A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies

Abstract

A higher order multilevel fast multipole algorithm (MLFMA) is presented for computing electromagnetic scattering from three-dimensional bodies comprising both conducting and dielectric objects. The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) approach for multiple homogeneous dielectric objects and the combined-field approach for conducting objects. The resultant integral equations are discretized by the method of moments (MoM), in which the conducting and dielectric surfaces/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions. Such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling. An implicit matrix-filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions. The resultant numerical system is then solved by MLFMA, which is tailored to accommodate the material properties of dielectric scatterers, and the solution is accelerated using an incomplete LU decomposition preconditioner. Numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems.

Solution of volume‐surface integral equations using higher‐order hierarchical Legendre basis functions

“…The enforcement of the continuity condition allows 780 unknowns to be eliminated. In Figure 11 the mono-static RCS obtained from the present method at 1 GHz is compared with the result of the MLFMM for SIE given in [Donepudi et al, 2003]. The discrepancies observed at the minimum levels are most likely due to different q steps utilized in the simulations.…”

Fast Algorithms and Hybrid Techniques

“…The dimensions of the conducting plate and the thickness of the coating are displayed in Figure 11.36 . Good agreement is observed between the FE -BI and moment -method solutions [40,104] . Good agreement is observed between the FE -BI and moment -method solutions [40,104] .…”

“…The corresponding formulation can be obtained by applying the Laplace transform to the frequency -domain formulation [107,108] . Figure 11.35 b displays the θθ -polarized monostatic RCS at 0.3 GHz [40,106] . This allows the truncation surface to be placed conformal to the object to be analyzed.…”

A Novel Multitrace Boundary Integral Equation Formulation for Electromagnetic Cavity Scattering Problems

“…Similar idea has also been used in the ultra weak variational formulation of discontinuous Galerkin finite element methods [53], [54]. Equations (11) and (12) enforce the necessary field continuity conditions for the tangential components of the electric and magnetic fields across the surface S. Equation (13) is the Silver − Müller radiation condition for the scattered field in the exterior region Ω 0 as r → ∞.…”

“…There is a large literature available on computation and analysis of cavity scattering problems, including the asymptotic techniques [1]- [3], finite-difference time-domain methods [4], finite element methods [5]- [7], and integral equation methods [8]- [11]. Nevertheless, because of the highly oscillatory and strong resonance nature of the solution for large and complex cavities, accurate and fast numerical analysis still presents significant mathematical and computational challenges.…”