Virtual validations. Implementaion towards the numerical tools

ith the growing number of on-board electronic systems, their ever-increasing complexity and the growing number of potential disruptors, it is becoming difficult but essential to control and ensure the smooth operation of these systems. This is all the more true as these systems are often designed to enhance both comfort and safety, for example in the aeronautical and automotive sectors. It is also clear that, even if every effort is made to verify the correct operating conditions in an electromagnetically disturbed environment when a product is launched on the market, it is essential to ensure that these conditions are maintained throughout the product's lifespan, and therefore to be able to periodically assess the evolution of the safety margins initially announced.

For all these reasons, today and during all phases of the product life cycle, a number of analyses are based on numerical simulation or physical analysis of phenomena described mathematically and resolved with the help of numerical calculation techniques. In Electromagnetic Compatibility (EMC) systems, from preliminary design through to detailed design, choice of technologies, specifications to suppliers, qualification of sub-assemblies, certification of the complete system, right through to maintenance under operational conditions, many phases can be accompanied by reasoning based on the resolution of the equations governing the behavior of electric and magnetic fields in space and time: Maxwell's equations.

Maxwell's equations, originally written in differential or integral form in the time or frequency domain, can take many forms, depending on the solution technique chosen. Digitizing them and solving a problem requires the development of a numerical algorithm based on a given technique. However, solving an electromagnetic problem is not straightforward, for a number of reasons:

• choice of physical model: the model is essentially linked to the modeller's vision of it; depending on the level of finesse (to what scale?), the model will be more or less complex and, as a result, will not necessarily reflect the same phenomena;

• choice of discretization: for the same model, discretization will make it more or less possible to track field variations, and will therefore give different results depending on the case;

• lack of knowledge of certain physical parameters (permittivities, etc.): in numerical simulation, these parameters must be entered, so the modeler must make a choice which may be dictated by a study of the sensitivity of observables to variability in these parameters.

Building numerical models naturally requires validation, either against known...