Modern devices are  complex in their geometric and physical make-up and depend on the interplay between electromagnetics, electronics, and photonics. Modelling them calls for new techniques that are modular and multi-scale.

In order to overcome these challenges, we will develop integral equations based methods based on domain decompositions:

1. The development of modular integral equations based on the concept of multi-trace spaces of electric/magnetic current spaces. These techniques provide an almost complete separation of the various domains and materials that make up the system.

2. The development of easy to use and highly effective quadrature methods, in conjunction with highly regular meshes. Indeed, it turns out that the stability of integral equations depends critically on the availability of these often neglected ingredients. 

3. The application of these methods to the simulation of real life devices and the deployment of their code on distributed computing infrastructure.