Michael J. Borden

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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 dimensions.(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)
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)
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)
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