[arjun-menon]

I was thinking, instead of that, what if you had a separate isolated tiny computer on spacecraft, that was powered by its solar panels (so there's no electrical wiring, or other connection to it), and have its own radio. And this separate computer could use the latest bleeding-edge CPU, and be encased in a radiation-hardened shell. It would use its radio to talk to the slower main computer, and do math really fast locally, and if need be, beam the results to Earth, or to a nearby orbiting satellite.

[angry_octet]

Unfortunately there isn't really any practical way to have a radiation hardened shell that is sufficiently effective. Eg. 5cm of aluminium stops only 30% of the galactic radiation. (Heavier elements (e.g. gold) are scattered by incoming particles causing incoming heavy ions which cause even more damage.)

So practically it would still experience significant radiation.

But having the main compute for Mars remain in orbit with the relay isn't a bad idea.