A fast space-adaptive algorithm to evaluate transient wave fields due to low-frequency source constellations

A novel, fast, and non-plane wave based algorithm to efficiently evaluate transient wave fields due to low-frequency source constellations is proposed. In the proposed scheme, transient sources are sampled at a fixed temporal discretization rate that is determined solely by the highest frequency in their temporal spectrum and that does not depend on the source geometry. Using a procedure inspired by Cadzow (1979), these samples are used to construct short, bandlimited subsignals that permit reconstruction of the fields they produce at a given time step. As a result, these fields are characterized by a few spectral samples that are efficiently calculated by the low-frequency, space-adaptive fast multipole method (FMM) at a computational cost that scales as N_s, the number of sources/observers; the computational complexity of the aforementioned low-frequency PWTD in contrast scalesas O(N_slogN_s). The new scheme´s numerical error can be controlled at will and decays exponentially fast with its computational cost. The proposed algorithm can be used to accelerate MOT based time domain integral equation solvers.