Finite Elements Tearing and Interconnecting (FETI)

Overview

Originally computers were only able to execute a large range of simple tasks in a serial manner, so one after another. Even though the speed of this task-execution (one measure for that is the clock speed of a processor) got faster, there's a limit for that. So people started in the 1960s already to use several such Central-Processing-Units (CPU) in parallel and execute tasks on them at the same time. However, such Multicore-CPUs had their break through in the 2000s and are widely used nowadays, e.g. on people's Smartphones and PCs (Dual-, Quad- and Octa-Core). As soon as one starts with the development of own solution-methods for structural dynamics problems and wants to utilize that parallel computing-power, one has to think about how to distribute work to the several CPUs in an efficient way. The FETI method is based on a so-called domain decomposition or substructuring-approach. At first this means nothing more than slicing your full model, e.g. a truss, wheel-suspension or trubine-blade, into smaller pieces and distributing these pieces to the CPU-cores. They can solve these pieces simultaneously, which reduces the overall computing time. However the CPU-cores have to communicate during that process and exchange information regarding the current solution. This communication is rather expensive and has to be kept as low as possible. Especially complex nonlinear models increase that communication. Despite these costs, this FETI-approach still shines through very good scalbility. Scalability means, that the computing decreases with more CPU-cores. While this sounds very natural at first, it is quite an issue in parallel computing, as there's always a serial portion of tasks, that is not parallelizable and forms a lower bound. So if you are using already many CPU-cores it might happen, that even more CPU-cores won't decrease or even increase computing time. This again leads to the previously mentioned need for a very careful design of such methods.

State of art

The FETI method itself has been published in the early 1990s already. Since then many advances have been made in applying it to nonlinear structural dynamics problems and improving the efficiency with preconditioners and recycling methods. These work fine in most engineering-cases, but significantly loose their advantages in special cases, such as combinations of very different materials and cases with strong local nonlinearities in one or a few substructures, which slows down few processors and requires much communication. Current research focuses on developing new methods and approaches to increase efficiency even for these cases. For example new recycling techniques to reuse more information from previous iterations, adaptive preconditioning or localization techniques are being developed.

Current Projects

In this project we aim for improving the issue of local nonlinearities. One approach to reduce communication is the localization or local solution of nonlinear problems as a preconditioning step. Another one is the adaptation of the time-steps to the requirements of each substructure and therefore having different time-step sizes. Although this sounds like a good idea, one has to determine when to synchronize the substructures. No overall satisfying method is currently known in literature and neither have these methods been applied to large problems with multiple substructures, yet. For instance there are issues with spurious reflections of high frequencies on the interfaces, which might then trigger damageing-events to early. This needs to be resolved while no artificial energy-dissipation may be introduced in order to get an accurate method. Moreover it still has to be evaluated, if and when this approach leads to a more efficient procedure. So there's still a lot of work to do on that field.

Contact

Andreas Seibold, M.Sc.

Current members

Andreas Seibold, M.Sc.

Former members

Dipl.-Ing. Michael Leistner