Seminars

Title: r-refinement in isogeometric analysis

Abstract:

In this talk, r-refinement in isogeoometric analysis will be
introduced. For r-refinement, the difference with h-refinement,
p-refinement and k-refinement is that the number of control points and the
degree of basis functions are unaltered and the positions of control
points on the computational domain are subjected to change upon the
required degree of accuracy. By r-refinement,  an optimal analysis-aware
parametrization of computational domain can be achieved. In the first
part, the r-refinement for analysis problems with exact solution will be
investigated, which also shows the importance of parametrization of
computational domain in isogeometric analysis. In the second part, the
case of problems with unknown solutions will be studied after presenting a
residual-based posteriori error estimation for isogeometric analysis. The
posteriori error estimation is obtained by inverse mapping from solution
field to computational domain, which uses the basic idea of isogeometric
analysis. Several examples for 2D and 3D problems will be presented to
show the effectiveness of r-refinement method in isogeometric analysis.