The detection of the radio signature of in-ice charged-particle showers is a promising technique for the study of ultra-high-energy neutrinos. Planned large-scale radio arrays require a thorough understanding of the generation and propagation of electromagnetic radiation in the heterogeneous environment of polar ice. In this contribution, we introduce Eisvogel, a simulation tool for the first-principles calculation of the time-domain signal observed by an antenna in such an experiment. Eisvogel calculates the exact antenna signal through the numerical convolution of the shower with a precomputed Green’s function that encodes the properties of the surrounding ice and the antenna and captures all electrodynamic effects. Numerically expensive calculations are thus amortized into the construction of the Green’s function, with the signal calculation for a given shower remaining very efficient. Here, we describe the structure of our code and the current stage of development, show a comparison with an established simulator, and outline future applications.