Reduced-Order Model With Equivalence Surface for Scattering Problems

A reduced-order model for analyzing scattering problems with surface integral equation method is proposed in this letter. An equivalent surface (ES) is introduced to enclose the scatterer and the corresponding interaction matrix between the ES and the scatterer is generated. A series of eigenvectors is obtained by performing randomized singular-value decomposition to the matrix. According to the equivalence principle, the wave input–output relation of the scatterer is encapsulated by a limited number of eigenvectors with a given truncation error, which can be precomputed and reused when the location of radiator changes but the scatterer does not. In addition, discrete empirical interpolation method is applied to further accelerate the calculation of the interaction between the radiator and the background. Numerical examples are provided to demonstrate the efficiency and accuracy of the proposed scheme.