FOSLS makes no bones about improving computer models

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Going with the flow

Manteuffel’s group, working with a doctor at Children’s Hospital in Denver, used FOSLS and multigrid methods to run computer models of blood flow.  In one case, they compared their method with a commercial computational fluid dynamics code.

The commercial code took a little over an hour to run one blood flow model.  When the size of the problem doubled, the computing time tripled.

The FOSLS-multigrid solver took about 42 minutes to solve the simple model.  When the problem size doubled, computing time also doubled.  That’s an indication of the method’s efficiency, because computing time increased at the same rate as the problem’s size.

That’s called linear growth.  Solution techniques are “optimal” if their computing time grows linearly as problems get bigger in size – and they always get bigger, either because there is more to model or because more accuracy is required.

Manteuffel has worked with other researchers to apply FOSLS to a computer model of surgery to correct a congenital heart defect.  The model could make the operation more effective, giving patients a better life.

They’ve also worked on a “virtual eye” to better understand the pressure increase that causes glaucoma.  Manteuffel and his fellow researchers are still working.  They want to make multigrid methods adaptive, so they’re applicable to a wider variety of problems.

“So far, we’ve been very pleased to be able to solve problems we never thought we could in this very economical fashion,” he adds.

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