Fast frequency sweep method for indirect boundary element models arising in acoustics

Fast frequency sweep algorithms aim at computing an approximation of the frequency response of a large-scale system within a frequency band of interest and with a desired frequency resolution in a more efficient manner than applying the direct method, namely solving for each frequency. This paper presents an approach for computing frequency sweeps of acoustic systems described by boundary element models (BEM). The matrices arising from indirect boundary element discretizations are fully populated, and their assembly is computationally demanding due to the double surface integral, therefore the possible speed-up offered by the proposed method is two-fold. On the one hand, it avoids solving a dense linear system at each frequency by extrapolating the response around few expansion frequencies, using information provided by derivatives and constructing Pade approximants. On the other hand, it bypasses forming the system matrices for each individual frequency by assembling them only at a few master frequencies and using interpolation for the rest [3].