An introduction to POD-greedy-Galerkin reduced basis method

PDEs can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer and electromagnetism. Accurate discretization methods (e.g., finite element or finite volume methods, the so-called FOM) are widely used to numerically solve these problems. However, when many physical and/or geometrical parameters are involved, the computational cost required by FOMs becomes prohibitively high, and this is not acceptable for the real-time computations that are becoming more and more popular for rapid prototyping. Therefore, there is the need to introduce ROMs (also referred to as RB methods) able to provide, as input parameters change, fast and reliable solutions at a reduced computational cost.