Hierarchical B-spline complexes of discrete differential forms
Abstract
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 isogeometric solution of problems arising in electromagnetics and fluid mechanics. We derive a sufficient and necessary condition guaranteeing exactness of the hierarchical B-spline complex for arbitrary spatial dimension, and we derive a set of local, easy-to-compute and sufficient exactness conditions for the two-dimensional setting. We examine the stability properties of the hierarchical B-spline complex, and we find that it yields stable approximations of both the Maxwell eigenproblem and Stokes problem provided that the local exactness conditions are satisfied. We conclude by providing numerical results showing the promise of the hierarchical B-spline complex in an adaptive isogeometric solution framework.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 05, 2018
- Source ID
- 10.1093/imanum/dry077
Entities
People
- Derek C. Thomas
- John Andrew Evans
- Kendrick M. Shepherd
- Michael A. Scott
- Rafael Vázquez Hernández
Organizations
- Air Force Office of Scientific Research
- Brigham Young University
- Consiglio Nazionale delle Ricerche
- Defense Advanced Research Projects Agency
- European Research Council
- National Science Foundation
- Swiss Federal Institute of Technology in Lausanne
- University of Colorado Boulder
- University of Texas at Austin