High-order div- and quasi curl-conforming basis functions for calderon multiplicative preconditioning of the EFIE

A new high-order Calderon multiplicative preconditioner (HO-CMP) for the electric field integral equation (EFIE) is presented. In contrast to previous CMPs, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of high-order quasi curl-conforming basis functions. Like its predecessors, the HO-CMP can be seamlessly integrated into existing EFIE codes. Numerical results demonstrate that the linear systems of equations obtained using the proposed HO-CMP converge rapidly, regardless of the mesh density and of the order of the current expansion

The Design of Dual Band Stacked Metasurfaces Using Integral Equations

An integral equation-based approach for the design of dual band stacked metasurfaces is presented. The stacked metasurface will generate collimated beams at desired angles in each band upon reflection. The conductor-backed stacked metasurface consists of two metasurfaces (a patterned metallic cladding supported by a dielectric spacer) stacked one upon the other. The stacked metasurface is designed in three phases. First the patterned metallic cladding of each metasurface is homogenized and modeled as an inhomogeneous impedance sheet. An Electric Field Integral Equation (EFIE) is written to model the mutual coupling between the homogenized elements within each metasurface, and from metasurface to metasurface. The EFIE is transformed into matrix equations by the method of moments. The nonlinear matrix equations are solved at both bands iteratively resulting in dual band complex-valued impedance sheets. In the second phase, optimization is applied to transform these complex-valued impedance sheets into purely reactive sheets suitable for printed circuit board fabrication by introducing surface waves. In the third phase, the metallic claddings of each metasurface are patterned for full-wave simulation of the dual band stacked metasurface. Using this approach, two dual band stacked metasurfaces are designed

Accurate and conforming mixed discretization of the chiral Müller equation

Scattering of time-harmonic fields by chiral objects can be modeled by a second kind boundary integral equation, similar to Muller's equation for scattering by nonchiral penetrable objects. In this contribution, a mixed discretization scheme for the chiral Muller equation is introduced using both Rao-Wilton- Glisson and Buffa-Christiansen funtions. It is shown that this mixed discretization yields more accurate solutions than classical discretizations, and that they can be computed in a limited number of iterations using Krylov type solvers

Calderon multiplicative preconditioner for the PMCHWT equation applied to chiral media

In this contribution, a Calderon preconditioned algorithm for the modeling of scattering of time harmonic electromagnetic waves by a chiral body is introduced. The construction of the PMCHWT in the presence of chiral media is revisited. Since this equation reduces to the classic PMCHWT equation when the chirality parameter tends to zero, it shares its spectral properties. More in particular, it suffers from dense grid breakdown. Based on the work in [1], [2], a regularized version of the PMCHWT equation is introduced. A discretization scheme is described. Finally, the validity and spectral properties are studied numerically. More in particular, it is proven that linear systems arising in the novel scheme can be solved in a small number of iterations, regardless the mesh parameter

Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure