The interaction of electromagnetic waves with living tissues is modeled by the time-harmonic Maxwell's equations in heterogeneous dispersive and dissipative regime (electromagnetic permittivity is a complex quantity depending on the frequency of the incident wave). In high-frequency regime, numerical simulation of such a PDE model is very challenging. The underlying PDE is indefinite and its highly oscilatory solution requires a precise discretisation leading to very large problems to solve. The purpose of this PhD project is to address mathematically some of these difficult issues and to provide an open source simulation code including the state-of-art in approximation and solution methods for these kind of problems. This PhD project is funded for 3 years by ANR (French National Research Agency) within the ￼project MEDIMAX (partner laboratories:
J.L. Lions (Paris 6, France), MAP5 (Paris 5, France), J.- A.D. (Nice, France), LEAT (Nice), Society EMTensor (Vienna, Austria). The PhD student will be based in Nice but benefit from the interaction with specialists in domain decomposition and high performance computing from Paris VI and Glasgow (UK) through short research visits, within the partnership of this project. The ideal candidate will have completed a degree in Mathematics or Computer Science (with an emphasis of Numerical Analysis of Partial Differential Equations), or equivalent degree in an engineering school. Knowledge of finite element methods and iterative solution techniques are highly desirable. Also, knowledge of oriented programming languages such as C/C++ are desirable.