D espite the impressive progresses attained by simulation capabilities and techniques, some challenging problems remain today intractable. These prob- lems, that are common to many branches of science and engineering, are of differ- ent nature. Among them, we can cite those related to high-dimensional models, on which mesh-based approaches fail due to the exponential increase of degrees of freedom. Other challenging scenarios concern problems requiring many direct solutions (optimization, inverse identifica- tion, uncertainty quantification ! ) or those needing very fast solutions (real time simulation, simulation based control ! ).

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