Efficient solutions of wave propagation problems in multi-layered, multiple scattering media

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This award supports a continuation of the research program of the Principal Investigator on the accurate and efficient numerical modeling of wave-scattering problems in various applications settings. In this project, the Principal Investigator will develop and analyze high-performance, efficient, accurate, and rapidly-convergent algorithms for evaluation of the interaction between waves and structures that involve multiple scatterers as well as multiple layers with different material properties. The solvers to be developed are relevant to diverse applications, such as radar and remote sensing, communication devices, geophysics, and photonics.The Principal Investigator will develop a family of algorithms that will focus mainly on (1) efficient boundary integral solutions of electromagnetic and elastic scattering problems in layered media that bypass the need for cripplingly expensive evaluations of layered Green's functions and (2) Schur complement Domain Decomposition methods for efficient solutions of multiple scattering problems. The computational methodology underlying the proposed work is based on a class of numerical solvers and surface-representation and meshing methodologies developed in recent years by the Principal Investigator and his collaborators. These are boundary integral solvers that can produce solutions with high-order accuracy, and no numerical dispersion, for realistic engineering geometries including features such as full aircraft, complex photonic or electronic devices, etc. In practice, and whenever applicable, these types of solvers have demonstrated order-of-magnitude faster numerics, for a given accuracy, than some of the most competitive solvers otherwise available: the new methods can enable solution of previously intractable problems.