Optimization in meshing and convergence for Finite Element Method in electromagnetism and high field gradient computation.

Objectives
An accurate computation of high field enhancement is a key factor for the optimization of nano/microstructures in plasmonics or optics.

Methods
Development of algorithms in order to increase the accuracy of the computation in eletromagnetic and optimization of remeshing process applied in nanotechnology, fluid dynamics,..

Results and prospects

An accurate computation of field enhancement in the vicinity of metallic structures is fundamental for the prediction of different physical phenomena such as SERS or fluorescence, and also for the design of nanostructures for specific applications. Several numerical models have been developed and are used to compute the field enhancement. Nevertheless, its evaluation can be very tedious and boring due to the plasmon resonance increasing the intensity level, and to the discontinuity of the field near the material edges.

In order to propose solutions to control the accuracy in the compuation field enhancement, we develop an improved adaptive mesh process that allows the accurate control of the numerical solution of interest derived from the solution of the partial defirential equation. This new adaptive mesh process is based on the a posteriori error indicator estimation on the physical solution. Such an adaptive meshing, in connexion with the Finite Element Method is applied to compute phenomenon involving high field gradients in near-field (electric intensity, Poynting's vector, optical forces,...). This new procedure accelerates drastically the convergence of the solution and minimizes both the memory requirement and the computational time.