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Literature Review: Parallel Computing on linear equations of linear elastic FEM stimulation with CUDA

Zheng Xia
School of Electrical and Computer Engineering, University of Ottawa, Ottawa, Canada
University of Ottawa, 2014

@article{xia2014literature,

   title={LITERATURE REVIEW: Parallel Computing on linear equations of linear elastic FEM stimulation with CUDA},

   author={Xia, Zheng},

   year={2014}

}

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Scientific computation is the field of study that uses computers to implement mathematical models of physical phenomena such as FEM in deformation measurement in virtual reality. Scientific and engineering problems that would be almost impossible to solve by hand whereas on a computer, it can be handled properly. A numerical algorithm calculating for different fields can be written as a code to run on a computer, where some values are given as a input, and after a small time period, answers are easily given by the computer operator. The problem is now that a small time period is relative. Obviously, for a computer to run a code in a few days that would take a scientist or engineers months or years is very impressive. But even a few days seems to be long enough for the amount of processing power resting on the programming. Personal computers nowadays usually come with a graphics processing unit (GPU) that runs programs faster than a CPU due to the great demand for the texture processing in the core of the GPU. On the other hand, researchers also have used scientific computation to model the universe and solve complex mathematical problems. Algorithms written to solve partial differential equations in this way can be quickly and efficiently. The researchers of this project were particularly interested in solving linear equations that describe the relation between the unknown displacements and the stress forces. That is, once the stiffness matrix K have been defined in a linear elastic deformable model, according to the factors of known, the unknown part (displacements and forces) can be calculated in a relative short time period.
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