Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

The identification of hidden conducting permeable objects from measurements the perturbed magnetic field taken over a range low frequencies is important in metal detection. Applications include identifying threat items security screening at transport hubs, location unexploded ordnance, and antipersonnel landmines areas former conflict, searching for archeological significance recycling valuable metals. solution inverse problem, or more generally locating classifying objects, has attracted considerable attention recently using polarizability tensors. tensor (MPT) provides characterization object small number coefficients, an explicit formula calculation their well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, build library them classification, requires repeated transmission typically accomplished approximately finite element discretization. To reduce computational cost, propose efficient reduced order model (ROM) that further reduces problem proper orthogonal decomposition rapid computation MPT signatures. Our ROM benefits posteriori error estimates accuracy predicted coefficients with respect those obtained solutions. These can be computed cheaply during online stage allowing prediction certified. increase efficiency signature, provide scaling results, enable immediate signature under changes size conductivity. We illustrate our approach by application homogenous inhomogeneous objects.