Matteo Alessandro Francavilla

EFIE Modeling of High-Definition Multiscale Structures

We propose a method to significantly improve the spectral properties of the EFIE MoM matrix for broad-band analysis of structures with fine details, non-uniform meshes, and large overall sizes. A multilevel approach allows to overlay fine meshes and quasi-Nyquist sampled meshes; the fine-mesh conditioning is solved via hierarchical basis functions, and the quasi-Nyquist sampled part is treated by an algebraic incomplete LU preconditioner. Numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten/twenty wavelengths and levels of detail from very moderate to extending over the whole structure.

Nested Equivalent Source Approximation for the Modeling of Multiscale Structures

We introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Greens function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures.

Hierarchical Fast MoM Solver for the Modeling of Large Multiscale Wire-Surface Structures

In this letter, we present the analysis of large multiscale wire-surface structures through the method of moments (MoM) discretization of the electric field integral equation (EFIE). The MoM system is solved via the Greens function interpolation with fast Fourier transform (GIFFT) fast solver, extended here to geometries with wires and wires connected to surfaces. The implemented solver is entirely integrated with a hierarchical hybrid preconditioner, to allow an efficient analysis, in terms of computational time and memory requirements, of realistic and topologically complex geometries.

A Nonconformal Domain Decomposition Scheme for the Analysis of Multiscale Structures

We present a domain decomposition (DD) framework for the analysis of impenetrable structures; it allows for the electric field integral equation (EFIE) and combined field integral equation (CFIE), and for open, closed, and open-closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The DD employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the subdomains can be performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes.

On the Numerical Simulation of Metasurfaces With Impedance Boundary Condition Integral Equations

Metasurfaces are thin metamaterial layers characterized by unusual dispersion properties of surface/guided wave and/or reflection properties of otherwise incident plane waves. At the scales intervening in their design, metasurfaces can be described through a surface impedance boundary condition. The impedance, possibly tensorial, is often “modulated,” i.e., it can vary from place to place on the surface (by design). We investigate on different integral equation formulations of the problem, with special attention to the stability properties of the resulting system matrix.

A Hierarchical Fast Solver for EFIE-MoM Analysis of Multiscale Structures at Very Low Frequencies

We present an EFIE fast solver that is stable down to very low frequencies, for very dense meshes and multi-scale problems. The proposed approach uses a split-potentials formulation in association to a hierarchic pre-conditioner for the underlying low-rank fast factorization. Potential splitting prevents the numerical cancellation problem that undermines the effectiveness of the low-rank factorization, negatively impacting on the necessary factorization tolerance. The fast method presented in this work can be directly implemented into existing codes.

Wideband Fast Kernel-Independent Modeling of Large Multiscale Structures Via Nested Equivalent Source Approximation

We propose a wideband fast kernel-independent modeling of large multiscale structures; we employ a nested equivalent source approximation (NESA) to compress the dense system matrix. The NESA was introduced by these authors for low and moderate frequency problems (smaller than a few wavelengths); here, we introduce a high-frequency NESA algorithm, and propose a hybrid version with extreme wideband properties. The equivalent sources of the wideband NESA (WNESA) are obtained by an inverse-source process, enforcing equivalence of radiated fields on suitably defined testing surfaces. In the low-frequency region, the NESA is used unmodified, with a complexity of O(N). In the high-frequency region, in order to obtain a fixed rank matrix compression, we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size, and the NESA testing surfaces are defined as the boundaries of the pyramids. This results in a directional nested low-rank (fixed rank) approximation with O(N log N) computational complexity that is kernel independent; overall, the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low-frequency NESA for multiscale problems. Numerical results and discussions demonstrate the validity of the proposed work.

A Doubly Hierarchical MoM for High-Fidelity Modeling of Multiscale Structures

We propose a novel doubly hierarchical method of moments for the analysis of large and multiscale structures. A reciprocal multilevel matrix compression method (rMLMCM) is combined with the multilevel fast multipole algorithm (MLFMA), and they are used for the small-scale and large-scale cluster interactions, respectively. The resulting system is preconditioned following the hierarchical multiresolution-incomplete LU approach, which has proven successful for solving multiscale complex structures. The proposed method is applied to electromagnetic compatibility analysis of the real life, complex structures. Numerical results demonstrate the proposed preconditioned rMLMCM/MLFMA is effective also for large structures with strongly nonuniform discretization.

Evaluation of the Modeling of an EM Illumination on an Aircraft Cable Harness

This paper describes the approach developed in order to model the electromagnetic response of a cable bundle, part of the electrical wiring interconnection system of a real aircraft, submitted to an external electromagnetic excitation. The aim of this study is to highlight the main challenges in the synthetic modeling and validation of a fully real setup, from the electromagnetic compatibility point of view. Both conducted and radiated excitations have been considered in the electromagnetic global model. The solution is obtained through a cooperative simulation approach involving one 3-D full-wave solver and a multiconductor transmission line solver. The results are compared with measurements and specific tools, such as feature selective validation and integrated error against log frequency, are used to assess the adequacy of the results.

Grid Infrastructure for Domain Decomposition Methods in Computational ElectroMagnetics

The accurate and efficient solution of Maxwells equation is the problem addressed by the scientific discipline called Computational ElectroMagnetics (CEM). Many macroscopic phenomena in a great number of fields are governed by this set of differential equations: electronic, geophysics, medical and biomedical technologies, virtual EM prototyping, besides the traditional antenna and propagation applications. Therefore, many efforts are focussed on the development of new and more efficient approach to solve Maxwells equation. The interest in CEM applications is growing on. Several problems, hard to figure out few years ago, can now be easily addressed thanks to the reliability and flexibility of new technologies, together with the increased computational power. This technology evolution opens the possibility to address large and complex tasks. Many of these applications aim to simulate the electromagnetic behavior, for example in terms of input impedance and radiation pattern in antenna problems, or Radar Cross Section for scattering applications. Instead, problems, which solution requires high accuracy, need to implement full wave analysis techniques, e.g., virtual prototyping context, where the objective is to obtain reliable simulations in order to minimize measurement number, and as consequence their cost. Besides, other tasks require the analysis of complete structures (that include an high number of details) by directly simulating a CAD Model. This approach allows to relieve researcher of the burden of removing useless details, while maintaining the original complexity and taking into account all details. Unfortunately, this reduction implies: (a) high computational effort, due to the increased number of degrees of freedom, and (b) worsening of spectral properties of the linear system during complex analysis. The above considerations underline the needs to identify appropriate information technologies that ease solution achievement and fasten required elaborations. The authors analysis and expertise infer that Grid Computing techniques can be very useful to these purposes. Grids appear mainly in high performance computing environments. In this context, hundreds of off-the-shelf nodes are linked together and work in parallel to solve problems, that, previously, could be addressed sequentially or by using supercomputers. Grid Computing is a technique developed to elaborate enormous amounts of data and enables large-scale resource sharing to solve problem by exploiting distributed scenarios. The main advantage of Grid is due to parallel computing, indeed if a problem can be split in smaller tasks, that can be executed independently, its solution calculation fasten up considerably. To exploit this advantage, it is necessary to identify a technique able to split original electromagnetic task into a set of smaller subproblems. The Domain Decomposition (DD) technique, based on the block generation algorithm introduced in Matekovits et al. (2007) and Francavilla et al. (2011), perfectly addresses our requirements (see Section 3.4 for details). In this chapter, a Grid Computing infrastructure is presented. This architecture allows parallel block execution by distributing tasks to nodes that belong to the Grid. The set of nodes is composed by physical machines and virtualized ones. This feature enables great flexibility and increase available computational power. Furthermore, the presence of virtual nodes allows a full and efficient Grid usage, indeed the presented architecture can be used by different users that run different applications.