No, and I don't think there will be one in the near future.
I was trying to find this myself. You can find computer programs that will let you AirPlay to the Mac (and maybe Windows), but not mirror. Not surprisingly the developer of the program I was interested in has been buried under requests for mirroring support.
According to their FAQ page mirroring uses Apples proprietary FairPlay encryption, and they don't have access to any API's that would let them tap into it.
And that is why this wildly popular feature is limited to AppleTV or an HDMI cable, durn it all.
I'd love to learn different.