Research
Research grants: K-State Faculty Enhancement Program Award (PI, 2018-2019), NSF DMS-1812693 (PI, 2018-2022), NSF DMS-2208293 (PI, 2022-2025), NSF DMS-2243854 (Co-PI, 2023-2026).
Preprints
(with T. H. Lan) Stable reconstruction of anisotropic objects from near-field electromagnetic data.
(with T. Truong) A stable imaging functional for anisotropic periodic media in electromagnetic inverse scattering.
(with T. Truong) On the numerical solution to an inverse medium scattering problem (dedicated to Prof. Duong Minh Duc).
Articles in Refereed Journals (Please note that some pdf files may not correspond completely to the published versions.)
(with I. Harris and T. Le) On reconstruction of small sources from Cauchy data at a fixed frequency, Applied Mathematics Letters 145 (2023), 108765.
(with K. Stahl and T. Truong) A new sampling indicator function for stable imaging of periodic scattering media, Inverse Problems 39 (2023), 065013.
(with T. Truong) Fast numerical solutions to direct and inverse scattering for bi-anisotropic periodic Maxwell's equations, AMS Contemporary Mathematics 784 (2023), 81-101.
(with T. Le, V. Nguyen, and T. Truong) Sampling type method combined with deep learning for inverse scattering with one incident wave, AMS Contemporary Mathematics 784 (2023), 63-80.
(with L. H. Nguyen and T. Truong) The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations, Computer and Mathematics with Applications 128 (2022), 239-248.
(with I. Harris and T.-P. Nguyen) Direct sampling methods for isotropic and anisotropic scatterers with point source measurements, Inverse Problems and Imaging 16(5) (2022), 1137-1162.
(with T. Le, H. Schmidt and T. Truong) Imaging of 3D objects with experimental data using orthogonality sampling methods, Inverse Problems 38 (2022), 025007.
(with T. Truong) Imaging of bi-anisotropic periodic structures from electromagnetic near field data, Journal of Inverse and Ill-posed Problems 30 (2022), 305-319, (dedicated to Prof. Michael Klibanov).
(with I. Harris, J. Sands and T. Truong) On the inverse scattering from anisotropic periodic layers and transmission eigenvalues, Applicable Analysis 1 (2022), 3065-3081.
(with M.V. Klibanov and T. Truong) Convexification numerical algorithm for a 2D inverse scattering problem with backscatter data, Inverse Problems in Science and Engineering 29 (2021), 2656-2675.
(with I. Harris) Orthogonality sampling method for the electromagnetic inverse scattering problem, SIAM Journal on Scientific Computing 42 (2020), B722-B737.
Direct and inverse electromagnetic scattering problems for bi-anisotropic media, Inverse Problems 35 (2019), 124001 (27pp), (dedicated to Prof. Armin Lechleiter).
(with M.V. Klibanov and A.E. Kolesov) Convexification method for a coefficient inverse problem and its performance for experimental backscatter data for buried targets, SIAM Journal on Imaging Sciences 12 (2019), 576-603.
(with M.V. Klibanov and L.H. Nguyen) A coefficient inverse problem with a single measurement of phaseless scattering data, SIAM Journal of Applied Mathematics 70 (2019), 1-27.
(with M.V. Klibanov, N.A. Koshev, L.H. Nguyen, A. Brettin and V.N. Astratov) A numerical method to solve a phaseless coefficient inverse problem from a single measurement of experimental data, SIAM Journal on Imaging Sciences 11 (2018), 2339-2367.
(with M.V. Klibanov, H. Liu and L.H. Nguyen) A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data, Inverse Problems and Imaging 12 (2018), 493-523.
*(with M.V. Klibanov, L.H. Nguyen and M.V. Fiddy) Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method, Journal of Inverse and Ill-posed Problems 26 (2018), 501-522 (*first author designation).
*(with M.V. Klibanov, A.E. Kolesov, L.H. Nguyen and N.T. Thanh) Single measurement experimental data for an inverse medium problem inverted by a multi-frequency globally convergent numerical method, Applied Numerical Mathematics 120 (2017), 176-196 (*first author designation).
*(with M. Fiddy, M.V. Klibanov, A.E. Kolesov, H. Liu and L.H. Nguyen) Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm, Journal of Computational Physics 345 (2017), 17-32 (*first author designation).
(with T.-N. Nguyen and M.-P. Tran) A Galerkin approximation for integro-differential equations in electromagnetic scattering from a chiral medium, Applicable Analysis 96 (2017), 159-172.
(with L. Borcea) Imaging with electromagnetic waves in terminating waveguides, Inverse Problems and Imaging 10 (2016), 915-941.
The Factorization method for the Drude-Born-Fedorov model for periodic chiral structures, Inverse Problems and Imaging 10 (2016), 519-547.
A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations, Applied Numerical Mathematics 98 (2015), 59-78.
(with T.-P. Nguyen) Electromagnetic scattering by periodic structures with sign-changing coefficients, Comptes Rendus Mathematique 353 (2015), 893-898 (C. R. Math. Acad. Sci. Paris).
(with A. Lechleiter) Scattering of Herglotz waves from periodic structures and mapping properties of the Bloch transform, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 145 (2015), 1283-1311.
Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves, Applicable Analysis 93 (2014), 1458-1476.
(with A. Lechleiter) A trigonometric Galerkin method for volume integral equations arising in TM grating scattering, Advances in Computational Mathematics 40 (2014), 1-25.
(with A. Lechleiter) Factorization method for electromagnetic inverse scattering from biperiodic structures, SIAM Journal on Imaging Sciences 6 (2013), 1111-1139.
(with A. Lechleiter) On uniqueness in electromagnetic scattering from biperiodic structures, ESAIM: Mathematical Modelling and Numerical Analysis 47 (2013), 1167-1184.
(with A. Lechleiter) Volume integral equations for scattering from anisotropic diffraction gratings, Mathematical Methods in the Applied Sciences 36 (2013), 262-274.
(with A. Lechleiter) Spectral volumetric integral equation methods for acoustic medium scattering in a 3D waveguide, IMA Journal of Numerical Analysis 32 (2012), 813-844.
Edited Book
(with L. H. Nguyen and T.-P. Nguyen) Advances in Inverse Problems for Partial Differential Equations, Contemporary Mathematics, volume 784, American Mathematical Society, Providence, 2023.
Articles in Refereed Proceedings
Shape Identification of Diffraction Gratings from Spectral Data: The TM Case, Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (2013).
(with A. Lechleiter) Volumetric integral equations for scattering from periodic structures, Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Waves (2011).