David C. Dobson, Fadil Santosa, Stephen P. Shipman, and Michael I. Weinstein, Resonances of a potential well with a thick barrier, preprint (2012).

Lyubima B. Simeonova, David C. Dobson, Kenneth M. Golden, and
Olakunle Eso, Spatial bounds on the effective complex permittivity for
time-harmonic waves in random media, preprint (2010).

Russell B. Richins and David C. Dobson, A numerical minimization scheme for the
complex Helmholtz equation, preprint (2010).

David C. Dobson and Eddie Wadbro, Optimization of transmission spectra
through periodic aperture arrays, Optim. Eng., to appear (2010).

David C. Dobson and Lyubima B. Simeonova, Optimization of periodic composite
structures for sub-wavelength focusing, Appl. Math. Optim. 60
(2009), 133-150.

David C. Dobson, Optimal mode coupling in simple planar
waveguides, in "Topological design optimization of structures,
machines, and materials -- status and perspectives", M. Bendsoe, N.
Oldhoff and O. Sigmund, eds., Springer, Dordrecht (2006), 311-320.

David C. Dobson and Fadil Santosa, *Optimal localization of
eigenfunctions in an inhomogeneous medium*,
SIAM J. Appl. Math., **64** (2004), 762--774.

Gang Bao, David C. Dobson, and Karim Ramdani, *A constraint
on the maximum reflectance of rapidly oscillating dielectric gratings*,
SIAM
J. Cont. Opt., **40** (2002), 1858--1866.

David C. Dobson and Joseph E. Pasciak, *Analysis
of an algorithm for computing
electromagnetic Bloch modes
using Nedelec spaces*,
Comp. Meth. Appl. Math., **1** (2001), 138-153.

Gang Bao and David C. Dobson, "Variational methods for diffractive
optics modeling", in *Mathematical Modeling in Optical Science*,
G.
Bao, L. Cowsar, and W. Masters, editors, SIAM, (2001), pp. 37-69.

David C. Dobson, Jayadeep Gopalakrishnan, and Joseph E. Pasciak, *An efficient
method for band structure calculations in 3D photonic crystals*,
J. Comp. Phys., **161** (2000), 668-679.

Steven J. Cox and David C. Dobson, *Band
structure optimization of two-dimensional photonic crystals in
H-polarization*,
J. Comp. Phys., **158** (2000), 214-224.

Gang Bao and David C. Dobson, *On
the scattering by a biperiodic structure*, Proc. AMS **128**
(2000), 2715-2723.

D.C. Dobson and P. Kaup, *Monitoring underground flows with
electromagnetic
methods*, Inverse Problems **15** (1999), 597-613.

David C. Dobson, *An
efficient method for band structure calculations in 2D photonic crystals*,
J.
Comp. Phys., **149** (1999), 363-376.

Steven J. Cox and David C. Dobson, *Maximizing
band gaps in two-dimensional photonic crystals*, SIAM J. Appl.
Math, **59** (1999),

2108-2120.

David C. Dobson, *Optimal
shape design of blazed diffraction gratings* , Appl. Math.
Opt., **40** (1999), 61-78.

J.A. Cox, D.C. Dobson, T. Ohnstein, and J.D. Zook, *Optical
performance
of high-aspect LIGA gratings II*, Opt. Eng. **37** (1998),
2878-2884.

David C. Dobson and Fadil
Santosa, *Nondestructive
evaluation of plates using eddy current methods* Int. J. Engng.
Sci., **36** (1998), 395-409.

Gang Bao and David C.
Dobson, *Modeling
and optimal design of diffractive optical structures*, Surv.
Math.
Ind., **8** (1998), 37-62.

David C. Dobson and Curtis
R. Vogel, *Convergence
of
an iterative method for total variation denoising* SIAM J.
Numer.
Anal., **34** (1997), 1779-1791.

J.A. Cox, J.D. Zook, T. Ohnstein, and D.C. Dobson, *Optical
performance
of high-aspect LIGA gratings*, Opt. Eng. **36** (1997),
1367-1373.

J.A. Cox, D.C. Dobson, T. Ohnstein, and J.D. Zook, "LIGA tunable
spectral filter performance", in Proc. SPIE Vol. 3008 (1997).

David C. Dobson, "Recovery
of blocky images in electrical impedance tomography", in *Inverse
Problems
in Medical Imaging and Nondestructive Testing*, edited by
H.W.
Engl, A.K. Louis, and W. Rundell, Springer-Verlag, Wien (1997), pp.
43-64.

David Dobson and Otmar Scherzer, *Analysis
of
regularized total variation penalty methods for denoising*,
Inverse
Problems, **12** (1996), 601-617.

