Isogeometric Analysis (IGA) has emerged over the past years as a powerful methodology for approximating solutions to boundary-value problems in science and engineering. In isogeometric analysis, the same spline functions that are used for the CAD representation of geometries are also used as a basis for constructing the numerical approximation. Isogeometric analysis therefore offers the prospect of bridging the gap between computational design and computational analysis, enabling direct computational analysis of CAD-engineered objects.

In addition to the aforementioned unification of computational analysis and design, the increased smoothness of spline approximations, relative to traditional finite elements, enables new numerical approximation techniques for, for instance, shells, cohesive-zone models of failure, Cahn-Hilliard type phase-field models, and free-boundary and shape-optimization problems.

School aim and audience

The advanced school Isogeometric Analysis: Fundamentals and Applications aims to acquaint its participants with the fundamentals of isogeometric analysis and its applications in fluid and solid mechanics. The course provides an introduction into spline technology, its use in computer aided design and engineering, and the use of splines to construct approximations to boundary-value problems. Furthermore, the course addresses the application of isogeometric analysis to applications where the higher-order smoothness providedby spline functions is indispensible, viz., shell theory, cohesive-zone models in failure mechanics, and free-boundary problems. The course ends with a treatment of more advanced topics, such as adaptive-refinement techniques in isogeometric analysis.

The advanced school is intended for graduate students and research professionals in computational engineering and applied mathematics. Although most of the material is self-contained, basic familiarity with differential equations and finite-element techniques is prerequisite.