Plenary Lecture

Handling the Boundary and Transmission Conditions in Some Linear Partial Differential Equations

Professor Franck Assous
Dept of Maths & Comput. Sc.
Ariel University Center
40700, Ariel, Israel
also with:
Bar-Ilan University
52900, Ramat-Gan, Israel
E-mail: franckassous@netscape.net

Abstract: The efficient numerical treatment of boundary conditions is constantly an interesting subject that can have many applications. These conditions can be treated as essential boundary conditions or for instance, by introducing Lagrange multipliers. Another approach which is of interest is related to the Nitsche Method. Several years ago, J. Nitsche introduced a way to impose weakly essential boundary conditions in the scalar Laplace operator. In this talk, we propose first a review of this approach for the Laplace problem. Then, we introduce a generalization of the Nitsche formulation to some linear partial differential equations. For example, we will consider the Maxwell equations for electromagnetic fields, where the boundary conditions involved are related to the tangential and the normal trace of the electromagnetic field. We will also consider the equations of elasticity. We will propose a variational formulation for easily handling interface conditions in multilayer material. In each case, numerical results will be shown to illustrate the method.

Brief Biography of the Speaker: Prof. Franck Assous received a Ph.D. degree in Applied Mathematics from the University of Paris (France). He then received the French "Habilitation a Diriger les Recherches" degree from the University of Toulouse (France). He worked more than 14 years at the Atomic French Agency (CEA) as a senior researcher. In parallel, he was teaching at the ENSTA School of Engineers (Paris) as an Assitant Professor, then at the Versailles University as an Associate Professor. He is currently working in Israel, where he is Professor of Applied Mathematics at the Ariel University Center (Israel), and at the Bar-Ilan University (Israel). His research project include numerical methods for Partial Differential Equations, with a particular interest for problems arising from models in the field of computational electromagnetism, plasma physics, elasticity. He is also interested in inverse problem in wave propagation problems.