Recent Articles

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.

Older Publications

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.