Large-Scale Structures in Acoustics and Electromagnetics Proceedings of a Symposium (1996) / Chapter Skim
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5 ALGORITHMIC ASPECTS AND SUPERCOMPUTING TRENDS IN COMPUTATIONAL ELECTROMAGNETICS
5 ALGORITHMIC ASPECTS AND SUPERCOMPUTING TRENDS IN COMPUTATIONAL ELECTROMAGNETICS
Pages 103-121
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From page 103... ...
To realize this potential, practical means must be developed for the rapid generation of gnds on and around the aircraft, and numerical algorithms that maintain high-order accuracy on such grids must be constructed. A structured grid and an unstructured grid-based finite-volume, time-domain Maxwell's equation solver have been developed incorporating modeling techniques for general radar absorbing materials.
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From page 104... ...
MaxweR's Equations In order to apply conservation principles (for example, in fluid dynamics, mass, momentum, and energy are conserved) , many of the governing equations representing appropriate physical processes are written in conservation form.
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From page 105... ...
and G are the fluxes in x, y, and z coordinate directions, respectively. The conservation form readily admits weak solutions such as shock waves.
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From page 106... ...
For treatment of complex geometries, a body-fitted coordinate transformation is introduced to aid in the application of boundary conditions. Under the transformation of coordinates implied by = t, ~ = t(t,x,y,z)
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From page 107... ...
Both approaches typically use explicit time integration, which means that the upper limit on the allowable size of the time step ~ is determined by the physical size and shape of the smallest cells, corresponding roughly to the time that light takes to cross one of these cells. Implicit integration schemes can choose larger time steps, but they require the inversion of a banded matrix the size of the whole and, and their ability to preserve phase information is not known.
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From page 108... ...
Thus, each polyhedral face has a co-face with a distinct face index, and each such co-face belongs to its own polyhedron. Polynomial Representation and Least Squares To go beyond representation of the fields as simple volume averages, we have chosen initially to implement linear polynomial functions for both E and H
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From page 109... ...
For a linear polynomial fit, there is a simpler alternative procedure that we have implemented to evaluate these linear terms. From the divergence theorem, the average value of any derivative over the cell volume can be rewritten as a surface integral: Ma ia &': V l ~nx plus, where n is the unit outward normal on the boundary odor and V`` is the cell volume.
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From page 110... ...
Because the illuminating fields are weak, the response of the materials can be taken as linear, so that an effective dielectric permittivity ~ and magnetic permeability ,u can be defined, both of which wall in general be complex at the illuminating frequency. The treatment of various limiting material conditions relevant to radar absorbing structures within the framework of time-domain electromagnetics is described below.
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From page 111... ...
Perfectly Conducting Surface At typical radar frequencies, the electncal conductivity of metals and other aircraft structural composites is sufficiently high that they can be treated as perfect electrical conductors. In this limit, the electromagnetic fields do not penetrate the conducting surface, and the components of the electric field tangent to the surface vanish at every point.
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From page 112... ...
Boundary Conditions Proper implementation of various boundary conditions associated with material properties such as perfectly conducting walls, resistive sheets, material interface, impedance boundaries, as well as computational boundary conditions such as nonreflecting outer boundaries are very crucial to accurately modeling problems in electromagnetics. In fact, higher-order accurate implementation of boundary conditions in any computational simulation in any discipline is the number one computational issue.
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From page 113... ...
The boundary condition procedure for perfectly conducting walls can also be appropriately modified and applied for impedance walls, where the surface tangential electric field, instead of being 0, is proportional to the tangential magnetic field. Outer Boundaries Along a given direction in space, the local electromagnetic fields can be grouped into forward and backward propagating combinations.
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From page 114... ...
Massively Parallel Computing With the emergence of massively parallel computing architectures with potential for teraflops performance, any code development activity must effectively utilize the computer architecture in achieving the proper load balance with minimum internodal data communication. Some of the massively parallel computing architecture issues addressed in the present study are Domain decomposition and load balancing Internodal message passing with minimum communication delays ~4
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From page 115... ...
Validation Once a CEM code is developed, the results must be validated against known exact solutions and carefully tailored experimental data. There are many computational issues such as and resolution, location of the outer boundary, and accuracy of the boundary condition procedures that can only be addressed through a careful study of many validation cases.
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From page 116... ...
, EMP/EMI/EMC, and bioelectromagnetics problems Ideal for CFD/CEM optimization studies The CEM code has been extensively tested for the following geometries: 1) Canonical obects such as spheres, cylinders, ogives, thin rods, cones, airfoils, and a circular disc 2)
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From page 117... ...
Future efforts will include coupling of the CEM codes with CFD and Computational Structural Mechanics for multidisciplinary optimization studies. ACKNOWLEDGMENT This work is funded by Rockwell JR&D, AFOSR, Army Research Laboratory at Aberdeen Proving Ground, NASA Ames Research Center, and the Elecromagnetic Code Consortium.
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From page 118... ...
~o 30 £~ D C CO ~ o no static RC S fo r HH Pol 7.
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From page 119... ...
scared ne~ ^^~~ ~ ~ ~ Fi~ 5.4 IS far s complete h~ 119 .
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From page 120... ...
Microstrin Patch Antenna Monooole Antenna 38 5= = Figure 5.5 Different applications ofthe CEM code. Slotted Wavequide Antenna Low Pass Filler 120
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From page 121... ...
Figure 5.6 Bioelec~omagnetic application of the CEM code.
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