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A novel algorithm to efficiently compute transient fields produced by known time dependent source constellations is proposed. The algorithm relies on domain decomposition and comprises two steps to be repeated for each subdomain. In the first step, delay and amplitude compensated fields, produced by currents residing within each subdomain are computed over a sparse set of points of a carefully designed non-uniform spherical grid surrounding the observation domain. During the second step, total fields in the observer domain are evaluated by interpolation, delay and amplitude restoration, and aggregation of subdomain fields.