I am originally from southwestern Ohio. I attended Miami University and then the University of Dayton for my B.S. and M.S. in mathematics, respectively. I ventured out east to the University of Delaware where I worked with Peter Monk and earned my Ph.D. in mathematics in the fall of 1998. After getting married in the summer of 1999, I took a post doctoral position that took us to Glasgow, Scotland, where I worked with Mark Ainsworth. After three amazing years, we moved back to the U.S. I have been at Monmouth University and living near the shore since the fall of 2002.

Education

Ph.D. in Mathematics, University of Delaware

M.S. in Mathematics, University of Dayton

B.S. in Mathematics, Miami University

Mathematical Interests

My mathematical research falls into the broad category of numerical analysis. In particular, I have an interest in numerical approximations of wave phenomena or scattering theory. Scattering theory can be divided into two categories: forward and inverse. In the forward problem, the main goal is to compute the scattered wave given an incident field and the medium in which the wave travels. In the inverse problem, one tries to determine the object that actually scattered the wave given the incident and scattered field.

Recently I have concentrated my efforts on the forward problem looking at discontinuous Galerkin methods and preconditioning techniques. I also have a more broad interest in applications of mathematics and enhancing this experience for undergraduates.

Selected Publications

Locating the Support of Objects Contained in a Two-Layered Background Medium in Two Dimensions, Inverse Problems, Volume 16, pages 275 – 292, 2000.

Recent Developments in Inverse Acoustic Scattering Theory, SIAM Review, Volume 24, Number 3, pages 369 – 414, 2000, (with David Colton and Peter Monk).

Scattering of Time-Harmonic Electromagnetic Waves by Anisotropic Inhomogeneous Scatterers or Impenetrable Obstacles, SIAM Journal on Numerical Analysis, Volume 37, Number 5, pages 1590 – 1617, 2000 (with Peter Monk).

Hierarchic hp-Edge Element Families for Maxwell’s Equations on Hybrid Quadrilateral and Triangular Meshes, CMAME, Volume 190(49-50), pages 6709 – 6733, 2001, (with Mark Ainsworth).

Hierarchic Finite Element Bases on Unstructured Tetrahedral Meshes, International Journal of Numerical Methods in Engineering, Volume 58, Number 14, 2103-2130, 2003, (with Mark Ainsworth).

Conditioning of Hierarchic p-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra, SIAM Journal on Numerical Analysis, Volume 41, Number 2, pages 731 – 750, 2003, (with Mark Ainsworth).

The use of the linear sampling method for obtaining super-resolution effects in Born approximation, Journal of Computational and Applied Mathematics, Volume 103, Issue 1, pages 145 – 158, 2007 (with M. Brignone and M. Piana).

Overlapping solution finite element method – higher order approximation and implementation, Appl. Numer. Math., Volume 62, Number 12, pages 1910-1924, 2012.

High-order discontinuous Galerkin methods for a class of transport equations with structured populations, Comput. Math. Appl., Volume 72, Number 3, pages 768 – 784, 2016.

High order DG overlapping solution FEM for the Helmholtz Equation, Book of abstracts for 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Minneapolis, Minnesota, USA, pages 97-98, 2017.

Professional Activities

Department Chair, July 2017 – present
Vice Chair, Undergraduate Studies Committee, July 2020 – present

Summer Research Program (2020)
Employing Thresholding And Wavelet Transformation To Remove Noise From An Audio Signal
Student: Mackenzie Dalton

Member of SIAM, COMAP

Recent Presentations: Employing the Overlapping Solution FEM to Multiple Scatterers, Finite Element Circus, Fall 2018