fighterly equivalent of Disintegrate

So, suppose we leave mages more or less as-is and decide we have to beef up fighters significantly to compete.

At 11th level mages can get Disintegrate, which is basically caster level x 2d6 in damage in one round, a small number of times per day, with an important special effect. A fort save reduces this to 5d6 regardless of of caster level.

So what's an appropriate fighterly equivalent? It doesn't seem right to aim for a fighter being able to do this much damage in one round at 11th level, since he can "keep doing it all day", but if he can't take out the same foe in the length of a typical combat, he's far behind in his basic ability to reduce enemy HP.

At 11th level a fighter has 3 iterated attacks, doing a max of weapon damage (say, 1d8) plus Str mod (say, +3 for a dedicated fighter), average about 7.5, very roughly equivalent to 2d6 per blow that hits. If all 3 hit, that's about 6d6, compared to Disintegrate's 22D6 at that level. I'm not sure what AC to assume he's up against, especially since the mage gets a ranged touch attack that ignores armour, but it seems pretty clear each of his attacks is less likely to hit than the mage's one attack is.

It seems to me that, even if we decide a fighter only needs to do 22D6 over a whole 3-4 round combat, we need to beef up his damage by a factor of 3 or more. Exactly how much more is up for debate, but does the basic argument for bumping up his damage make sense? If so I can calcuate a few detailed scenarios for comparison.
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