Abstract

There is a need for integrated geometric design and high fidelity simulation for rationalising the industrial product design cycle. Conventional computer aided geometric design and finite element simulation packages use different mathematical representations for geometrical modeling. Since these two representations are incompatible with each other, it is extremely difficult and time consuming to engineer parts efficiently. My research is focused on developing computational methods, based on isogeometric analysis paradigm, which addresses this issue.

In this talk, I will introduce a new manifold-based approach for constructing smooth bivariate basis functions of arbitrary order. The manifold is constructed as a collection of overlapping charts, which are defined from a given unstructured finite element mesh. Each chart contains a local polynomial approximation space and a partition of unity basis function, which is used for gluing the charts into a manifold. I will demonstrate that with the obtained smooth basis functions, optimal convergence orders can be obtained in the finite element context.