`TECSER project home page`

`Novel high performance numerical solution techniques for RCS computations`

`Project objectives`

During the last decades computational electromagnetism has taken on great technological importance and has progressively become a central discipline in present-day computational science. Indeed, computational electromagnetism is nowadays not only used for the virtual design of industrial products or military systems and devices, but also proves to be a valuable tool in the study of problems related to the medical domain (for therapeutic or diagnosis purpose) or addressing societal questions (e.g. for the numerical assessment of potential adverse effects of electromagnetic waves).

From the mathematical point of view, electromagnetic wave propagation problems are modeled by the system of Maxwell equations. For a certain class of problems (i.e., low frequency propagation problems), a static or quasi-static approximation can be adopted leading to reduced forms of the original system of Maxwell equations. The scientific and technical activities undertaken in the TECSER project are concerned with the intensive parallel simulation of high frequency electromagnetic wave propagation problems which require the numerical resolution of the full set of three-dimensional Maxwell equations. The underlying wave propagation phenomena can be purely unsteady or they can be periodic (because the imposed source term follows a time-harmonic evolution). Although time-domain formulations of wave propagation problems correspond to the most general situation, time-harmonic formulations are relevant for a large class of problems. From the numerical resolution point of view, time-harmonic formulations raise several difficulties and challenges related to the mathematical properties of the algebraic systems resulting from the discretization step. The TECSER project considers applications for which a time-harmonic behavior can be assumed and the underlying mathematical model is the frequency domain Maxwell equations. The target applications involve heterogeneous propagation media or/and complex shape objects with domains including geometrical details or singularities. The discretization step results in very large algebraic systems of equations whose size is intrinsically related to the characteristic wavelength of the problem that can be very small either because of the high frequency of the incident wave or because the wave speed in the underlying media is small due to the electromagnetic properties (e.g. the electric permittivity) characterizing this media. Ideally, numerical methodologies that accurately and efficiently solve such problems should combine the following ingredients: (a) high order finite element (possibly adaptive) methods on unstructured meshes for the discretization of the time-harmonic Maxwell equations, (b) boundary element methods for the treatment of the infinite propagation domains, and (c) high performance scalable linear system solvers adapted to modern, hierarchical, massively parallel computing systems.