Société de Calcul Mathématique SA
Mathematical Modeling 2
Once modeling is carried out, one can perform simulations: they are "virtual experiments", in general on a computer, where one changes various parameters to measure their influence. One can thus simulate deliveries, the design of a car, the takeoff of a rocket, etc. Simulation is much less expensive than the real experiment, and it can be repeated as often as one wants, with all the modifications which one wants.
If you want a simulation to be effective, two requirements appear, and they are contradictory:
In fact, the two requirements must be taken into account from the beginning: one has to know in advance what precision is wanted and what execution time is acceptable.
SCM has made a specialty of time-effective simulations, in particular for the Ministry for Defense.
This is the final phase of the resolution. Once modeling is made, once the influence of the various parameters is tested, one seeks the "adjustment" which gives the best result. This starts with a theoretical approach, which gives the form of the optimal solution. But one then needs, by simulation, to test this solution and to check that it satisfies the practical constraints which are imposed, that it is sufficiently fast, sufficiently reliable, sufficiently robust, etc.
To pile up containers in the compartment of a plane is a problem of optimization. The question is to best fill out a given volume, but a good solution moreover respects a certain number of constraints:
We take care of all real constraints in all optimization problems that are given to us. We proceed by "successive approximations": we propose to the client a first solution which looks satisfactory to us, and incorporate all real constraints gradually. Experience shows that there is always a constraint, nobody had thought of at the beginning!
Depending on specific needs, we develop special scientific software answering a precise request. For instance, we developed for EDF (French Electricity) a software allowing to detect the defects in the tubes of the vapor generators, in nuclear power plants. It uses the signals recorded by a probe in Eddy currents. Another example is a software reconstructing certain elements in marine cartography, using data collected by sonars.
The software is the ultimate stage of the process of modeling/simulation/optimization described above: once the problem has been suitably analyzed and solved, the software represents the solution in visible form: it is the "final product".
Now, you will discover our domains of intervention