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Gordon Bell Prize Winners Simulate Earth’s Mantle

Copyright: Vadim Sadovski

There’s a fundamental difference with explicit solvers, where one does not have to solve a large, nonlinear system. Instead, one repeatedly applies a (large) matrix to vectors, usually to compute time steps in a simulation. How to obtain good parallel scalability for computing matrix-vector applications is well-known. Thus, many computations done on supercomputers are explicit, but this method only applies to simulations of certain kinds of physical phenomena.

Our problem required implicit solvers. Implicit problems are globally coupled, and when you’re cutting the problem into small pieces, the amount of information these small pieces need to exchange isn’t local anymore. In principle, each variable can influence one another, and that makes it fundamentally different from explicit problems. One component of our algorithm uses a hierarchy of different resolutions and can thus exchange information efficiently on both local and global scales.

ISM: Do you see this as a different way to solve these huge problems?
It’s just a different type of problem that requires a stronger and more robust type of solver than others. I can’t imagine how you could avoid an implicit solver with this kind of problem where everything is globally coupled. By using an explicit solver, you end up with a much different solution, totally inaccurate and clearly unreliable. This is one of those hard problems where the global coupling between multiscale phenomena obliges you to use an implicit solver to get accurate results; there is no other choice.

ISM: Do you see this having applications in other disciplines?
From a geophysical perspective, we have solved the forward problem. We think we know certain things. We run the physics and we get an answer. Then we compare that answer to what we observe. Often with science problems, we want to infer something from the data itself. That’s called an inverse problem.

Because we can do the forward problem well, we can do the physics correctly and efficiently and we can now do global, plate dynamics and mantle flow as an inverse problem. That’s the next big thrust of our collaboration as we try to infer the forces inside the earth directly from the data using our new software as a framework. Because implicit problems can now scale to huge parallel computers, I think that is going to have a big general-science impact.

ISM: Are you demonstrating a better way to scale on these massively parallel systems?
Research centers have been building larger and larger supercomputers. Now, one of the main challenges is how algorithms must be adapted such that they can scale to millions of cores and thus fuel computations that have the potential to lead to breakthrough science.

Some problems can relatively easily be partitioned into small pieces. Each piece is then solved on a few hundred processors, and then the computed information is exchanged. This does not require supercomputers with extremely fast networks, one of the strengths of the BG/Q machines. The BG/Q architecture has several networks for communication, which is required to solve tightly coupled problems that require millions of messages to be sent through the network every second.

When I started getting interested in algorithms for parallel computers, the largest machines had a couple thousand processors. It was unimaginable to have methods that would scale to a million processors because it was just so far out there. Today, one of the interesting aspects of this work is demonstrating that these machines can be used efficiently for large, tightly coupled problems and that one can optimize codes to actually get good performance.

ISM: How long did it take to actually develop this dynamic model?
The code has changed several times, but I started working on these and related problems about eight years ago. Of course, things get rewritten as new machines and new methodologies come into use, and there were a lot of other people who contributed to this project.

Jim Utsler, IBM Systems Magazine senior writer, has been covering the technology field for more than a decade. Jim can be reached at jjutsler@provide.net.

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