Free Surface Fluid Mechanics and Electromagnetic Scattering: Stable, High-Order Perturbation Techniques

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

Abstract 0406007, Nicholls, University of Notre Dame Free Surface Fluid Mechanics and Electromagnetic Scattering: Stable, High-Order Perturbation Techniques The Principal Investigator (PI) proposes the investigation of fundamental phenomena in free-surface ideal fluid flows, and electromagnetic and acoustic scattering. Among the applications are the efficient, stable, high-order computation of traveling three-dimensional, capillary-gravity water waves, and a numerical investigation of their dynamic stability. Another problem the PI will address is the imposition of "non-reflecting" boundary conditions for differential equations posed on unbounded domains, particularly in the setting of electromagnetic and acoustic scattering. The PI also proposes a synthesis of two major areas of his research through the study of backscattering returns of electromagnetic radiation from traveling ocean waves. A unifying element in this project, and the principal numerical tool the PI will employ, is a class of boundary perturbation methods first introduced by O. Bruno & F. Reitich in the context of numerical simulation of acoustic and electromagnetic scattering problems. These methods have subsequently been significantly refined and stabilized by Reitich and the PI for the BVP of computing Dirichlet-Neumann operators, and approximating scattering configurations. Among these refinements, the PI & Reitich developed the method of "Transformed Field Expansions" (TFE) which enables the reliable, high-order, stable perturbative computation of BVP and FBP. While this method is extremely successful in resolving simulations well outside the reach of competing methods, it is somewhat disadvantaged in terms of computational complexity in comparison to other techniques (e.g. boundary integrals/elements). A final project that the PI proposes is the investigation of two refinements of this TFE approach to increase its efficiency. Fixed and free boundary problems arise in all areas of engineering and the sciences. Two particular instances of relevance in this proposal are the classic free boundary problem of the motion of surface waves on a large body of water (e.g. a lake, sea, or ocean), and the fixed boundary problem of scattering of electromagnetic or acoustic waves from an irregular surface. The accurate and reliable simulation of surface waves is used not only to model the capabilities of open-ocean structures (e.g. oil platforms), but also in the study of transport of pollutants and other substances of environmental interest across lakes, seas, and oceans. Applications of electromagnetic and acoustic scattering come in problems of radar, imaging, and sensing to name just a few. Many numerical techniques are available for the simulation of these problems and one of the goals of this proposal is the utilization and improvement of a class of techniques discovered and refined by the Principal Investigator (PI) and collaborators. In particular, when the problems mentioned above are simulated in full three dimensions, the computations become quite intensive and the issues truly become those of high-performance computing.