Maxwell SolverŠ Large Structure Analysis Software

The Maxwell Solver (MS) development program began in September of 1994 under the auspices of the ONR SBIR program (N00167-94-C-0077). It is effectively complete and has met or exceeded expectations. The MS software represents a unique National capability as regards accuracy and CPU efficiency in the characterization of EM interactions from large structures. Figure 1 shows a comparison of the Maxwell Solver vs. two of the most efficient and widely used flat facet models. It is noteworthy that even on geometry dominated by flat structure scattering, the MS still shows significant CPU savings while maintaining equivalent or better accuracy. Many of the benchmarks generated were done by impartial third parties. These efficiencies are obtained because of a sophisticated selective search method, redundancy checking, advanced adaptive algorithms as well as a direct curvi-linear integration technique. An example of the advanced adaptive algorithm appears in Figure 2. A 4x4 "hard" subpatching of the geometry was compared to an advanced adaptive run. The adaptive run ran 800% faster than the 4x4 run. This latter numerical efficiency has exceeded expectations and approaches the theoretically lower limit. The accuracy of both of the above results exceeds or matches other high frequency code results. The MS software can accurately represent EM interactions with very fast computational speeds by using state-of-the-art curvilinear base algorithms and by having the software decide when to include higher order effects to the EM computations. All aspects of the sophisticated algorithms within the MS have been validated against measurement or alternative EM analysis tools. A partial list of the innovations already included in the Maxwell Solver appear follow.

ˇ        Integration Interpolation - The starting point for the development of the MS software was the analysis of scattering from doubly curved surfaces. A phase expansion about nine control points was utilized in order to provide a closed form solution to the optics integration. This expansion led to a natural representation of a soft shadow boundary condition that is a more physical representation than a hard shadow boundary imposed by alternative developments.

ˇ        Selective Search Shadow - The selective search shadow operation employed by the MS software effectively converts a factorial search operation into a linear one. The CPU saving with this implementation is several orders of magnitude. The geometry is pre-processed and placed in a set of cubes in three-dimensional space. At point of rigorous shadow computation, a ray is traced through the lattice structure to determine an ordered set of cubes. Patches associated with these cubes are then precisely tested for blockage. No loss of accuracy is introduced. Historically, the storage for this algorithm became preclusive for very large problems. By restructuring this algorithm, the MS development team has completely precluded any such limitation. A binary search / table look-up hybrid procedure is utilized. The result is that for large problems that may have required 100 Mbytes or even 1 Gbyte of RAM run-time storage, the algorithm now only requires a flat .5 Mbytes of storage, largely independent of problem size.

ˇ        Curvilinear Multi-Bounce - The MS analyzes doubly curved patches without transforming them to flat facets. This methodology is also utilized in the multi-bounce algorithms. Standard shooting and bouncing ray (SBR) methods utilize a forward ray tracing method and subsequently integrate a ray footprint on the last patch, back to the observer. These approaches generally require 10 rays per linear wavelength or 100 rays per square wavelength of surface area. For a patch comprising 10K wavelengths, this would imply the tracing and subsequent integration of a million rays. For the MS software, this same patch generally requires only about 25 rays (or a factor of 40,000 fewer rays). The procedure employed is a hybridization of a GO forward search technique, with an interpolative-based retrace. A forward GO search is utilized to test for potential patch-patch interactions. Next, the control points of the integration are rigorously retraced in order to determine if they are active. This smart retrace is sub-patched adaptively in a user transparent manner. The control point activation information is then utilized to perform the bistatic integration back to the observer (radar). The MS software utilizes sophisticated redundancy testing in both the multi-bounce and shadowing algorithms. These redundancy algorithms exhibit compiler type search efficiency and insure that identical operations are never performed more than once. Thus, for example, if a shadow search operation has already been performed in the context of a previous integration, it need not and will not be duplicated in the context of a subsequent multi-bounce search in the MS software.

ˇ        Sea Surface Effects - The MS currently uses the sea surface model proposed in the Engineer's Refractive Effects Prediction System (EREPS) published by Naval Oceans System Center (NOSC) in February of 1990. This publication represents a quality piece of work. However, forward scattering effects determined by this investigation were predicated on a database of measured results, which may be somewhat limited. In this EREPS formulation, the forward scattering sea component provides a phase (for VV polarization) and an amplitude correction, which may be extracted from the em integrals and thus provides an "after the fact" perturbation of the multi-path sea components of the total RCS. Ongoing work at Ohio State University (OSU) may lead to an advanced analytical technique for sea scattering, which will likely pose phase, and amplitude corrections which are inseparable from the em integrals. If of interest to ONR, the incorporation of this work into the proposed effort may be included as an option task in year two. The method proposed would be based on a recent Navy SBIR program, the Maxwell Solver (MS). The asymptotic surface integration in the MS is split into a weighted phase and amplitude distribution around each of nine "control points", which describe what is termed a bi-quadratic, doubly curved patch. Because of the interpolative weighting distribution, each of these integrals is primarily dependent on the phase and amplitude distribution of the excitation, in the local vicinity of their associated control point. Thus, each control point may be excited with a plane wave of different phase, direction and amplitude. The result is that an advanced sea surface model which results in varying amplitude and phase of the incident multi-path field, for a given angle of incidence, may be handled by reworking the sea surface system excitation integrals.

ˇ        Higher Order Effects - One of the more important contributions of the Maxwell Solver development program has been in the pragmatic characterization of traveling wave effects on very large structures. In the interests of CPU efficiency, these effects are formulated as corrections to the standard PTD, in the coordinate frame of the CAD patch. To date, this has precluded the need to trace geodesic paths through the geometry. Although these geodesic paths are a convenient theoretical coordinate frame, their computation is intensive and thus numerically inconvenient.

ˇ        Advanced Adaptive Algorithm - The advanced adaptive algorithm has had a positive impact on accuracy, CPU efficiency and ease of use for the end user. This algorithm enhances three separate computations in the Maxwell Solver software. It adaptively sub-patches the geometry in select angular regions so as to focus computational resources on those scatterers requiring additional accuracy. An example might be a cavity, within a ship geometry. This cavity would be detected and sub-patched in those angular regions where the cavity is visible. It is emphasized that the adaptive nature of the MS is but one more of the many features, which serves to separate this existing MS large structure analysis tool, from any other analysis tool of its type in the world.