A multilevel algorithm for fast evaluation of wave fields in the time domain

A fast multilevel algorithm with optimal memory requirements for rapid evaluation of transient wave fields radiated by known source constellations is presented. The proposed algorithm is designed to accelerate marching on in time (MOT), resulting in a fast and computationally adaptive solvers. The multilevel computational sequence relies on a hierarchical decomposition of the scatterer into radiating sub-domains combined with the usage of delay- and amplitude- compensated fields for representing the far zone interactions. Specifically, these modified fields are sampled over adaptive temporal and spatially nonuniform grids. Overall, the algorithm progressively aggregates partial field contributions of increasing sizes sub-domains resulting to produce the total radiated field.