We call quantum mechanics and classical mechanics ab initio methodes for the same reason within their respective application fields, namely because they are based on fundumental rules and equations that describe the behaviour we see in nature (or the experiment) that can not be reduced or explained further with a more detailed model. Classical electromagnetism therefore is only a ab inito method (with is first principles the maxwell equations) if it is only used for classical problems, since it breaks down and needs a more fundamental explenation in the context of relativity or quantum mechanics.