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Accelerating Double Precision FEM Simulations with GPUs

Dominik Goddeke, Robert Strzodka, Stefan Turek
Universitat Dortmund, Fachbereich Mathematik
18th Symposium Simulation Technique (ASIM’05), Erlangen, Germany, Sep. 2005

@inproceedings{Goeddeke:2005:ADP,

   author={Dominik G{“o}ddeke and Robert Strzodka and Stefan Turek},

   title={Accelerating Double Precision {FEM} Simulations with {GPUs}},

   booktitle={18th Symposium Simulationstechnique (ASIM’05)},

   year={2005},

   series={Frontiers in Simulation},

   editor={Frank H{“u}lsemann and Matthias Kowarschik and Ulrich R{“u}de},

   pages={139–144},

   month={sep}

}

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In visualization and computer graphics it has been shown that the numerical solution of PDE problems can be obtained much faster on graphics processors (GPUs) than on CPUs. However, GPUs are restricted to single precision floating point arithmetics which is insufficient for most technical scientific computations. Since we do not expect double precision support natively in graphics hardware in the medium-term, we demonstrate how to accelerate double precision iterative solvers for Finite Element simulations with current GPUs by applying a mixed precision defect correction approach. Our prototypical algorithm already runs more than two times faster than a highly tuned pure CPU solver while maintaining the same accuracy. We present a series of tests and discuss multiple optimization options.
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