Michael J. Borden

Learn More
We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and immersed boundary analysis. We use the principle of B-spline subdivision to derive a local refinement procedure , which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher(More)
This paper presents methods and applications of sheet insertion in a hexahedral mesh. A hexahedral sheet is dual to a layer of hexahedra in a hexahedral mesh. Because of symmetries within a hexahedral element, every hexahedral mesh can be viewed as a collection of these sheets. It is possible to insert new sheets into an existing mesh, and these new sheets(More)
Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle concave refinement regions and self-intersecting hex sheets. The Selective Approach method is a(More)
Sweeping algorithms provide the ability to generate all hexahedral meshes on a wide variety of three-dimensional bodies. The work presented here provides a method to refine these meshes by first defining a path through either the source or the target mesh and next by locating the sweeping layer to initiate the refinement. A major contribution of this work(More)
  • 1