This idea combines 3 pieces of information. If any one of them are wrong we can just mark it bad science. A link is provided for each of the pieces so you'll know it wasn't conjured up using some kind of magic spell.
1. The Hafele and Keating Experiment - In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation. They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, DC, they had gained about 0.15 microseconds compared to the ground-based clock.
2. Supercomputers operate at nanosecond speeds, where microseconds are considered slow - "IBM. announced yesterday that the Blue Gene/L system had attained a sustained performance of 36.01 trillion calculations per second, or teraflops, eclipsing the top mark of 35.86 teraflops reached in 2002 by the Earth Simulator in Yokohama. The new speed was reached during internal testing at IBM's production center in Rochester, Minn.
3. Gravity isn't distributed evenly across the earth. A new gravity map of the Earth suggests that if you want to lose weight you should go to India, where the pull of gravity is slightly less than it is elsewhere on the planet. You would be slightly less than 1% lighter there.
So here's the idea... Stick the supercomputer on a boat and sail it to the Indian Ocean where gravity is lower to take advantage of the time distortion effect. You'll get more nanoseconds for your nanosecond, so to speak.
Speaking of gravity, and its relationship to time, there doesn't seem to be a lot of literature out there describing what might be taking place at the center of gravity in the Earth-Moon system (which due to synchronicity is about 1000 miles beneath the earth's surface). Since that is the greatest point of gravity in the system time should be moving slightly slower. Maybe there's not enough of a discrepancy in the two reference points (earth's surface and this center of gravity) for this area to make any difference as it makes its way under the surface (or more accurately the system makes its way around this point). There might be a bigger discrepancy, and effect, when considering the sun with its much larger gravitational force though.