A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderon multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwave-length geometric features. Numerical examples demonstrate the efficiency of the proposed scheme.

In this contribution, we demonstrate that recent improvements in “fast methods” allow for fully error-controlled full-wave simulations of two-dimensional objects with sizes over a million wavelengths using relatively simple computing environments. We review how a fully scalable parallel version of the Multilevel Fast Multipole Algorithm (MLFMA) is obtained to accelerate a two-dimensional boundary integral equation for the scattering by multiple large dielectric and/or perfectly conducting objects. Several complex and large-scale examples demonstrate the capabilities of the algorithm. This implementation is available as open source under GPL license (http://www.openfmm.net).

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 was also demonstrated that the spectral properties of the Caldero-n preconditioner are conserved during discretization if the EFIE operator is discretized with Rao-Wilton-Glisson expansion functions and the preconditioner with Buffa-Christiansen expansion functions. In this article we will show how the Calderon multiplicative preconditioner (CMP) can be combined with fast multipole methods to accelerate the numerical solution, leading to an overall complexity of O(N logN) for the entire iterative solution. At low frequencies, where the CMP is most useful, the traditional multilevel fast multipole algorithm (MLFMA) is unstable and we apply the nondirectional stable plane wave MLFMA (NSPWMLFMA) that resolves the low frequency breakdown of the MLFMA. The combined algorithm will be called the CMP-NSPWMLFMA. Applying the CMP-NSPWMLFMA at open surfaces or very low frequencies leads to certain problems, which will be discussed in this article.

The present paper numerically investigates the micromagnetic behavior of permalloy nanostrips, starting from the space-time integration of the Landau-Lifshitz-Gilbert equation. The analysis is performed on objects with variable longitudinal size of the order of some hundreds of nanometers. The attention is focused on the role of geometrical properties (e.g., scaling factor and end shape) and of thermal agitation on magnetization reversal processes. The thermal effects are included in the model following the Langevin approach.

In finite ferromagnetic wires, the demagnetizing effects along the wire axis have a substantial influence on the reversal processes. By considering infinite wires, these effects are annihilated and only the sample dimensions, cross-sectional geometry, and material properties determine the magnetization reversal. The magnetization reversal is now initiated by small thermal fluctuations. With decreasing cross-sectional dimensions, three different reversal modes can be distinguished: reversal with (i) domain formation; (ii) vortex formation; and (iii) precessional switching combined with buckling. For different cross-sectional dimensions and lattice axes orientations, the 3-D magnetization dynamics and evolution of the different micromagnetic energy terms are investigated, resulting in a clear understanding of the reversal modes.

Large planar microwave structures, such as frequency selective surfaces and reflectarrays, are of practical use in many applications. These structures' scattering cross sections are of great interest to the design engineer. During the design cycles, reliable full-wave simulations of these large planar structures can provide useful information. Often, however, the computational requirements (both in term of memory consumption and CPU solving time), needed to accurately compute such scattering cross sections, are huge.

Time domain electric field integral equations often are used to analyze transient scattering from perfect electrically conducting objects. When discretized using marching-on-in-time recipes they give rise to linear systems of equations that can be solved for the induced currents for all time steps. Unfortunately, when the scatterer is approximated by increasingly dense meshes, the condition number of these systems grows rapidly, slowing down the convergence of iterative solvers. Here, time domain Calderon identities are derived and subsequently used to construct a Calderon-preconditioned time domain electric field integral equation that can be discretized even with dense meshes using Buffa-Christiansen basis functions. Numerical results that demonstrate the effectiveness and accuracy of the proposed method are presented.

Progress in science is usually an almost continuous process only taking small steps at a time. The invention of the PML [1] by J.-P. Bérenge definitely was not continuous. The impact of this invention on computational electromagnetics and beyond cannot be overestimated. This was immediately clear for the audience that in 1994 attended the dedicated lecture at the IEEE Antennas and Propagation Symposium in Seattle. A short conversation of the first author with Bérenger several years later in Paris revealed that for J.-P. Bérenger this invention was a simple and obvious solution to a problem on his desk. He needed something that absorbed without reflection incident waves that arrived from almost any direction and for all frequencies.

An improvement of the perfectly matched layer multilevel fast multipole algorithm (PML-MLFMA) for simulating large planar microwave structures is presented. By exploiting the low-rank property of the PML-MLFMA multimodal aggregation and disaggregation matrices, considerable reductions in memory usage and computation time are obtained. The method has been extensively validated, demonstrating complete error controllability when simulating large planar microwave structures. Reductions in memory requirements and CPU time of more than 60% and 40% have been achieved.

The scattering of time-harmonic electromagnetic waves by perfect electrical conductors (PECs) can be modelled by several boundary integral equations, the magnetic and electric field integral equations (MFIE and EFIE) being the most prominent ones. These equations can be discretized by expanding current distributions in terms of Rao-Wilton-Glisson (RWG) functions defined on a triangular mesh approximating the scatterer's surface and by testing the equations using the same RWG functions. The main advantage of the MFIE is that it is well-posed in the easy-to-understand L2-norm. Discretization of the MFIE leads to systems that can be solved efficiently using iterative solution techniques. In this contribution, the cause for the MFIE's inaccuracy is discussed, and a new discretization scheme is proposed. Numerical results are presented that demonstrate the improvement realized by the new scheme over the classical one.

Using the proposed preconditioning technique, fast convergence can be obtained. This is illustrated for a simulation of a straight wire. In Fig. 1 the number of iterations needed by the proposed regularized Green function preconditioned EFIE solver is compared with that needed by a Calderon preconditioned [3] and unpreconditioned solver. The number of iterations required by the proposed preconditioner is almost independent of the number of unknowns. The number of iterations needed using the unpreconditioned system, or the Calderòn preconditioned system, is O(N). Similar results apply for wires of other lengths.

Calderón preconditioning is very succesful in stabilising the EFIE and the use of BC functions makes the formalism valid on open surfaces. Through applying a broadband fast multipole method, the complexity can be reduced from O (N 2 ) to O(N log N), allowing the simulation of very large structures. In the high frequency case a localised version of the preconditioner must be used to avoid excessive scattering of the eigenvalues of the combined operator.

A Calderon multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Calderon-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation.

Magnetic field integral equation (MFIE) and Calderon preconditioned electric field integral equation (EFIE) operators applied to toroidal surfaces have nontrivial nullspaces in the static limit. The nature of these nullspaces is elucidated and a technique for generating a basis for them presented. In addition, the effects of these nullspaces on the numerical solution of both frequency and time-domain MFIE and CalderOacuten preconditioned EFIEs are investigated. The theoretical analysis is accompanied by corroborating numerical examples that show how these operators' nullspaces affect real-world problems.

The Multilevel Fast Multipole Algorithm (MLFMA) is a well known and very successful method for accelerating the matrix‐vector products required for the iterative solution of Helmholtz problems. The MLFMA is based on an addition theorem which suffers from the so‐called low‐frequency (LF) breakdown, due to numerical roundoff error. Here, a new addition theorem will be developed which does not suffer from an LF breakdown. Instead it suffers from a High‐Frequency (HF) breakdown. The new addition theorem is based on a novel set of distributions, the so called pseudospherical harmonics, closely related to the spherical harmonics. The so‐called translation operators can be calculated in closed form, which allows the easy implementation of an LF‐stable MLFMA.

A new approach to discretize the electric field integral equation (EFIE) that hybridizes Calderón and hierarchical techniques is presented. The benefits of these two techniques are combined and inherited by the proposed method. The result is an EFIE solver which is immune from low-frequency breakdown, well-conditioned in the presence of densely discretized structures and exhibits only minimal computational overhead. The hybridization is achieved by observing that hierarchical techniques link the conditioning of the global EFIE problem to that of a reduced size problem that can be successfully regularized by a properly tailored Calderón approach. Numerical results will show the performance of the proposed method and its advantages over to the state of the art.

We have indicated how the hierarchical partitioning approach can be used to obtain a scalable parallel MLFMA implementation in both two and three dimensions. In three dimensions, the radiation patterns need to be repartitioned at every level, both in elevation and azimuth. The hierarchical approach was implemented in an asynchronous fashion in an open-source two-dimensional solver which can be downloaded free of charge (http://www.openfmm.net). The accurate scattering at a very large two-dimensional cylinder with a diameter of 1.2 million of wavelengths was reported.

This paper compares two numerical schemes for the simulation of magnetization dynamics in 3-D particles. The first one is based on the finite-difference computation of the Landau-Lifshitz equation and on the magnetostatic field evaluation by fast Fourier transforms. The second one handles the spatial discretization of the effective field expression by a nodal finite-element method and solves the Poisson equation with a finite-element/boundary-element technique. The convergence of the methods is studied by varying the time and space discretization.

Often transsexualism is presumed to be rather rare. The medical literature often cites a prevalence of 1 in 11,900 for male to female transsexualism and 1 in 30,400 for female to male transsexualism. A detailed analysis of the publications behind these numbers reveals that these numbers underestimate the relative number of individuals that is confronted with transsexualism, the so-called inherent prevalence of transsexualism. Based on data extracted from earlier publications it is possible to derive a lower bound for the inherent prevalence of transsexualism in the Netherlands and Belgium. This analysis results in inherente prevalencies for sex reassignment surgeries that are about four times higher than the above cited numbers. The prevalence of transsexualism will be significantly higher since not all transsexuals will undergo sex reassignment. 

In this paper we wish to focus on some recent advances in the multilevel fast multipole algorithm (MLFMA). Three different topics will be discussed briefly: a seamless extension of the MLFMA to low frequencies, an asynchronous parallelization of the MLFMA suitable for grid computing environments and a new Calder on based preconditioner for the electric field integral equation (EFIE). This will be illustrated by three scattering examples in frequency and time domain.