Efficient High Frequency Integral Equations And Iterative Methods

Project: Research project

Project Details


The project is distinguished by its great wealth of potential scientific applications and broad educational activities. Indeed, the numerical algorithms to be developed in the research activities are applicable to realistic configurations in physics, acoustic/electromagnetic, and other disciplines. The major theoretical and computational difficulties in these fields result from the presence of complicating factors such as complex geometries (including aircraft, satellites, radars, antennas, etc.), high-frequency scattering, amongst others. The obtained methods will provide the ability to simulate such systems accurately in order to be applied to the design of engineering vehicles and devices, including military and non-military radar, remote sensing satellites, noise reduction, stealth technology, and many others that will be positively impacted by the results of this proposal. The solvers obtained will be made readily available to industrial scientists, which will contribute to maintaining their competitiveness in particular in the aerospace industry. The educational impact will be significant in several areas. Graduate and undergraduate students will be rigorously trained in both scientific computing and mathematical analysis in order to enable them to face future challenges in science and technology. They will acquire the skills needed in state-of-the-art in applied numerical methods, and this will provide them great opportunities to join high technological industries and contribute in further advancing the U.S technology while having a successful career.The investigator plans to develop efficient and accurate algorithms for acoustic/electromagnetic wave propagation problems in complex structures. The new proposed research activities will have a significant impact in enabling advances in numerical methods and mathematics, and will result in a new family of numerical algorithms with enhanced capabilities over those currently available. The investigator plans to develop a robust non-overlapping domain decomposition method for the Helmholtz equation based on the utilization of optimized transmission conditions on the artificial interfaces and appropriate use of the adaptive radiation condition technique. This also will allow the design of an effective algorithm coupling finite and boundary elements. In the case of the high frequency regime, the investigator proposes to (1) use asymptotic expansions of solutions of the Helmholtz equation, namely the normal derivative of the total field, to rigorously develop a O(1) high frequency integral equations solver, (2) analyze the stability and convergence of the resulting algorithms, and (3) suitably combine high performance computing with the new proposed methods to efficiently tackle real-life problems. Parallel computing and mathematical analysis will be used to help achieve these goals.
Effective start/end date8/1/177/31/20


  • National Science Foundation


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