Isogeometric design and analysis

Isogeometric analysis (IGA) aims to bridge the geometric divide between CAD systems and FEA software tools. It is founded on the idea of using the same basis functions to represent the CAD geometry and to approximate the physical quantities appearing in analysis. It promises to revolutionize the design and analysis processes for automobile, aerospace and marine industry by eliminating the need for model conversion, approximation and meshing. Over the last decade, research in isogeometric design and analysis has undergone tremendous growth and has led to substantial progress in both computer-aided design and finite element analysis fields. Different geometric representations such as NURBS, T-splines, triangular splines and subdivision surfaces have been investigated for use in isogeometric analysis. In particular, various volume parameterization techniques have been developed for isogeometric analysis. Further, tighter integration of CAD and analysis through isogeometric analysis has empowered applications in shape optimization. The objective of this special issue is to capture the state-ofthe-art regarding the theoretical foundations, the computational methods, and the applications of isogeometric analysis and its integration with CAD. In this issue, we present thirteen articles in several topic areas, including domain parameterization, quadrature rules, shape optimizations, new IGAmethods andnovel IGA applications. On domain parameterization, Buchegger and Jüttler presented a patch adjacency graph based approach to planar multi-patch domain parameterization. Sauer et al. proposed to create volumetric mesh from T-spline surfaces through a T-spline boundary zone beneath the surface. Chan et al. proposed an approach for constructing spline representation of a domain of interest from voxel-based data through PHT-spline represented level set. Lei et al. developed a volume preserving mesh parameterization approach based on optimal mass transportation. On quadrature, Barton and Calo presented Gauss–Galerkin quadratures for quadratic and cubic spline spaces based on the homotopy continuation concept. On shape optimization, Wang et al. presented normalization approaches for the descent search direction in isogeometric shape