Multi-resolution Isogeometric Analysis -- Efficient adaptivity utilizing the multi-patch structure
In Isogeometric Analysis (IgA), one often relies on a configuration of multiple conforming patches to realize an exact representation of the computational domain (multi-patch IgA). On each patch, the discretization is usually based on a tensor product spline space and the conformity is guaranteed by imposing the same grid size on each patch. One drawback of a tensor product spline basis is the lack of localized refinement. Local refinement strategies are essential for adaptive methods necessary for the efficient approximation of solutions of low regularity. In the last decades, multiple local refinement techniques have been developed for spline based discretization. However, the implementation seems especially cumbersome in the context of multi-patch IgA.
In this talk we consider a multi-patch based approach for adaptive refinement, employing subdivision of entire patches into smaller subpatches to localize refinement. On each subpatch, one has the ability to vary the grid sizes independently. With this approach, we moderately increase the number of patches, recover convergence rates of other adaptive schemes and increase the numbers of degrees of freedom only mildly, compared to other approaches for spline based local refinement.
