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Using GPU-based Computing To Accelerate Finite Element Problems

Jacob Watt
The University of Texas at Arlington
The University of Texas, 2012

@article{watt2012using,

   title={Using Gpu-based Computing To Accelerate Finite Element Problems},

   author={Watt, J.},

   year={2012},

   publisher={Aerospace Engineering}

}

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Historically Graphics Processing Units (GPU) have been used for offloading graphical visualization and made popular in use for video games, but with the development of NVIDIA’s CUDA architecture and programing language there has been an increase in the use of GPUs in general purpose (GPGPU) programing. Problems involving large systems of linear equations, such as the Finite Element Analysis (FEA), can benefit greatly from the parallel computing capabilities of GPUs. In my thesis I will solve Poisson’s equation and discuss the advantages and disadvantages of the massively parallel environment of GPUs. I will show that on a unstructured grid that the matrix-vector multiplication can be run 15.4 times faster on the GPU when compared to an Intel i5 CPU. For all cases, 2-D triangular elements with linear basis functions were used. When the linear algebra problem is solved using the biconjugate gradient stabilized method (BiCGSTAB), the method runs 14.4 faster on the GPU as compared to the serial C code. And lastly, solving the whole FEA including data setup, element integration, assembly, and memory transfer times preforms 11.8 faster on the NVIDIA GPU compared to the serial code run on an Intel i5 CPU.
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