"In our computation," says Peskin, "there's a regular cubic lattice on which the flow variables are stored, and there's the more complicated geometry of the heart muscle that is stored as a series of fibers." Peskin and McQueen pioneered this technique, the "immersed boundary" method, in creating their heart model, and it is now used by other researchers on a multitude of problems involving fluids interacting with a movable, elastic boundary. The heart, in effect, is immersed within the computational grid, and if a valve ring -- a hole that fluid should flow through -- isn't big enough compared to the size of the grid, flow can be partially blocked.
Doubling the grid size in each dimension (128 x 128 x 128) meant eight times as many grid points and, consequently, required eight times as much computer memory. On the Y-MP, the researchers found that the increased data spilled over into disk storage, slowing processing to such an extent that a single heartbeat would have taken three years. On the C90, the same calculation took a matter of days.
"It turns out there was no way we were going to get good results with the coarser grid," says Peskin, "and we were stuck there because of the computer that was available. The new computer gave us a chance to succeed we didn't have before."
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