Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization

• We discuss the use of the sum-factorization for the calculation of the integrals arising in Galerkin isogeometric analysis.
• We give an estimate of the quadrature computational cost and compare with the standard approach.
• We perform numerical tests.
• Sum-factorization significantly reduces the quadrature computational cost.

In this paper we discuss the use of the sum-factorization for the calculation of the integrals arising in Galerkin isogeometric analysis. While introducing very little change in an isogeometric code based on element-by-element quadrature and assembling, the sum-factorization approach, taking advantage of the tensor-product structure of splines or NURBS shape functions, significantly reduces the quadrature computational cost.