Jan Sokolowski, Katarzyna Szulc.
Pré-publication de Laboratoire de Mathematiques et Applications de Metz, 2006 - UMR 7122, 2006

Others

Wprowadzenie do Scilab-a
P. Fulmanski, K. Szulc.
Translation from french of Une intraduction a Scilab by Bruno Pinçon.