GPU accelerated computation of the isogeometric analysis stiffness matrix

Due to high regularity across mesh elements, isogeometric analysis achieves higher accuracy per degree of freedom and improved spectrum properties, among others, compared with finite element analysis. However, this inherent feature of isogeometric analysis increases the density of the 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 for real-world applications. 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 graphics processing units to drastically accelerate computations.