Fadil Santosa

Since coming to the University of Minnesota, I have worked on many applied mathematics problems. Many of these problems come from industrial applications. I have kept up my interests in inverse problems in eddy current method and image processing. Below are short descriptions of some of my activities.

• Fiber optics and photonic bandgap structures
• Optimal design problems in optics
• Electrical impedance imaging
• Level set approach to inverse problems
• Eddy current method
• Image processing

Recent publications (see CV for complete publication list)

1. A level-set approach for inverse problems involving obstacles. Control, Optimization, and Calculus of Variation, 1 (1996). (view)
2. Recovery of blocky images from noisy and blurred data. (with D. Dobson), SIAM J. Appl. Math., 56 (1996), pages 1181-1198 (view)
3. A computational algorithm for minimizing total variation in image restoration. (with Y. Li), IEEE Trans. Image Processing, 5 (1996), pages 987-995. (view)
4. A method for imaging corrosion damage in thin plates from electrostatic data. (with P. Kaup and M. Vogelius), Inverse Problems, 12 (1996), pages 279-293. (view)
5. Nondestructive evaluation of plates using eddy current methods. (with D. Dobson), International Journal of Engineering Science, 36 (1998), pages 395-409. (view) .
6. Quantitative imaging of corrosion in plates by eddy current methods. (with B. Luong), SIAM Journal on Applied Mathematics, 58 (1998), pages 1509-1531. (view)
7. Reconstruction of a 2-D binary obstacle by controlled evolution of a level-set. (with A. Litman and D. Lesselier), Inverse Problems, 14 (1998), pages 685-706. (view)
8. Efficient calculation of Jacobian and adjoint vector products in wave propagational inverse problem using automatic differentiation. (with T. Coleman and A. Verma), J. Comp. Phys., 157 (2000), pp. 234-255. (view)
9. Wave propagation in a 2-D optical waveguide. (with R. Magnanini), SIAM J. Appl. Math. 61 (2000), 1237-1252. (view)
10. Scattering in a 2-D optical waveguide. (with R. Magnanini), in Computational and Analytical Methods in Scattering and Applied Mathematics, a Volume to the Memory of Ralph E Kleinman, Santosa and Stakgold eds., CRC Press. (view)
11. Application of a Micro-Genetic Algorithm in optimal design of a diffractive optical element. (with S. Rudnaya), to appear in System Modelling and Optimization, M.J.D. Powell and S. Scholtes, eds, Kluwer, 2000. (view)
12. Multi-Pole representation of small acoustic sources. (with W. Symes), Chinese Journal of Mechanics, Series A, 16 (2000), pp. 15-22. (view)
13. An efficient approach to calculate current distributions for electro-deposition of chip interconnections. (with M. Vogelius), preprint. (view)
14. Enhanced electrical impedance tomography via the Mumford-Shah functional. (with L. Rondi), Control, Optimisation, and Calculus of Variations, 6 (2001), 517-538. (view)
15. Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum. (with S. Osher), J. Comp. Phys. 171 (2001), 272-288. (view)
16. Control of the wave equation by time-dependent coefficient. (with A. Chambolle), Control, Optimisation and Calculus of Variations, 8 (2002), Special Volume: A tribute to J.L. Lions, 375-392. (view)
17. Asymptotic Analysis and Design of Diffractive Optical Elements (with S. Rudnaya, A. Chiareli, and D. Misemer), J. Engineering Mathematics, 43 (2002), 255-279. (view)
18. Rational Design of a Diffractive Homogenizer for a Laser Beam (with D. Misemer and S. Rudnaya), J. Engineering Mathematics, 43 (2002), 189-199. (view)

Newer papers

1. Analysis of a variational approach to progressive lens design. (with J. Wang and R. Gulliver), SIAM J. Appl. Math. 64 (2003), 277-296. (view)
2. A numerical method for progressive lens design. (with J. Wang), Mathematical Models and Methods in Applied Sciences (M3AS) 14 (2004), 619--640. (view)
3. Guided waves in a photonic bandgap structure with a line defect (with H. Ammari), SIAM J. Appl. Math. 64 (2004), 2018-2033. (view)
4. Optimal localization of eigenfunctions in an inhomogeneous medium (with D. Dobson), SIAM J. Appl. Math. 64 (2004), 762-774. (view)
5. Minimax design of optically transparent and reflective coatings. (with G. Erdmann), J. Opt. Soc. Am. A. 21 (2004), 1730-1739. (view)
6. A topology-preserving level set method for shape optimization (with O. Alexandrov), J. Comp. Phys. 204 (2005), 121-130. (view)
7. An approximate method for scattering by thin structures (with S. Moskow and J. Zhang), SIAM J. Appl. Math. 66 (2005), 187-205. (view)
8. An inverse problem in nondestructive evaluation of spot-welds (with E. Francini and T. Hoft), Inverse Problems 22 (2006), 645-661. (view)
9. Scattering of electromagnetic waves by this dielectric planar structures (with H. Ammari and H. Kang), SIAM J. Math. Anal. 38 (2007), 1329-1342. (view)
10. Maximization of the quality factor of an optical resonator (with C.Y. Kao), submitted (view)
11. Position registration from voltage measurements (with C. Toews), submitted (view)
12. Asymptotic and numerical techniques for resonances of thin photonic structure (with J. Gopalakrishnan and S. Moskow), submitted (view)

    If you want further information, please write me.