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The upcoming Nancy Grace Roman Space Telescope will carry out a wide-areasurvey in the near infrared. A key science objective is the measurement ofcosmic structure via weak gravitational lensing. Roman data will beundersampled, which introduces new challenges in the measurement of sourcegalaxy shapes; a potential solution is to use linear algebra-based coadditiontechniques such as Imcom that combine multiple undersampled images to produce asingle oversampled output mosaic with a desired "target" point spread function(PSF). We present here an initial application of Imcom to 0.64 square degreesof simulated Roman data, based on the Roman branch of the Legacy Survey ofSpace and Time (LSST) Dark Energy Science Collaboration (DESC) Data Challenge 2(DC2) simulation. We show that Imcom runs successfully on simulated data thatincludes features such as plate scale distortions, chip gaps, detector defects,and cosmic ray masks. We simultaneously propagate grids of injected sources andsimulated noise fields as well as the full simulation. We quantify the residualdeviations of the PSF from the target (the "leakage"), as well as noiseproperties of the output images; we discuss how the overall tiling pattern aswell as Moir\'e patterns appear in the final leakage and noise maps. We includeappendices on interpolation algorithms and the interaction of undersamplingwith image processing operations that may be of broader applicability. Thecompanion paper ("Paper II") explores the implications for weak lensinganalyses.

Simulating image coaddition with the Nancy Grace Roman Space Telescope: I. Simulation methodology and general results