Many engineering and physical applications require the numerical evaluation of partial differential equations (PDEs) over a range of parameters. The most used technique to discretize PDEs is the nite element (FE) method, which produces a piecewise polynomial approximation of the solution. It is well-known that, in various situations, FE approximations are possible only at high computational cost. Therefore, when solutions at many parameter values are of interest, the repeated computation of numerical solution thought the FE method becomes prohibitive. Model order reduction (MOR) methods provide approximations of the solution at low computational cost, overcoming the limitations of standard numerical techniques.
The focus will be on MOR methods for time-harmonic wave propagation problems, where the wavenumber may vary in a given interval of interest. Similar techniques are useful also in the framework of parametric eigenvalue problems arising from parametric PDEs. Such mathematical models are used, e.g., in structural dynamics, geophysics, seismology, acoustics and vibro-acoustics.