Fast Uncertainty Quantification in Low Frequency Electromagnetic Problems by an Integral Equation Method Based on Hierarchical Matrix Compression

A parametric model order reduction method combined with a polynomial spectral approximation is applied for the first time to a Volume Integral Equation method accelerated by a low–rank matrix compression technique. Such an approach allows for drastically reducing the computational cost required by uncertainty quantifications in electromagnetic problems. Moreover, the proposed numerical tool can be adopted for computing stochastic information (e.g. mean, variance, probability density function) of any electromagnetic quantity of interest, in order to test the reliability of industrial devices with uncertainties on the material parameters. Conductive, dielectric, and magnetic media which exhibit uncorrelated and correlated random material parameters are considered by the proposed method.