Ph.D., University of Delaware
- Office Hours
- Wednesdays 9:00-10:00am
- Courses this Semester
- MA 225--Calculus with Analytic Geometry III
- Regularly Taught Courses
- MA 237--Programming and Technology in Mathematics
- Research Interests
My research is in scattering theory, or, more specifically, the scattering of electromagnetic or acoustic waves. 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. I tend to concentrate my efforts in the area of numerical analysis, where I mainly focus on the computational aspects of scattering theory. More specifically, I work on finite element methods for the forward problem and regularization/sampling techniques for the inverse problem.
- Scholarly Articles
Inverse Scattering in a Layered Background, Proceedings of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, 1998.
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).
The Finite Element Approximation of Scattering in a Layered Medium, Analytical and Computational Methods in Scattering and Applied Mathematics, Fadil Santosa and Ivar Stakgold (Eds.), pages 67 – 84, 2000, (with 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).
Hybrid arbitrary order edge based finite element methods for electromagnetic scattering problems, Proceedings of the 17th ACES Conference Monterey 2001, (with Mark Ainsworth, Oubey Hassan, Paul Ledger, Ken Morgan and Nigel Weatherill).
hp-Finite Element approximations of Maxwell’s equations on curvilinear hybrid meshes, Proceedings of the European Conference on Computational Mechanics, Cracow, Poland, 2001, (with Mark Ainsworth, Paul Ledger, Ken Morgan, O. Hassan and Nigel Weatherill).
Approximations of Maxwell’s equations using p-version Nédélec finite elements on tetrahedral meshes, ACME Conference Proceedings, Swansea, pages 97 – 102, 2002, (with Mark Ainsworth, Paul Ledger and Ken Morgan).
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).
Computation of Maxwell eigenvalues using higher order edge elements in three-dimensions, IEEE Transactions on Magnetics, Volume 39, Number 5, pages 2149 – 2153, 2003, (with Mark Ainsworth, Paul Ledger and Ken Morgan).
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).
Computation of Maxwell Eigenvalues on Curvilinear Domains Using hp-Version Nédélec Elements, Numerical Mathematics and Advanced Applications, F. Brezzi et al. (Eds), Springer-Verlag Italia, 2003, (with Mark Ainsworth).
Numerical Validation of the Linear Sampling Method, Inverse Problems, Volume 18, pages 511 – 527, 2002, (with Andrea Tacchino and Michele Piana).
Evidence of exponential convergence in the computation of Maxwell eigenvalues, CMAME, Volume 194, pages 587 – 604, 2003, (with Paul Ledger).
FIST: A Fast Visualizer for Acoustic and Electromagnetic Inverse Scattering Problems, Simulation Modeling Practice and Theory, Volume 14, Issue 2, pages 177 – 187, 2006, (with F. Mazzone, A. Massone, and M. Piana).
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).
The Linear Sampling Method, a New Regularization Solution and Real Data, Conference Proceedings of the 23rd Annual Review of Progress in Applied Computational Electromagnetics, Verona, Italy, pages 1927 – 1933, 2007 (with M Brignone and R. Aramini).
Inverse Scattering and Edge Detection: The Threshold Problem for the Linear Sampling Method, Conference Proceedings for the 23 Annual Review of Progress in Applied Computational Electromagnetics, Verona, Italy, pages 1276 – 1282, 2007 (with M. Piana, M. Brignone and R. Aramini).
Postprocessing of the Linear Sampling Method By Means of Deformable Models, SIAM J. Sci. Comput., Volume 30, Number 5, pages 2613 – 2634, 2008 (with R. Aramini, 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.
ILU preconditioning for a Higher Order Finite Element Approximation with a Nonsymmetric Matrix, Conference Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, USA, 2013.
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.