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Computation of the Isogeometric Analysis Stiffness Matrix on GPU

Alexander Karatarakis, Panagiotis Karakitsios, Manolis Papadrakakis
Institute of Structural Analysis and Antiseismic Research National Technical University of Athens, Zografou Campus, Athens 15780
3rd South-East European Conference on Computational Mechanics – an ECCOMAS and IACM Special Interest Conference (SEECCM III), 2013

@article{karatarakis2013computation,

   title={Computation of the Isogeometric Analysis Stiffness Matrix on GPU},

   author={Karatarakis, Alexander and Karakitsios, Panagiotis and Papadrakakis, Manolis}

}

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Due to high regularity across mesh elements of isogeometric analysis, this new method achieves higher accuracy per degree of freedom and improved spectrum properties, among others, compared to finite element analysis. However, this inherent feature of isogeometric analysis reduces the sparsity pattern of stiffness matrix and requires more elaborate numerical integration schemes for its computation. For these reasons, the assembly of the stiffness matrix in isogeometric analysis is a computationally demanding task, which needs special attention in order to be affordable in real-world implementations. In this paper we address the computational efficiency of assembling the stiffness matrix using the standard element-wise Gaussian quadrature. A novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits, among them its amenability to parallelization and the efficient utilization of the graphic possessing units to drastically accelerate computations.
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