Johannes Markkanen

Discretization of Volume Integral Equation Formulations for Extremely Anisotropic Materials

A stable volume integral equation formulation and its discretization for extremely anisotropic materials is presented. The volume integral equations are written in terms of the volume equivalent currents. The equivalent currents are expanded with piecewise constant basis functions, and the Galerkins scheme is applied for testing the equations. Numerical results show that the behavior of the formulation is more stable than the behaviors of the more conventional volume integral equation formulations based on fluxes or fields, when the scatterer is extremely anisotropic. Finally, the developed method is applied to analyze a highly anisotropic material interface which approximates the ideal DB boundary.

Analysis of Volume Integral Equation Formulations for Scattering by High-Contrast Penetrable Objects

The volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three-dimensional inhomogeneous objects. The properties of the volume electric and magnetic field integral equations (VEFIE and VMFIE) are investigated. Numerical experiments show that if the Galerkins method with the lowest mixed-order basis functions is used to discretize the equations the accuracy of the VMFIE can be significantly poorer than the accuracy of the VEFIE, in particular, for high-contrast objects at high frequencies. The accuracy of the VMFIE can be essentially improved with full first order (linear) basis functions. The linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background.

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwells has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwells equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwells equations are discussed.

Broadband Multilevel Fast Multipole Algorithm for Electric-Magnetic Current Volume Integral Equation

A volume integral equation method given in terms of the equivalent electric and magnetic volume currents and discretized using non-conforming element-wise constant approximations is applied to electromagnetic scattering analysis of inhomogeneous and anisotropic objects. A broadband version of the multilevel fast multipole algorithm (MLFMA) combining low frequency stable planewave expansion technique with the high frequency MLFMA and utilizing global interpolators based on trigonometric polynomials is used to accelerate the computations.

Material realizations of extreme electromagnetic boundary conditions and metasurfaces

The paper discusses the correspondence between electromagnetic boundary conditions and interface conditions. In particular, the focus is on the synthetic approach where the interest is in finding material realizations for given boundary conditions. Material realizations are approximative but not unique because, especially if anisotropic and bianisotropic materials are allowed, there are different material classes with which any given boundary condition can be mimicked. As examples, the PEC, PMC, PEMC, and DB boundary conditions are discussed. By comparing the scattering characteristics, it is demonstrated how well certain extreme-parameter material realizations are able to simulate the boundary effect.

Volume integral equation methods in computational electromagnetics

This paper discusses numerical properties of volume integral equation formulations in electromagnetic scattering by isotropic, anisotropic and bi-anisotropic objects. The volume integral equation formulation written in terms of the volume current densities and discretized with element-wise defined discontinuous functions is found to lead to more robust and efficient solutions on a wide range of material parameters than the more conventional formulations based on the conforming discretizations.

Realization of spherical D′B′ boundary by a layer of wave-guiding medium

Abstract In this paper the concept of wave-guiding medium, recently introduced for planar structures, is defined for the spherically symmetric case. It is shown that a quarter-wavelength layer of such a medium serves as a transformer of boundary conditions between the two interfaces. As an application, the D′B′-boundary condition, requiring vanishing of normal derivatives of the normal components of D and B field vectors, is realized by transforming the DB-boundary conditions. To test the theory, scattering from a spherical DB object covered by a layer of wave-guiding material is compared to the corresponding scattering from an ideal D′B′ sphere, for varying medium parameters of the layer.

Computation of Scattering by DB Objects With Surface Integral Equation Method

Electromagnetic scattering by objects with a DB boundary condition (normal components of the electric and magnetic flux densities D and B vanish at the boundary surface) is investigated. Scattering of arbitrary-shaped three-dimensional objects is analyzed with the surface integral equation method. A significant difference compared to the more conventional boundary conditions is that the uniqueness of the solution to the scattering problem with DB boundary depends on the connectivity of the object. For a simply connected object the solution is unique but for a multiply connected object some additional conditions are required. It appears that these additional conditions are satisfied if divergence-free basis functions are used to expand the unknown surface current densities. The developed method is applied to calculate polarizabilities, scattering efficiencies, and radar cross sections (RCS) of the DB sphere and cube, and the results are compared with those of the PEC cube and sphere.

Numerical methods for scattering problems expressed in terms of normal field components and their normal derivatives

Surface integral equation methods are developed for the analysis of time-harmonic electromagnetic scattering by arbitrarily shaped objects when the boundary conditions are expressed in terms of the normal field components and their normal derivatives.

Proceedings of the 2016 URSI Commission B International Symposium on Electromagnetic Theory, EMTS 2016

The components of the radiation patterns can be spanned with trigonometric polynomials in Multilevel Fast Multipole Algorithm (MLFMA) allowing development of simple global interpolators with exceptional accuracy control. In this article the basic properties of these functions are studied in one variable case. It is shown how the orthogonality of the basis functions can be utilized to develop simple operations suitable for creating fast and accurate MLFMA implementations.