Hardware-Oriented Multigrid Finite Element Solvers on GPU-Accelerated Clusters

Stefan Turek, Dominik Goddeke, Sven H.M. Buijssen, Hilmar Wobker
Institut fur Angewandte Mathematik, TU Dortmund, Germany
Chapter 6 in: Jakub Kurzak, David A. Bader and Jack J. Dongarra (eds.): Scientific Computing with Multicore and Accelerators, CRC Press, Dec. 2010


   author={Stefan Turek and Dominik G{“o}ddeke and Sven H.M. Buijssen and Hilmar Wobker},

   title={Hardware-Oriented Multigrid Finite Element Solvers on {GPU}-Accelerated Clusters},

   booktitle={Scientific Computing with Multicore and Accelerators},

   publisher={CRC Press},




   editor={Jakub Kurzak and David A. Bader and Jack J. Dongarra}


The accurate simulation of real-world phenomena in computational science is often based on an underlying mathematical model comprising a system of partial differential equations (PDEs). Important research fields that we pursue in this setting are computational solid mechanics and computational fluid dynamics (CSM and CFD, see Section 3). Practical applications range from material failure tests, as for instance crash tests in the automotive industry, to fluid and gas flow of any kind, for instance in chemical or medical engineering (e.g., simulation of blood flow in the human body to predict aneurysms) or flow around cars and aircrafts to minimize drag and lift forces. Moreover, the coupling of both models is essential for fluid structure interaction settings (FSI) which represent problem fields of very high technological importance. Such configurations include polymer processing or micro fluidic problems exhibiting very complex multiscale behavior due to nonlinear rheological or non-isothermal constitutive laws, and also due to self-induced oscillations of the structural parts in the flow field. In all these cases, the fluid part is mostly laminar, but highly viscous.
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