8 Reduced-order modeling for applications to the cardiovascular system

The capability to provide fast and reliable numerical simulations is of paramount importance when dealing with complex applications arising from medicine. More than for other branches of engineering and applied sciences, performing accurate computations in a short amount of time - minutes, rather than hours, or even days - is crucial when dealing with problems arising from life sciences, like, e. g., in the simulation of the cardiovascular system. Moreover, many sources of variability carried by subject-specific features have to be incorporated into the mathematical models, to quantify their impact on the computed results. For these reasons, bringing computational results into clinical practice represents a great challenge. Reducedorder modeling techniques such as the reduced basis method represent a key tool towards the possibility to address these challenges, thus making the numerical modeling of the cardiovascular system a new, fascinating testbed for these methodologies.