David C. Dobson and Fadil
Santosa, *Recovery
of
blocky images from noisy and blurred data*, SIAM J. Appl.
Math., **56** (1996), 1181-1198.

D. Dobson and J.A. Cox, "Optimal design of low order diffractive
structures", in *Diffractive and Micro-Optics* Vol. 5, OSA
Technical
Digest Series (Optical Society of America, Washington DC), (1996), 5-8.

J.A. Cox, J.D. Zook, T. Ohnstein, and D.C. Dobson, "Optical performance of high aspect LIGA gratings", in Proc. SPIE Vol. 2383A (1995).

Gang Bao and David C.
Dobson, *Diffractive
optics in nonlinear
media with periodic structure*, Euro. J. Appl. Math., **6**
(1995), 573-590.

David C. Dobson,
"Controlled
scattering of light waves: optimal design of diffractive optics",
in
*Control Problems in Industry,* edited by I. Lasiecka and B.
Morton,
Birkhauser, Boston (1995), 97-118.

Gang Bao, David C. Dobson, and J. Allen Cox, *Mathematical
studies
in rigorous grating theory* J. Opt. Soc. Am. A, **12** (1995),
1029-1042.

David C. Dobson, "A
boundary
determination problem from the design
of diffractive periodic structures", in *Free Boundary Problems:
Theory
and Applications*, J.I. Diaz, M.A. Herrero, A. Linan, and J.L.
Vazquez,
eds., Pitman Research Notes in Mathematics Series 323, Longman (1995),
108-120.

David C. Dobson and Fadil Santosa, *Resolution and stability
analysis
of an inverse problem in electrical impedance tomography --dependence
on
the input current patterns*, SIAM J. Appl. Math. **54** (1994),
1542-1560.

Gang Bao and David C. Dobson *Second harmonic generation in
nonlinear
optical films*, J. Math. Phys. **35** (1994), 1622-1633.

D. C. Dobson, *A variational method for electromagnetic
diffraction
in biperiodic structures*, RAIRO Model. Math. Anal. Numer. **28**
(1994), 419-439.

David C. Dobson and Fadil Santosa, *An image-enhancement
technique
for electrical impedance tomography*, Inverse Problems **10**,
(1994),
317-334.

Gang Bao, David C.
Dobson, and
J. Allen Cox, "Mathematical issues
in the electromagnetic theory of gratings", in *Diffractive Optics:
Design,
Fabrication, and Applications* OSA Technical Digest Series (Optical
Society of America, Washington DC), (1994).

David C. Dobson and J.
Allen
Cox, "Mathematical modeling for diffractive
optics", in *Diffractive and Miniaturized Optics (Critical Reviews)*,
edited
by Sing Lee, SPIE CR-49 (1994), 32-53.

David C. Dobson, *Optimal design of periodic antireflective
structures
for the Helmholtz equation*, Euro. J. Appl. Math. **4** (1993),
321-340.

Gang Bao and David C. Dobson, "Nonlinear optics in periodic
diffractive
structures", in *Second International Conference on Mathematical and
Numerical Aspects of Wave Propagation*, edited by R.Kleinman, et.
al.,
SIAM (1993), 30-38.

David C. Dobson, "Exploiting ill-posedness in the design of
diffractive
optical structures", in *Mathematics in Smart Structures*, edited
by H. T. Banks, SPIE Proc. 1919 (1993), 248-257.

David C. Dobson, *Phase reconstruction via nonlinear
least-squares*,
Inverse Problems **8** (1992), 541-557.

David C. Dobson, *Estimates
on
resolution and stabilization for
the linearized inverse conductivity problem*, Inverse Problems **8**
(1992), 71-81.

David C. Dobson, *Convergence of a reconstruction method for
the
inverse conductivity problem*, SIAM J. Appl. Math. **52**
(1992),
442-458.

David C. Dobson, "Designing periodic structures with specified low
frequency scattered far-field data", in *Advances in Computer
Methods
for Partial Differential Equations VII *, edited by R.
Vichnevetsky,
D. Knight and G. Richter, IMACS (1992), 224-230.

David Dobson and Avner Friedman, *The time-harmonic Maxwell
equations
in a doubly periodic structure*, J. Math. Anal. Appl. **166**
(1992),
507-528.

David C. Dobson and J. Allen Cox, "An integral equation method for
biperiodic diffraction structures", in *International Conference on
the
Application and Theory of Periodic Structures*, J. Lerner and W.
McKinney,
editors, SPIE Proc. 1545 (1991), 106-113.