Background
Professor Gibson received his Ph.D. in Computational Mathematics from
North Carolina State University in 2004 under the direction of Professor
H. T. Banks. Previously, he obtained a Master's Degree in Applied
Mathematics with Concentrations in Numerical Analysis and Mathematical
Modeling at the University of Tennessee, Knoxville, in August of 2001,
and a Bachelor's Degree in Mathematics with a Concentration in
Computational and Applied Analysis and a minor in Computer Science from
Worcester Polytechnic Institute in Worcester, MA, in August of 1998.
Before coming to Oregon State University, he was an NIA (National
Institute for Aerospace) postdoctoral research fellow at the CRSC
(Center for Research in Scientific Computation) working with engineers
from NASA Langley.
More information can be seen on his curriculum
vitae.
Research
Currently, Professor Gibson is working with
NASA Langley
Research Center on inverse problem techniques related to non-destructive
evaluation (NDE) of space shuttle foam. His primary research interests are
- computational electromagnetics
- finite element and finite difference methods
- inverse problems
Research topics coinciding with primary interests include
- direct and indirect (sparse) linear solvers
- high performance and parallel computing
- parameter identification and sensitivity analysis
- optimization and regularization techniques
- modeling uncertainty in coefficients of PDE's
- homogenization involving Maxwell's equations
Applications include
- modeling dielectric heterogeneities
- electromagnetic detection of gaps or voids in space shuttle foam
- generating synthetic data involving complicated geometries for crack
detection techniques
Teaching
Communications
Selected Refereed Journal Publications
-
- H.T. Banks, V.A. Bokil, and N.L.Gibson, "Analysis of
stability and dispersion in a finite element method for Debye and
Lorentz dispersive media", accepted into Numerical Methods for
Partial Differential Equations, 2008, PDF
Online.
- H.T. Banks, V.A. Bokil, and N.L. Gibson, "Parameter estimation versus
homogenization techniques in time-domain characterization of composite
dielectrics", Journal of Inverse and Ill-Posed
Problems, 15, no. 2, 117-135, 2007, PDF
Online.
- H. T. Banks and N. L. Gibson, "Void detection in foam with knit lines using THz
pulse interrogation", Mathematical and Computer Modelling 44, nos. 9-10, 807-
815, 2006, PDF Online.
- H. T. Banks and N. L. Gibson, "Electromagnetic inverse problems
involving distributions of dielectric mechanisms and parameters",
Quarterly of Applied Mathematics, 64, no. 4, 749-795, 2006, PDF
Online.
- H. T. Banks, N. L. Gibson, and W. P. Winfree, "Gap detection with
electromagnetic terahertz signals", Nonlinear Analysis: Real World
Applications 6, no. 2, 381-416, 2005, PDF Online.
- H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and
B. Miara, "Homogenization of periodically varying coefficients in
electromagnetic materials", Journal of Scientific
Computing, 28, no. 2, 191-221, 2006,
PDF
Online.
- H. T. Banks and N. L. Gibson, "Well-posedness in
Maxwell systems with distributions of
polarization relaxation parameters", Applied Mathematics Letters
18, 423-430, 2005, PDF Online.
- S. Gavrilets and N. L. Gibson, "Fixation probabilities in a spatially
heterogeneous environment", Population Ecology 44, no. 2, 51-58,
2002 PDF Online.
Presentations
- Applied
Mathematics and Computation Seminar, Oregon State University,
Corvallis, OR. "Gradient-based Methods for
Optimization", November, 2007.
- Conference on Applied Inverse Problems 2007:
Theoretical and Computational Aspects, University of British Columbia
Campus Vancouver, Canada.
" Electromagnetic Characterization of Damage in
Complex Dielectrics", Identification of Defects and Cracks
Minisymposium organized by Shiro Kubo,
June 2007.
- Mathematics REU, Oregon State University, Corvallis, OR.
"Finding damage
in Space Shuttle foam",
July, 2007.
- Mathematics Colloquium, Oregon State University, Corvallis, OR.
"Electromagnetic characterization of damage
in Space Shuttle foam",
March, 2007.
- Applied
Mathematics and Computation Seminar, Oregon State University,
Corvallis, OR. "Inverse Problem for Distributions of Dielectric
Parameters", November, 2006.
- Review of Progress in Quantitative NDE, Portland, OR. "2D Modeling
of Pulsed THz Interrogation of SOFI with Knit Lines",
Terahertz Imaging Session, chaired by H. Ringermacher, August, 2006.
- Third International Conference "Inverse Problems : Modeling and
Simulation", Oldeniz-Fethiye, TURKEY. "Parameter Identification
using Electromagnetic Interrogation of Heterogeneous Dielectrics", Inverse
Problems Related to Scattering in Complex Structures Session, organized by
Dr. J. A. Burns and Dr. H. T. Banks, May, 2006.
- Colloquium Talk, Sandia National
Laboratories, Albuquerque, NM.
"On Various Inverse Problems in Electromagnetics
Involving Distributions of Dielectric Parameters", February,
2006.
- Sixth SIAM Conference on Control and its Applications, New Orleans,
LA. "Electromagnetic Inverse Problem Involving Distributions of Dielectric
Parameters", Inverse Problems in Electromagnetics and Biology
Minisymposium, organized by H. T. Banks and A. S. Ackleh, July 2005.
- 29th Annual SIAM Southeast Atlantic Section Meeting, Charleston, SC. "Gap
Detection with Electromagnetic Terahertz Signals", Inverse Problems in
Electromagnetics and Biology Minisymposium, organized by H. T. Banks and
N. L. Gibson, March 2005.
- SAMSI Multiscale Working Group Closing Workshop, RTP, NC. "Multiscale and
Polarization in Dielectric Materials: A Probabilistic Approach", invited by
R. C. Smith, September 2004.
- "Journees Jeunes" at Laboratoire J.-L. Lions/Paris VI, Paris,
France. "Pulsed Terahertz Electromagnetic Inverse Problems", invited by
D. Cioranescu, March 2004.
- Applied Math Graduate Student Seminar, North Carolina State
University. "Electromagnetic Crack Detection Inverse Problems Using
Terahertz Interrogating Signals", October 2003.
