122 citations · 252 across the 8 of their papers we have counts for
8 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…
Isogeometric Bézier dual mortaring: The biharmonic problem
Di Miao, Michael A. Scott, Michael J. Borden +2
In this paper we develop an isogeometric Bézier dual mortar method for the biharmonic problem on multi-patch domains. The well-posedness of the discrete biharmonic problem requires…
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…
Bézier Projection
Di Miao, Michael J. Borden, Michael A. Scott +1
In this paper we demonstrate the use of Bézier projection to alleviate locking phenomena in structural mechanics applications of isogeometric analysis. Interpreting the well-known…
A New Algorithm for the Evaluation of Generalized B-splines
Ian D. Henriksen, Emily J. Evans, Derek C. Thomas
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish thi…
Bézier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis
Derek C. Thomas, Michael A. Scott, John A. Evans +2
We introduce Bézier projection as an element-based local projection methodology for B-splines, NURBS, and T-splines. This new approach relies on the concept of Bézier extraction an…
Hierarchical analysis-suitable T-splines: Formulation, Bézier extraction, and application as an adaptive basis for isogeometric analysis
Emily J. Evans, Michael A. Scott, Xin Li +1
In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. Th…
Delay differential equation models for single and coupled bubble dynamics in a compressible liquid
Derek C. Thomas, Yurii A. Ilinskii, Mark F. Hamilton
Various models for interacting spherical bubbles in a compressible liquid based on delay differential equations are considered. It is shown that most previously proposed models for…