CURRICULUM VITAE Personal Information Name Rachid Touzani Birth February 1st 1955, Kenitra´ (Morocco) Citizenship French Office Address Universite´ Clermont Auvergne Laboratoire de Mathematiques´ Blaise Pascal 63000 Clermont-Ferrand, France Phone: +33 (0)4 73 40 77 06 e-mail: [email protected] Current Situation Professor at the Universite´ Clermont Auvergne, Engineering school Polytech Clermont–Ferrand (Department of Mathematical Engineering) Professional degrees 1976 – 1978 Master in Mathematics at the University of Besanc¸on (France). 1979 – 1981 PhD Thesis (French) at the University of Besanc¸on, France. Advisor: Prof. P. Lesaint. 1985 – 1988 PhD Thesis (Swiss) at the Swiss Federal Institute of Technology, Lausanne, Switzerland. Advisor: Dr. P. Caussignac. Positions 1982 – 1985 Research Assistant at the Department of Civil Engineering. Swiss Federal School of Engineering, Lausanne, Switzerland. 1985 – 1988 Research Assistant at the Department of Mathematics Swiss Federal School of Engineering, Lausanne, Switzerland. 1988 – 1992 Senior Researcher at the Department of Mathematics Swiss Federal School of Engineering, Lausanne, Switzerland. Since 1992 Professor of Applied Mathematics at the Blaise Pascal University, now Universite´ Clermont Auvergne, France. Teaching 1 1981 – 1982 Undergraduate courses in Numerical Analysis at the University of Besanc¸on (France). 1984 – 1992 Undergraduate courses in Vector Analysis and Numerical Analysis at the Swiss Federal School of Technology (Lausanne, Switzerland). 1992 – 1994 Graduate courses in Numerical Analysis of Partial Differential Equations at the Blaise Pascal University, (Clermont–Ferrand, France) Graduate courses in Numerical methods in optimization at the Mechanics En- gineering School (IFMA) of Clermont–Ferrand, France. 1994 – Present Undergraduate courses in Lebesgue Integration at the Engineering School of Clermont–Ferrand, Department of Mathematical Engineering. Graduate courses in Mathematical and Numerical Analysis of Partial Differ- ential Equations at the Engineering School of Clermont–Ferrand, Department of Mathematical Engineering. Postgraduate courses in Numerical methods and scientific computing at the Blaise Pascal University. Postgraduate courses in Optimization in engineering at the Swiss Federal In- stitute of Technology (Lausanne, Switzerland). Postgraduate courses in Object oriented programming of the finite element method (Ecole´ des Mines, Sophia Antipolis, France). Research ◦ Mathematical analysis and implementation of a numerical method to solve heat conduction problems involving a free boundary: Doctorat Thesis (Old french thesis), Advisor: Prof. Pierre Lesaint, University of Besanc¸on, France. This work has been accomplished from 1979 to 1982. ◦ Implementation of a finite element code simulating two and three dimensional incompress- ible fluid flow taking into account thermal diffusion and convection effects (Boussinesq equa- tion). This research was realized at the Civil Engineering Department at the Swiss Federal School of Engineering, Lausanne, Switzerland from 1982 to 1985, and has consisted in simulating heat island phenomena involved in environment modelling. ◦ Derivation of a new Discontinuous Galerkin method to solve three-dimensional boundary layer equations for incompressible fluid flow. Mathematical analysis of the method and com- puter implementation. Derivation of an element numbering algorithm to follow inflow for the Discontinuous Galerkin method. This research was realized in the Department of Mathematics of the EPFL and was my PhD thesis work between 1985 and 1988. Advisor: Dr. Philippe Caussignac. ◦ I have worked on mathematical modelling and numerical solution of a large scale indus- trial problem consisting in simulating electromagnetic casting of Aluminium. This problem involves multiphenomena (electromagnetism, hydrodynamics, two-phase heat transfer, free boundary). This work was realized, from 1988 to 1990, in the framework of research project granted by 2 the company Alusuisse, Currently Alcan. In this project, I have managed computer imple- mentation of the chosen numerical method. In addition, I have worked on theoretical aspects of mathematical and numerical analysis of the mathematical model, in collaboration with Jacques Rappaz. ◦ I have managed, from 1990 to 1993, with the Swiss Army, a research project on numerical simulation of absorption processes of chemical species by activated Carbon beds. For this, I have developed a numerical scheme to solve the problem (A hyperbolic system of semilinear equations). ◦ I have managed, from May 1991 to September 1992, a research project, supported by Swiss Energy Foundation (NEFF) and the Amysa Yverdon company. This project consisted in nu- merical simulation of induction heating processes taking account for ferromagnetic effects. ◦ I have worked on the mathematical justification of electromagnetic models in the presence of thin conductors. This work consists in obtaining, by asymptotical techniques simplified mathematical models having better approximability properties than Maxwell’s equations. In particular, they enable coupling Maxwell equations with Kirchhoff circuit differential equa- tions. This work was achieved in collaboration with Y. Amirat at the Blaise Pascal University. ◦ I have developed and implemented a C++ library for solving Partial Differential Equations by the Finite Element Method. This library (called OFELI as Object Finite Element LIbrary) is under the GNU Public License and is available in the sourceforge server. ◦ I have managed, from 1998 to 2003, a research project with the Michelin company on adaptive finite element methods for elasticity problems with unilateral contact. ◦ In collaboration with Thierry Dubois (Assistant Professor), I am currently working on the development of stabilized finite element methods for the space discretization of incompress- ible Navier-Stokes equations, coupled with projection schemes for time discretization. In this domain, we also work on numerical simulation of transition to turbulence in a thermal flow governed by the Boussinesq equations. An article is being written for the presentation of the obtained results. ◦ I have started, since 2002, to work on numerical approximation of free boundary problems us- ing level set formulations. These formulations enable calculating front evolution with topol- ogy change. In particular, numerical simulation of free boundaries involve transmission prob- lems for which classical finite element approximation give poor accuracy. We are working on the remedy to this difficulty by developing some particular finite element methods (or im- mersed interface methods) where enrichment of the finite element space enable taking into account the singularity due to the interface. This work is realized in collaboration with F. Bouchon, S. Clain, (Blaise Pascal University), G. Peichl and K. Kunisch (University of Graz, Austria) and P. Gremaud, C. Kuster, PhD student (North Carolina State University, USA). ◦ I have developed, since 1998, a library of classes in C++, that implements the finite ele- ment method for the numerical solution of various partial differential equations. This li- brary is available under the LGPL license (Gnu Lesser General Public License) on the website ofeli.org. Since its installation, this library have had several thousands of downloads. 3 ◦ I have started, since 2009, started working on the mathematical modelling and numerical simulation of inductively coupled plasma torches. The modelling involves coupling of com- pressible Navier-Stokes and eddy current equations. With S. Clain and D. Rochette we have developed a numerical code for this purpose. ◦ I have worked, between 2011 and 2015, as a consultant for the company LEAP Energy in Malaysia on the development of software, using the library OFELI, for the numerical simula- tion of fluid flow in reservoir engineering. PhD students ◦ Stephane´ Clain: Mathematical and numerical analysis of an induction heating model, May 1994. S. Clain was Assistant Professor in Clermont–Ferrand from 1998 to 2005 and is Professor at the University of Toulouse since 2005. ◦ Pierre Beal:´ Modelling of contact between elastic rods with large displacements. January 1998. P. Beal´ is the manager, since 2000, of the company Numtech that develops software for numer- ical simulation in atmospheric processes (www.numtech.fr). ◦ Jean-Roch Julien: Alternating Direction schemes for compressible fluid flow using structured meshes. J.-R. Julien is currently Software engineer in the Bosch company, Lyon, France. ◦ Severine´ Gauthier: Numerical solution of three-dimensional eddy current problems. September 1998. S. Gauthier is a software engineer in the Michelin company. ◦ Sebastien´ Zimmermann: A finite volume scheme with projection for time dependent Stokes equa- tions. February 2006. S. Zimmermann is currently teacher of Mathematics in a High School in France. ◦ Malcom Djenno: New numerical methods for the Stokes and Level Set Equations. December 2007. M. Djenno is Assistant Professor in the Masuku University, Franceville, Gabon. Administration Activity Local: ◦ Head of the Department of Mathematical Engineering and Modelling at the Engineering School of the Blaise Pascal University (1999 – 2009). ◦ Member of the board of the Blaise Pascal University (1994–2007 and 2008–2012). 4 ◦ Member of the Editorial Board of the journal Annales Math´ematiquesBlaise Pascal (Since 1998). ◦ Head of the group Partial Differential Equations and Numerical Analysis of the Laboratory of Mathematics