Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving ~he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems

The Interaction of Life Sciences & Engineering Technologies in Man/Systems Integration

Advancing technology has led to increasingly sophisticated systems, requiring cooperative interdisciplinary solutions to achieve optimal man/system integration. The life sciences and engineering have started to exchange ideas, techniques, and approaches to this common problem area. The difficulties encountered in such relationships are largely a matter of tradition and the absence of dialogue rather than any basic technical incompatibility. A basis for resolving these differences and the results of such endeavors are discussed

Acceleration of the Surface Test Integral Using Vertex Functions

In recent years, many papers have reported on the efficient and accurate evaluation of the double surface integrals that arise in the Method of Moments. Most have focused on the careful evaluation of the inner integral and assumed that the outer integral is sufficiently smooth to be easily evaluated numerically. More recently, several papers have appeared where the double integral is treated as a whole using the divergence theorem. These papers show promising results, though their implementation may imply changes to the integration paradigm for the associated codes. Here, instead, we investigate a technique that improves the numerical evaluation of the test integral without affecting the treatment of the source integral. From the integrand of the outer integral, we subtract pairs of quasi-static, so-called vertex functions defined on the source triangle. The approach is compared to standard Gauss-triangle schemes to demonstrate its effectiveness

6-D MoM Reaction Integrals Evaluated via the Divergence Theorem

In this contribution we propose an accurate and efficient numerical evaluation of 6-D reaction integrals that appear in the Method of Moment (MoM) discretization of Volume Integral Equations (VIEs)

Evaluation of Static Potential Integrals on Triangular Domains

Static potential integrals for constant and linear sources on triangles are derived in a straightforward way. The new representations, as presented, are robust with respect to machine evaluation in important limiting cases. The potential integrals comprise up to six functions, each dependent on the relative position and orientation (with respect to an observation point) of a vertex and edge, respectively, of the source triangle. Gradients of the potentials are derived by differentiation, thus preserving relations between the representations. Each such vertex function reveals any anomalous functional behavior near its associated vertex or edge, which is useful information for devising test integral schemes. Potential plots in the source plane of an equilateral triangle illustrate such behavior, as do similar plots for each vertex function and gradient components near their associated edge and vertex

COVARIANCE ADJUSTMENT IN STUDIES INVOLVING OBSERVATIONAL FACTORS OR COVARIATES INFLUENCED BY TREATMENTS

We extend the definition of adjusted treatment means in the analysis of covariance to deal with the case where some of the covariates are influenced by treatments or where some of the factors are observational. In these cases, comparison of treatment means adjusted to a common value of the covariate may be inappropriate. Partially adjusted means are defined and it is shown that special cases include the usual adjusted means (adjusted to a common value for each of the covariates) and unadjusted means. In fact, in a multifactorial experiment, one can, by appropriate choice of adjustment, compare adjusted means for one factor but unadjusted means for the second factor. Partially adjusted means can be computed by any linear models software which will estimate linear combinations of the parameters