Parallisation of the MLFMM for distributed memory systems

A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.

Diagonalization of the fast multipole method (FMM) for the Helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves. The resulting k-space integral over the Ewald sphere is numerically evaluated. Storing the k-space quadrature samples of the method of moments (MoM) basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems. In this paper, it is proposed to expand the k-space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules. Aggregations, plane wave translations, and disaggregations in the realized multilevel fast multipole method (MLFMM) are carried out using the k-space samples of a numerical quadrature rule. However, the incoming plane waves on the finest MLFMM level are expanded in spherical harmonics again. Thus, due to the orthonormality of spherical harmonics, the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients. Overall, the resulting MLFMM can save a considerable amount of memory without compromising accuracy and numerical speed.

To study wave scattering from random lossy dielectric rough surfaces with large permittivities using the method of moments, a dense grid is needed for accurate results. A dense grid requires more CPU and memory. The physics‐based two‐grid (PBTG) method can reduce both CPU and memory requirements. In this paper, the PBTG is used in conjunction with the multilevel fast multipole method (FMM) to solve wave scattering from one‐dimensional random lossy dielectric rough surfaces. The proposed algorithm has the computational complexities of O(Ndg) for near‐field interactions and O(Ncg) for nonnear‐field interactions, where Ndg and Ncg are the number of sampling points on the dense and coarse grids, respectively. Using the proposed algorithm, wave scattering from Gaussian and non‐Gaussian rough surfaces is investigated and illustrated. Special emphasis is put on checking the accuracy of the algorithm and energy conservation.

The MLFMM (Multilevel Fast Multipole Method) is an alternative formulation of the technology behind the MoM (Method of Moment) and is applicable to much larger structures than the MoM, making full-wave current-based solutions of electrically large structures a possibility. This fact implies that it can be applied to most large models that were previously treated with the MoM without having to change the mesh. In this paper we discuss the development and implementation of volumetric integral equations for both dielectric and magnetically permeable materials using curvilinear hexahedral elements. Both piecewise constant and higher order basis functions will be examined in the context of volumetric multilevel fast multipole method implementation. Comparisons with corresponding finite element-boundary integral solutions will also be presented and compared in terms of accuracy and efficiency.

Complex scattering problems are solved with the multilevel fast multipole method (MLFMM). Geometries include metallic structures (wires and surfaces) as well as dielectric bodies (volume and surface equivalence principle). Validation and application examples show the large savings in memory and run-time of the MLFMM as compared to the standard method of moments (MoM). Limitations regarding dielectric bodies are addressed, which are encountered when attempting to model highly lossy dielectric bodies with a high permittivity.

The application of a parallelized multilevel fast multipole method (MLFMM) is described and illustrated through examples for the solution of large scale and complex EMC problems. Furthermore, to reduce the modeling complexity of such EMC problems, we propose a combination of field with network theory to split large problems into smaller sub-problems which can be analyzed individually and then again assembled together by means of network theory.

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrate do n high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined.

Numerical computations of electromagnetic radiation and scattering problems for arbitrarily shaped and electrically large objects in the same environment are preferably performed by combining the method of moments (MoM) with the uniform geometrical theory of diffraction (UTD). Composite metallic/dielectric objects with arbitrary shape are handled efficiently with the finite element boundary integral (FEBI) method. For large scale problems, the MoM solution is accelerated by the multilevel level fast multipole method (MLFMM). On the other hand, electrically large objects with relatively simple shape are treated sufficiently with ray-based high-frequency methods, like geometrical optics (GO) and UTD. However, until now MoM-UTD hybrid approaches have been restricted to conventional MoM formulations with only the electric field integral equation (EFIE), resulting in limited modeling capabilities. The same restrictions also exist in the hybrid FEBI-UTD method. The paper presents MLFMM-UTD hybridization for the combined field integral equation (CFIE), in order to extend further the applicability of the FEBI-UTD method. The resulting modeling technique is referred to as the FEBI-MLFMM-UTD method. The MLFMM-UTD hybridization is performed in the translation procedure on the various MLFMM levels, by taking into account additional contributions received at the testing groups due to UTD objects. Due to different ray directions for outgoing and incoming waves, appropriate interpolation and anterpolation procedures must be applied to consider the UTD contributions.

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion being that going above 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order is not worthwhile. In this paper, we challenge this conclusion, providing results that demonstrate the potential performance gains with Higher-Order MLFMM and showing some modifications to the traditional MLFMM that can benefit both Higher-Order and standard discretizations.

a Design Concept of Piecewise Variable Wall Thickness of Radome Is Proposed to Simulate the Radome which Has Variable Wall. the Paper Calculates the Far Field of a Medium-Size Radome in the Case of Piecewise Variable Thickness by Three Methods as Follows: Method of Moment (MOM), Multilevel Fast Multipole Method (MLFMM) and Physical Optics&amp; the Method of Moments (PO/MOM) Respectively. after Comparing the Results, we Find that the PO/MOM Method Have the Superiority in Simulation of Radome’s Electromagnetic because it’s More Accuracy and Less Memory Consuming than the other Two Methods. Also it Proves the Feasibility of the Design Concept of Piecewise Variable Thickness for Radome.

A large circular loop antenna is used to excite the TE 41 mode at operation frequency of 9 GHz inside a circular waveguide section to launch a vortex beam. The effect of the antenna location inside the waveguide on its effective input impedance is modeled using transmission-line relations and optimal location for matching is determined. The analytical model results are confirmed using multi-level fast multipole method (MLFMM) full-wave simulations.

Front-fed parabolic reflectors are among the most commonly used antennas in the industry. While in spaceborne applications, membrane reflectors are very promising due to their lightweight and foldable features. However, considering the large size, small thickness and low stiffness, solar radiation and microwave radiation will have considerable influences on the antennas’ shape accuracy as well as the radiation characteristics. In this article, a theoretical approach is presented to solve the multi-physical effects of the parabolic antenna. The deformation of the reflector is derived by the shallow shell theory, taking into account the solar pressure, the microwave pressure and the thermal effects due to solar and microwave heating. The far-field electromagnetic radiation pattern is then obtained by considering the deformation of the reflector. On the other hand, a numerical approach combining the finite element method, the multi-level fast multipole method, and the large element physical optics is also presented. Numerical examples suggest good agreement between the theoretical and numerical results. The methods have been applied into the analysis of design models in the Space Solar Power Station project. Also, these approaches can be directly extended into other space membrane reflector antennas.

Antenna measurement errors occur due to reflections and diffractions within the measuring chamber. In order to extract and correct the undesired signals, a technique based on test-zone field compensation and spherical wave expansion is applied to Compact Antenna Test Range (CATR) and Spherical Near-Field (SNF) measurements of a base transceiver station antenna. The required spherical test-zone field is acquired by simulating the corresponding measurement environment with the multi-level fast multipole method. Due to the numerical complexity of the problem, only the parts of the chamber with a significant influence on the measurement results are modeled. Comparing the determined directivities after applying the correction method, an exact overlap is achieved between the SNF and CATR solution.

In R. Mueller et. al. (2006) the design of a UHF direction finding antenna with optimised radar cross section (RCS) was introduced. In the present paper the monostatic RCS of the antenna is characterised up to 18 GHz. Measured results of the RCS are compared to simulated results which are obtained using the new commercially available multilevel fast multipole method (MLFMM) ( U. Jakobus and J. van Tonder, 2005).