4 citations · 6 across the 7 of their papers we have counts for
7 papers
Combinatorial maps for hierarchical splines
Caleb B. Goates, Kendrick M. Shepherd, Derek C. Thomas
Hierarchical splines are an important part of multiscale and adaptive isogeometric analysis formulations. The Bézier meshes of these splines are an essential part of their definiti…
Counterexamples to Proofs for Volumetric Parameterization of Topological Sweeps
Caleb B. Goates, Kendrick M. Shepherd
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameteri…
Tusqh: Topological Control of Volume-Fraction Meshes Near Small Features and Dirty Geometry
Brian Shawcroft, Kendrick M. Shepherd, Scott Mitchell
This work develops a framework to create meshes with user-specified homology from potentially dirty geometry by coupling background grids, persistent homology, and a generalization…
Construction of exact refinements for the two-dimensional hierarchical B-spline de Rham complex
Diogo C. Cabanas, Kendrick M. Shepherd, Deepesh Toshniwal +1
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a dis…
Locally-verifiable sufficient conditions for exactness of the hierarchical B-spline discrete de Rham complex in
Kendrick Shepherd, Deepesh Toshniwal
Given a domain , the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on ,…
The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout
Kendrick M. Shepherd, René R. Hiemstra, Thomas J. R. Hughes
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such…
Hierarchical B-spline complexes of discrete differential forms
John A. Evans, Michael A. Scott, Kendrick Shepherd +2
In this paper, we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometr…