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The mixed MFIE and Calder´on preconditioned EFIE both can be used to accurately model the scattering of time-harmonic electromagnetic waves by two-dimensional perfect electrical conductors. In the case those conductors are bounded by smooth surfaces, the spectra of the linear systems are clustered around a single non-zero finite value. This configuration is optimal for the iterative solution of these...
A method is presented for reducing the number of subsequent integrations in impedance integrals containing the dynamic Green's function. The method works whenever a point can be found that is coplanar (or collinear) to both the basis and test support. This is always the case for singular impedance integrals. As an example, explicit formulas are given for the self-patch impedance integrals for the...
Razor blade testing schemes have been proposed in the past for both the EFIE and MFIE. The regularity of these testing functions is, strictly speaking, not sufficient for the discretization to be conforming. However, as will be shown in the contribution, it does yield physical solution currents at low frequencies. This is similar to the low-frequency behavior of the mixed discretization of the MFIE...
This paper studies the weak scaling behavior of the parallel computation of the translation operator in the three-dimensional (3D) Multilevel Fast Multipole Algorithm (MLFMA). First, two algorithms and their serial complexities are investigated. Then, the parallelization of these two algorithms and the arising issues regarding the complexity are discussed.
In this paper large full-wave simulations are performed using a parallel Multilevel Fast Multipole Algorithm (MLFMA) implementation. The data structures of the MLFMA-tree are partitioned according to the so-called hierarchical partitioning scheme, while the radiation patterns are partitioned in a blockwise way. To test the implementation of the algorithm, a full-wave simulation of a canonical example...
Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is “proper”: Testing functions belong to...
A storage data structure and strategy is proposed for the storage of Gegenbauer polynomial expansions, used in the numerical computation and storage of the bianisotropic scalar Green's function and its partial derivatives. The data structure allows the error to be controlled and keeps in check the computational complexity of the evaluation procedure.
In this contribution, a method is presented for reducing the number of subsequent integrations that occur in impedance integrals with Green's functions of the form Rν, with R the distance between source and observation point. The method allows the number of integrations to be reduced to 1 in the two dimensional case and 2 in the three dimensional case, irrespective of the number of subsequent integrations...
The Magnetic Field Integral Equation (MFIE) is a widely used integral equation for the solution of electromagnetic scattering problems involving perfectly conducting objects. It is usually discretized by means of RWG functions as both basis and test functions. This discretization of the MFIE is well-known for its good condition number. However, it is equally well-known for the inferior accuracy of...
This paper presents the progress in the development of a scalable parallel MultiLevel Fast Multipole Algorithm (MLFMA) for three-dimensional (3D) electromagnetic problems. Scalability stands for the ability to handle a larger problem on a proportionally larger parallel computer architecture. As a partitioning scheme, hierarchical partitioning (HP) is used, which divides the work load in a very balanced...
This paper shows the homogenization of a magnetic metamaterial, consisting of so-called Swiss rolls, using MLFMA simulations. First, the resonance frequency of a single Swiss roll is determined. Next, a bianisotropic model is used to determine the macroscopic material parameters of an ensemble of Swiss rolls by S-parameter retrieval. Finally, the macroscopic material parameters (the permeability,...
Recently, a novel discretization for the magnetic field integral equation (MFIE) was presented. This discretization involves both Rao-Wilton-Glisson (RWG) basis functions and Buffa-Christiansen (BC) basis functions and is dubbed `mixed'. The scheme conforms to the functional spaces most natural to electromagnetics and thus can be expected to yield more accurate results. In this contribution, this...
Boundary element methods (BEMs) are an increasingly popular approach to the modeling of electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullu-lated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes...
The paper discusses about the scattering of time-harmonic waves by dielectric objects can be described by several integral equations. All of these result from the Stratton-Chu intergral representation formulas for the fields in the interior and exterior region. The most popular integral equations are the Poggio-Miller-Chew-Harrington-Wu-Tsai equation (PMCHWT) and the Miiller equation. The former results...
Boundary integral equations are the principal tools for efficiently simulating electromagnetic fields in structures with piecewise constant material parameters. A specific trait of boundary integral equations is that the Green function of the Helmholtz equation appears as the integration kernel. Hence, discretizing a boundary integral equation leads to a dense linear system. Many such acceleration...
In this paper the properties of an ensemble of Swiss rolls are investigated. By fitting an analytical solution to the results of the simulation, the macroscopic permeability and permittivity are determined. For the simulations, boundary integral equations are used, discretized by the method of moments (MoM), which leads to a set of linear equations. To reduce the CPU-time needed to solve the set of...
The Method of Moments (MoM) is one of the most popular techniques for solving electromagnetic scattering problems. Its main advantage is that, when used to discretise a Boundary Integral Equation (BIE), only the surface of the objects needs to be discretised. Many other techniques require discretisation of the volume as well, leading to an increase of unknowns and requiring an artificial boundary...
Over the past years, we have developed several parallel implementations of the MLFMA in two and three dimensions, for the broadband EM characterization of large structures. We have reviewed how the hierarchical partitioning can result into scalable algorithms. Asynchronous techniques allow for the simulation of problems with a large number of dielectric objects. Experiments indicate that large scale...
Calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation (EFIE) for perfect electric conductors at lower frequencies. Previous authors have shown that, by using a dense matrix preconditioner based on the Calderon identities, the low frequency instability is removed while still maintaining the inherent accuracy of the EFIE. It...
The Multilevel Fast Multipole Algorithm (MLFMA) is widely used for the acceleration of matrix-vector products in the iterative solution of scattering problems. The MLFMA, however, suffers from a low-frequency (LF) breakdown. This breakdown is usually avoided by hybridizing the MLFMA with a method that does not fail at LF. For example, the Green function can be decomposed using the spectral representation...
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