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We present STARFORGE (STAR FORmation in Gaseous Environments): a newnumerical framework for 3D radiation MHD simulations of star formation thatsimultaneously follow the formation, accretion, evolution, and dynamics ofindividual stars in massive giant molecular clouds (GMCs) while accounting forstellar feedback, including jets, radiative heating and momentum, stellarwinds, and supernovae. We use the GIZMO code with the MFM mesh-free LagrangianMHD method, augmented with new algorithms for gravity, timestepping, sinkparticle formation and accretion, stellar dynamics, and feedback coupling. Wesurvey a wide range of numerical parameters/prescriptions for sink formationand accretion and find very small variations in star formation history and theIMF (except for intentionally-unphysical variations). Modules formass-injecting feedback (winds, SNe, and jets) inject new gas elementson-the-fly, eliminating the lack of resolution in diffuse feedback cavitiesotherwise inherent in Lagrangian methods. The treatment of radiation usesGIZMO's radiative transfer solver to track 5 frequency bands (IR, optical, NUV,FUV, ionizing), coupling direct stellar emission and dust emission with gasheating and radiation pressure terms. We demonstrate accurate solutions forSNe, winds, and radiation in problems with known similarity solutions, and showthat our jet module is robust to resolution and numerical details, and agreeswell with previous AMR simulations. STARFORGE can scale up to massive ($>10^5M_\odot $) GMCs on current supercomputers while predicting the stellar($\gtrsim 0.1 M_\odot$) range of the IMF, permitting simulations of both high-and low-mass cluster formation in a wide range of conditions.

STARFORGE: Toward a comprehensive numerical model of star cluster formation and feedback