Cross element integration for superconvergent frequency computation with cubic isogeometric formulation

Abstract

A superconvergent cross element integration technique is presented for the cubic isogeometric formulation referring to the frequency computation of wave equations. More specifically, a four-element integration cell with 11-point quadrature and an intermediate two-element integration cell with 6-point quadrature are developed in accordance with the optimization of discrete isogeometric frequency error. These cross-element quadrature rules stand in sharp contrast to the conventional 4-point element based integration for the cubic isogeometric formulation, which needs 16 quadrature points within four elements per spatial dimension, especially for multi-dimensional scenarios. Meanwhile, a superconvergence with two added accuracy orders upon the 6th order accurate standard cubic isogeometric approach is naturally embedded in the proposed cross element integration technique by construction. Consequently, both efficiency and accuracy advantages are simultaneously realized in the proposed cross element integration method for cubic isogeometric formulation. The efficacy of the proposed superconvergent methodology is consistently validated by several representative numerical examples.