Pasi Ylä-Oijala

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.

Electromagnetic Scattering From Rough Surface Using Single Integral Equation and Adaptive Integral Method

An efficient algorithm for electromagnetic wave scattering from rough dielectric surfaces is developed. The algorithm is based on the single magnetic field integral equation (SMFIE) and the surface is discretized using Rao-Wilton-Glisson (RWG) triangular basis functions. The new feature of the algorithm is the application of the adaptive integral method (AIM) with SMFIE for speeding up the calculation. The developed new method utilizes the flexibility of RWG functions to model arbitrary rough surface and the speed of FFT, enabling accurate simulations over large surfaces.

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.

Shape Sensitivity Analysis and Gradient-Based Optimization of Large Structures Using MLFMA

A fast method for computing the action of shape-differentiated electric field integral equation (EFIE) system matrix to a vector is derived exploiting the multilevel fast multipole algorithm (MLFMA). The proposed method is used in conjunction with the adjoint-variable method (AVM) to compute the shape gradient of arbitrary objective functions depending on shape of a metallic scatterer. The method is demonstrated numerically by optimizing the shape of a parabolic reflector illuminated with a half-wave dipole.

Calderon Preconditioned Surface Integral Equations for Composite Objects With Junctions

A Calderon preconditioned (CP) surface integral equation method is developed for the analysis of scattering by piecewise homogeneous dielectric and composite metallic and dielectric objects. The method is based on the electric current formulation (ECF), which only uses the electric surface currents as unknowns. In the ECF the ill-conditioned electric field integral operator and the well-conditioned magnetic field integral operator appear on separate equations, making the application of the CP much easier than e.g., in the PMCHWT formulation where these operators are mixed. In particular, using ECF, Calderon multiplicative preconditioner (CMP) can be straightforwardly extended for composite objects with junctions. Numerical examples demonstrate that the developed formulation, CMP-ECF, is well-conditioned on a very broad frequency range.

BROADBAND MULTILEVEL FAST MULTIPOLE ALGORITHM FOR ACOUSTIC SCATTERING PROBLEMS

A broadband multilevel fast multipole algorithm (MLFMA) for the acoustic scattering from a sound-hard obstacle is presented. The formulation is based on the Burton–Miller boundary integral equation and Galerkins method, avoiding any hypersingular integral operators. The resulting matrix equation has good iterative properties for all frequencies and avoids the interior resonance problem. The main novel feature is the use of a broadband MLFMA to accelerate the iterative generalized minimal residual (GMRES) solver. The algorithm is based on a combination of Rokhlins translation formula for large division cubes and the spectral representation of the Greens function for cubes smaller than one half wavelength, thereby avoiding the sub-wavelength breakdown of the high-frequency MLFMA.

Error-controllable and well-conditioned mom solutions in computational electromagnetics: ultimate surface integral-equation formulation [open problems in cem]

The ultimate goal in computational electromagnetics is to develop numerical methods and algorithms that are effective, stable, and give accurate and error-controllable results over a wide range of frequencies, material parameters, geometries, and applications. This article discusses obstacles and challenges in achieving that goal with frequency-domain surface integral-equation methods.

A Global Interpolator With Low Sample Rate for Multilevel Fast Multipole Algorithm

A new, improved version of a global interpolator utilizing trigonometric polynomials is presented for the high-frequency multilevel fast multipole algorithm. The number of required points to sample the outgoing and incoming field patterns is low, almost half in some levels, compared with the earlier published versions. Compared with local interpolators based on Lagrange interpolating polynomials, the proposed technique performs even more favorably and reduces the number of sample points by a factor of eight. The numerical examples demonstrate that the interpolator allows full numerical accuracy control during the aggregation and disaggregation phases, regardless of the number of the levels in the octree.

Analytical Shape Derivatives of the MFIE System Matrix Discretized With RWG Functions

An analytical formula for the shape derivative of the magnetic field integral equation (MFIE) method of moments (MoM) system matrix (or impedance matrix) is derived and validated against finite difference formulas. The motivation for computing the shape derivatives stems from adjoint variable methods (AVM). The Galerkin system matrix is constructed by means of Rao-Wilton-Glisson (RWG) basis and testing functions. The shape derivative formula yields an integral representation which is of same singularity order as the integrals appearing in the traditional MFIE system matrix.