Abstract
Inverse scattering is a systematic approach to nondestructive testing, geophysical prospecting, remote sensing, and medical imaging. Being both nonlinear and ill-posed, inverse scattering problems are among the most challenging in computational science. In this chapter we expose the intimate connection between these problems and reduced-order modeling techniques, which allow significant reduction in computational complexity and efforts. Exploiting the natural symmetries of the electromagnetic field equations we develop and analyze reduced-order models for the parametric inversion problems arising in effective medium theory, metamaterials, and photonics. These models are Padé approximations of the measured scattered field. The achieved significant computational gain allows us to solve these large numerical problems by simple inspection of a two-dimensional objective functional.
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Remis, R.F., Budko, N.V. (2009). A Model-Order Reduction Approach to Parametric Electromagnetic Inversion. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_1
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DOI: https://doi.org/10.1007/978-3-642-03344-5_1
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