Abstract
Although isogeometric analysis possesses many advantages over classical finite element methods, the computational costs of matrix assembly (especially for high polynomial degrees) constitute a bottleneck in isogeometric numerical simulations. To address this issue, we propose an efficient algorithm for the formation of isogeometric Galerkin matrices based on the interpolation, look-up and sum factorization techniques. This method consists of three steps: First, we project the common factors occurring in the integrals into an appropriate spline space via the interpolation or quasi-interpolation operator. Subsequently, the entries of the stiffness and mass matrices are approximated by a sum of integrals of tensor-product B-splines. Second, to perform an exact integration of the integrands in the approximated matrices, a look-up table for the standardized B-spline tri-product integrals is built. Finally, the system matrices are efficiently assembled by invoking the sum factorization technique. We present a detailed analysis of the computational costs, in order to compare the new method with the existing approaches for all polynomial degrees. Several numerical tests confirm that the proposed method ensures the efficiency of matrix assembly. In addition, the extension of our approach to matrix-free applications is also discussed.
Published Version
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