Is there any other computation theory besides the one in automata theory?
There is indeed computability-theory for non-discrete settings. This area is called computable analysis. A decent tutorial to computable analysis is here (if you have an institutional subscription, or can get it from a library):

https://link.springer.com/chapter/10.1007%2F978-0-387-68546-5_18

The tutorial focuses quite a bit on the case where we are computing with real numbers, or at least elements of metric spaces. Computable analysis can handle much more situations though. Roughly speaking, we probably have reasonable computability-notions for any kind of space appearing in ordinary mathematics.

It turns out that many concepts from the classical, discrete computability theory still apply, but topological aspects also become very relevant.