In a very broad acceptation, shape and topology optimization is about finding the best domain (which may represent, depending on applications, a mechanical structure, a fluid channel,…) with respect to a given performance criterion (e.g. robustness, weight, etc.), under some constraints (e.g. of a geometric nature).
Understanding Earth's interior mechanisms, assessing seismic hazard due to earthquakes and volcanoes, securing our access to hydrocarbon resources and monitoring CO2 storage sites, all represent crucial issues for modern societies.