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This letter presents strategies on how to optimize graphics processing unit (GPU)-based finite-element matrix-generation that occurs in the finite element method (FEM) using higher-order curvilinear elements. The goal of the optimization is to increase the speed of evaluation and assembly of large finite-element matrices on a single GPU while maintaining the accuracy of numerical integration at the desired level. For this reason, the choice of the optimal Gaussian quadratures for curvilinear finite elements focused on accuracy, memory usage, and runtime of numerical integration is discussed. Moreover, we show how to efficiently utilize symmetry of local mass and stiffness matrices on a GPU in the numerical integration step. The performance results, obtained on a workstation equipped with one Tesla C2075, indicate that the proposed strategies retain the accuracy of computations, allow generation of larger sparse linear systems, and provide 2.5-fold acceleration of GPU-based finite-element matrix-generation.