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Advanced Electromagnetic Modeling and Analysis Tools for Complex Aircraft Structures and Systems
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Navy STTR 20.B - Topic N20B-T028

Naval Air Systems Command (NAVAIR) - Ms. Donna Attick navairsbir@navy.mil

**Opens: June 3, 2020**
- **Closes: July 2, 2020 **
**(12:00 p.m. ET)**

N20B-T028 TITLE: Advanced Electromagnetic Modeling and Analysis Tools for Complex Aircraft Structures and Systems

RT&L FOCUS AREA(S): General Warfighting Requirements (GWR)

TECHNOLOGY AREA(S): Air Platform

OBJECTIVE: Develop a software package that ensures geometric fidelity is not compromised for the generation of a computational electromagnetics (CEM) mesh formed by high-order curved elements. Apply the software package to model large-scale problems (thousands of wavelengths long in each dimension) using exact physics methods.

DESCRIPTION: The field of computational electromagnetics (CEM) came to existence in the middle 1960s. Since that time, there has been substantial progress in the mathematical aspects of CEM as well as in taking advantage of advances in computer technology. The combination of these two has resulted in electromagnetic modelling and simulation (EM&S) software that can successfully address a variety of EM scenarios. There are still, however, problems of large electrical size that current CEM technologies cannot address. One example of interest is the radiation characteristics of installed antenna arrays coupled with radomes with the cavity-like structures where the array resides (and other objects within that cavity) and with the external structure of the aircraft platform. Another example of equal importance is the signature of maritime targets in a variety of sea states. The computational domain in this case can be enormous especially for near-grazing incidence. It is not possible to address such problems with sufficient accuracy using approximate (high frequency) methods; moreover, near-field parameters of interest may not be obtainable at all by such methods as, for example, the driving point or the mutual impedance of a platform installed antenna array. Exact-physics methods, on the other hand, generate such a large number of unknowns that would challenge even the largest computer clusters. For these reasons, there has been a movement in recent years in both time-domain and frequency-domain, toward high-order algorithms that use large cell sizes (~10 wavelengths) to minimize the number of cells in the volume computational domain and thus the computational burden for solving very large problems that are in thousands of wavelengths in each dimension [Refs 1-2]. While using such large cell sizes, however, it is imperative to use high-order curved elements [Refs 3-6] instead of many small, flat facets to capture the geometry with the necessary fidelity. For targets with small- and large-scale geometric features, the process of creating high-order, curved elements is still in a state of infancy to guarantee no grid crossovers and no negative Jacobian in any cell in the computational domain.

Develop methods for generating curved volume meshes for complex targets that will conform to a prescribed geometry and be suitable for use with high-order solvers. This should lead to more robust and computationally efficient EM tools to predict the near- and far-field characteristics of large-scale problems that involve complex structures, installed antenna arrays, radomes and interior regions accurately. The number of unknowns generated should be such that the solver could run in low-level clusters (128-256 cores and 2-4 GB standard memory size per core). A graphical user interface (GUI) that encompasses the entire computational process that includes the preprocessing tools for geometry import and generation of high-order curved elements, high-order processing tools, and a comprehensive set of post processing tools for data output and visualization, should intelligently guide the user through any projected application. The design of the GUI should consider ISO/IEC 25022:2016 usability metrics.

While the main thrust of this SBIR topic is to develop a high-order mesh generation capability, there is also interest in producing an integrated high-order CEM environment. The environment must be capable of addressing large-scale problems accurately and efficiently, while utilizing minimal computational resources. The process of combining high-order curved elements with high-order solvers and large cell sizes (up to 10 wavelengths) must be demonstrated through test problems, such as a perfect electric conductor (PEC) sphere of 100-wavelength in diameter.

PHASE I: Develop and demonstrate procedures for high-order mesh generation from a hybrid linear element mesh, while retaining computer aided design (CAD) geometry fidelity. Develop a preliminary software package design that can create a high-order (up to 10th order) curved elements for a complex geometry. Demonstrate the process of combining high-order, curved elements with high-order solvers and large cell sizes (up to 10 wavelengths), for test problems such as a PEC sphere of 100-wavelength diameter, and provide accuracy measures when compared to Mie series solution for bistatic radar cross section. The Phase I effort will include plans for software to be developed in Phase II.

PHASE II: Complete the development of the software package from Phase I, compatible with existing high-order CEM software tools (time and frequency domain). The delivered software package, compatible with Windows and Linux OS platforms, must predict near-field and far-field characteristics of complex systems. Ensure the high-order curved elements preserve the small- and large-scale critical features of the geometry. Implement the tool(s) with a GUI for problem setup and results analysis. Ensure that the GUI design emphasizes ease-of-use in the context of configuring, visualizing, and executing on arbitrary complex targets. Port codes on clusters of central processing units and/or graphical processing units (CPUs/GPUs). Test and demonstrate the resulting codes on cases of interest.

PHASE III DUAL USE APPLICATIONS: Complete development of the CEM software application suitable for transition and for commercial use. The CEM software application will have widespread use in the DoD, industry and academia for analysis of highly complex electromagnetic problems.

REFERENCES:

1. Hesthaven, J. & Warburton, T. “Nodal Discontinuous Galerkin Methods.” Springer: New York, 2000. https://link.springer.com/book/10.1007/978-0-387-72067-8#about

2. Huttunen, T., Malinen, M. & Monk, P. “Solving Maxwell's Equations Using The Ultra Weak Variational Formulation.” Journal of Computational Physics, 2007, pp. 731-759. https://www.sciencedirect.com/science/article/pii/S0021999106004712

3. Fidkowski, K. & Darmofal, D. “A Triangular Cut-Cell Adaptive Method for High-Order Discretizations of the Compressible Navier-Stokes Equations.” Journal of Computational Physics, 2007, pp. 1653-1672. https://www.sciencedirect.com/science/article/pii/S0021999107000757

4. Sanjaya, D. & Fidkowski, K. “Improving High-Order Finite Element Approximation Through Geometrical Warping.” American Institute of Aeronautics and Astronautics, 2016, pp. 3994-4010. https://arc.aiaa.org/doi/abs/10.2514/1.J055071

5. Persson, P.-O. & Peraire, J. “Curved Mesh Generation and Mesh Refinement Using Lagrangian Solid Mechanics.” 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, 2009. https://arc.aiaa.org/doi/abs/10.2514/6.2009-949

6. Xie, Z., Sevilla, R., Hassan, O. & Morgan, K. “The Generation of Arbitrary Order Curved Meshes for 3D Finite Element Analysis.” Computational Mechanics, 2013, pp. 361-374. https://link.springer.com/article/10.1007/s00466-012-0736-4

KEYWORDS: Computational Electromagnetics, Modeling, Curved Surfaces, Software Applications, High-Order Solver, Electrically Large, Perfect Electric Conductor, PEC: Electromagnetic Fields