Efficient, accurate and rapidly convergent algorithms for solutions of wave propagation problems in configurations complex material and geometrical features

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TurcDMS-1008076 The investigator develops efficient, accurate and rapidlyconvergent algorithms for evaluation of the interaction betweenelectromagnetic fields and complex structures. Specifically, theinvestigator and his collaborators develop a family of algorithmsthat focus mainly on (1) Fast, high-order numerical solutions forwave-propagation problems in domains that contain geometricsingularities, and (2) Scattering problems from penetrableelectromagnetic periodic structures, with a particular emphasison resonant problems relevant to the design of photonic crystalsand Negative Index Materials (NIM). The investigatorconcentrates on development and implementation of a massivelyparallel computational framework based on integral equationformulations capable of producing fast and high-order solutionsof wave scattering problems of realistic complexity. Theapproach consists of the following main elements: (a) High-orderresolution of the singularities of the solutions of the boundaryintegral equations in non-smooth domains; (b)Pseudodifferential-calculus-based design and analysis ofwell-conditioned integral equation formulations leading to smallnumbers of Krylov-subspace iterations for a wide range ofelectromagnetic transmission problems; and (c) Use of equivalentsources, FFT-based acceleration algorithms, and implementationsthat take advantage of the newly available Graphic ProcessingUnits (GPUs) computational platforms to dramatically enhancecomputational times and capabilities. The algorithms that are developed as part of this projectare of fundamental significance to diverse applications such aselectromagnetic interference and compatibility (electroniccircuits), dielectric/magnetic coated conductors, and compositemeta-materials (photonic crystals and Negative Index Materials). The simulation of electromagnetic wave propagation in complexstructures gives rise to a host of significant computationalchallenges that result from non-coercive formulations,oscillatory solutions, geometric singularities, resonances, andill-conditioning in the high-frequency regime. The recentefforts of the investigator and his collaborators resulted in thedevelopment of a highly efficient computational methodology thatresolved several of these difficulties and whose extensionenables the fulfillment of an ambitious plan: to simulate withhigh fidelity realistic scattering environments with a highdynamic range.