We present a simulation capability for micro-scale light-emitting diodes (µLEDs) that achieves comparable accuracy to CPU-based finite-difference time-domain simulation but is more than 107 times faster. Our approach is based on the Fourier modal method (FMM)-which, as we demonstrate, is well suited to modeling thousands of incoherent sources-with extensions that allow rapid convergence for µLED structures that are challenging to model with standard approaches. The speed of our method makes the inverse design of µLEDs tractable, which we demonstrate by designing a metasurface-enhanced µLED that doubles the light extraction efficiency of an unoptimized device.