Variationally consistent domain integration for isogeometric analysis

Spline-type approximations for solving partial differential equations are the basis of isogeometric analysis. While the common approach of using integration cells defined by single knot spans using standard (e.g., Gaussian) quadrature rules is sufficient for accuracy, more efficient domain integration is still in high demand. The recently introduced concept of variational consistency provides a guideline for constructing accurate and convergent methods requiring fewer quadrature points than standard integration techniques. In this work, variationally consistent domain integration is proposed for isogeometric analysis. Test function gradients are constructed to meet the consistency conditions, which only requires solving small linear systems of equations. The proposed approach allows for significant reduction in the number of quadrature points employed while maintaining the stability, accuracy, and optimal convergence properties of higher-order quadrature rules. Several numerical examples are provided to illustrate the performance of the proposed domain integration technique.