Isogeometric analysis (IGA) consists of using the same higher-order
and smooth spline functions for the representation of geometry in
Computer Aided Design as for the approximation of solution fields
in Finite Element Analysis. Now, about fifteen years after its
creation, substantial works are being reported in IGA, which make
it very competitive in scientific computing. This book provides a
contemporary vision of IGA by first discussing the current
challenges in achieving a true bridge between design and analysis,
then proposing original solutions that answer the issues from an
analytical point of view, and, eventually, studying the shape
optimization of structures, which is one of the greatest
applications of IGA. To handle complex structures, a full
analysis-to-optimization framework is developed, based on
non-invasive coupling, parallel domain decomposition and immersed
geometrical modeling. This seems to be very robust, taking on all
of the attractive features of IGA (the design-analysis link,
numerical efficiency and natural regularization), giving us the
opportunity to explore new types of design.
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