In this talk, I detail the development of a tapestry of approximations for highly accurate simulation of high mass ratio inspirals. Due to the precision requirements for waveform templates important for LISA data analysis, one of the significant goals of self force calculations is to compute waveforms that track the phase of the long evolution of EMRIs to a precision far better than one radian. One of the methods is a multiscale expansion which exploits the separation of scales between the slow radiation-reaction time and the fast orbital time. In this talk, I will discuss in detail the mathematical techniques of the multiscale approximation method and other approximations in the various regions of the spacetime. The set of techniques I refer to as the multiscale tapestry approximation comprise the only currently available method of assuring sub-radian accuracy in the computed waveform.