Rectified unstructured T-splines with dynamic weighted refinement for improvement in geometric consistency and approximation convergence

T-splines developed on unstructured meshes are called unstructured T-splines, which have the problem of geometric inconsistency and unfairness of mesh density evolution over regular or irregular elements during the refinement. Geometric inconsistency means that the geometry defined by an unstructured T-spline keeps changing throughout the refinement. The unfairness of mesh density evolution pertains to different scalings of regular and irregular elements during the refinement, which drags down the convergence of the approximation result in isogeometric analysis. This paper proposes rectified unstructured T-splines to solve these two problems with the dynamic weighted refinement and rectified T-spline basis functions. Owing to the dynamic weighted refinement, the mesh size scaling tends to 12 fairly everywhere on unstructured meshes, and geometric consistency is improved with the rectified T-spline basis functions. The approximation convergence is also greatly enhanced for isogeometric analysis from the original unstructured T-splines, which is quite meaningful for engineering simulations.