**Session:** **Theoretical aspects of Isogeometric Analysis and recent applications**

Isogeometric analysis (IgA) is a method for the numerical simulation of problems governed by partial differential equations. One of the key points of IgA is the retainment of the description of the domain where the PDE is defined as given by a CAD system (so in terms of B-splines, NURBS or their generalizations), instead of approximating it by a triangular/polygonal mesh. Indeed the term "Isogeometric" is due to the fact that the solution space for dependent variables is represented in terms of the same functions which describe the geometry (i.e. splines). Other good features are the gain of high flexibility in the smoothness of the discretization space, and the simplification of mesh refinement by eliminating the need for communication with the CAD geometry once the initial mesh is constructed. The research on IgA has been oriented into two main directions. On one hand to apply the available CAGD techniques to different PDEs, ranging from fluids, structures, phase-field modeling, electromagnetics, shape and topology optimization, till discrete and diffuse modeling of crack propagation. On the other hand to develop new and more flexible representations like hierarchical splines, generalized Tchebychev splines, and locally-refinable B-splines and to investigate on the related theoretical issues. Another important aspect is also the consistent treatment of trimmed patches and multi-patch geometry. The purpose of this special session is to give an overview on several theoretical and applicative aspects of IgA recently arisen.

**Organizers:**

- Alessandra Aimi,
*alessandra.aimi@unipr.it* - Maria Lucia Sampoli,
*marialucia.sampoli@unisi.it* - Alessandra Sestini,
*alessandra.sestini@unifi.it*

**Talks:**

- A.S. Boiardi,
*IGA-Energetic BEM for the numerical solution of 2D wave scattering problems in the space-time domain* - A. Bressan,
*Preconditioners for adaptive spaces or spaces for preconditioners?* - F. Calabrò,
*Effcient Quadrature in Isogeometric Galerkin methods and Isogeometric Boundary Element methods* - A. Falini,
*A multi-patch IgA-BEM model for 3D Helmholtz problems* - C. Garoni,
*Spectral Analysis of Isogeometric Immersed Discretizations* - C. Giannelli,
*C^1 hierarchical spline constructions on planar multi-patch geometries for adaptive IGA* - E. Sande,
*Optimal spline spaces are outlier free* - D. Toshniwal,
*Smooth splines on unstructured meshes* - E. Zampieri,
*Collocation Isogeometric Approximation of acoustic wave problems*