Edward Fuselier's Home Page

Edward Fuselier

Associate Professor of Mathematics
High Point University
Department of Mathematical Sciences
363 Couch Hall
(336) 841-9343
Office Hours: by appointment

Mailing Address:

Department of Mathematical Sciences
1 N University Pkwy
High Point, NC 27262

Classes, Spring 2025

MTH 1400 - Precalculus
MTH 2510 - Mathematical Methods for Engineers II
MTH 4910 - Undergraduate Research I
Current students can access course content via Blackboard.

Research Interests

Radial Basis Functions and Their Applications
Kernel Approximation on the Sphere and other Manifolds
Divergence-free and Curl-free Positive Definite Functions
Approximation on Graphs
Scientific Computing

Publications

(with J.P. Ward) Locally supported, quasi-interpolatory bases for the approximation of functions on graphs, Linear Algebra and its Applications, 703 (2024), 369-394, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2024.09.011.

(with J. Pampush, P. Morse, M. Skinner, and R. Kay) Sign-oriented Dirichlet Normal Energy: Aligning Dental Topography and Dental Function in the R-package molaR, Journal of Mammalian Evolution, 29(4) (2022), 713–732.

(with K. Drake and G. Wright) Implicit Surface Reconstruction with a Curl-Free Radial Basis Function Partition of Unity Method. SIAM Journal on Scientific Computing, 44(5) (2022), A3018-A3040.

(with J. Pampush, P. Morse and G. Yapuncich) Applying BayesModelS to body mass prediction; comparisons with traditional approaches and recommendations for future paleontological reconstructions, Journal of Human Evolution, 161 (2021), 103077.

(with K. Drake and G. Wright) A Partition of Unity Method for Divergence-Free or Curl-Free Radial Basis Function Approximation. SIAM Journal on Scientific Computing, 43(3) (2021), A1950-A1974.

(with G. Wright) A Radial Basis Function Method for Computing Helmholtz-Hodge Decompositions, IMA Journal of Numerical Analysis, 37(2) (2017), 774-797.

A Comparison of Numerical Techniques Through the Study of the Simple Pendulum, SIMIODE (2016), ”6-2-T-EulerCromerPendulum,” https://www.simiode.org/resources/1657.

(with V. Shankar and G. Wright) A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations, Computers and Fluids, 128 (2016), pg 41-52.

(with G. Wright) Order-preserving approximation of derivatives with periodic radial basis functions, Advances in Computational Mathematics, Volume 41 (2015), Issue 1, pg 23-53. (journal link)

(with T. Hangelbroek, F. Narcowich, J. Ward and G. Wright) Kernel Based Quadrature on Spheres and Other Homogeneous Spaces, Numerische Mathematik, 127 (2014), no. 1, pg 57-92.

(with T. Hangelbroek, F. Narcowich, J. Ward and G. Wright) Localized Bases for Kernel Spaces on the Unit Sphere, SIAM Journal on Numerical Analysis, Volume 51 (2014), no. 5, pg 2538-2562 archive link.

(with G. Wright) A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces, Journal of Scientific Computing, (2013) (journal link).

(with G. Wright) Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs, SIAM Journal on Numerical Analysis, 47 (2009) no.5, 3213-3239. (journal link)

(with F. Narcowich, J. Ward and G. Wright) Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere, Mathematics of Computation, 78 (2009), 2157-2186. (journal link)

Improved Stability Estimates and a Characterization of the Native Space for Matrix-valued RBFs, Advances In Computational Mathematics, 29 (2008), no. 3, 269-290. (journal link)

(with N. Benitez, T. Broadhurst, D. Coe and H. Ford) LensPerfect: Gravitational Lens Massmap Reconstruction Yielding Exact Reproduction of all Possible Images, The Astrophysical Journal. 681 (2008), no. 2, 812-830. arXiv:0803.1199

Sobolev-type Approximation Rates for Divergence-free and Curl-free RBF Interpolants, Mathematics of Computation, 77 (2008), no. 263, 1407-1423. (journal link)

Refined Error Estimates for Matrix-Valued Radial Basis Functions, Ph.D. Thesis, Texas A&M University, May 2006.

(with D. R. McCarthy) Reduction in Transport by the Parallel Velocity Shear Instability Due to Reversed Magnetic Shear, Physics of Plasmas, August 2001, 3645-3651.

Education

Ph.D. Mathematics, Texas A&M University , May 2006
B.S. Mathematics, Southeastern Louisiana University , December 2000

Positions Held

Assistant Professor, High Point University , August 2009 - Present
Assistant Professor, United States Military Academy , May 2006 - May 2009

Misc Links