On the Hierarchical Preconditioning of the Combined Field Integral Equation

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical non-solenoidal basis is used for the non-solenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory

Improved Discretization of the Full First-Order Magnetic Field Integral Equation

The inaccuracy of the classical magnetic field integral equation (MFIE) is a long-studied problem. We investigate one of the potential approaches to solve the accuracy problem: higher-order discretization schemes. While these are able to offer increased accuracy, we demonstrate that the accuracy problem may still be present. We propose an advanced scheme based on a weak-form discretization of the identity operator which is able to improve the high-frequency MFIE accuracy considerably - without any significant increase in computational effort or complexity.Comment: 3 pages, 1 figure, accepted for the 15th European Conference on Antennas and Propagation 2021 (EuCAP

Fast integral methods for conformal antenna and array modeling in conjunction with hybrid finite element formulations

Fast integral methods are used to improve the efficiency of hybrid finite element formulations for conformal antenna and array modeling. We consider here cavity-backed configurations recessed in planar and curved ground planes as well as infinite periodic structures with boundary integral (BI) terminations on the top and bottom bounding surfaces. Volume tessellation is based on triangular prismatic elements which are well suited for layered structures and still give the required modeling flexibility for irregular antenna and array elements. For planar BI terminations of finite and infinite arrays the adaptive integral method is used to achieve O(NlogN) computational complexity in evaluating the matrix-vector products within the iterative solver. In the case of curved mesh truncations for finite arrays the fast multipole method is applied to obtain O(N1.5) complexity for the evaluation of the matrix-vector products. Advantages and disadvantages of these methods as they relate to different applications are discussed, and numerical results are provided

Phase Retrieval for Partially Coherent Observations

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets are coherently linked to each other - which is a reasonable assumption for our objective of antenna measurements. Two classes of measurement setups are discussed which can provide this kind of extra information: multi-probe systems and holographic measurements with multiple reference signals. We propose several formulations of the corresponding phase retrieval problem. The simplest of these formulations poses a linear system of equations similar to an eigenvalue problem where a unique non-trivial null-space vector needs to be found. Accurate phase reconstruction for partially coherent observations is, thus, possible by a reliable solution process and with judgment of the solution quality. Under ideal, noise-free conditions, the required sampling density is less than two times the number of unknowns. Noise and other observation errors increase this value slightly. Simulations for Gaussian random matrices and for antenna measurement scenarios demonstrate that reliable phase reconstruction is possible with the presented approach.Comment: 12 pages, 14 figure

Linear Phase Retrieval for Near-Field Measurements with Locally Known Phase Relations

A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in practice be acquired with multi-channel receivers. Due to the linearity of the formulation, a reliable phaseless transformation is achieved, which completely avoids the problem of local minima - the Achilles heel of most existing phase retrieval techniques. Furthermore, the necessary number of measurements are kept close to that of fully-coherent antenna measurements. Comparisons with an already existing approach exploiting local phase relations demonstrate the accuracy and reliability for synthetic data.Comment: 5 pages, 3 figures, 1 table, submitted to the 15th European Conference on Antennas and Propagation 2021 (EuCAP

Hybrid finite element modelling of conformal antenna and array structures utilizing fast integral methods

Hybrid finite element methods (FEM) which combine the finite element and boundary integral methods have been found very successful for the analysis of conformal finite and periodic arrays embedded on planar or curved platforms. A key advantage of these hybrid methods is their capability to model inhomogeneous and layered material without a need to introduce complicated Green's functions. Also, they offer full geometrical adaptability and are thus of interest in general-purpose analysis and design. For the proposed hybrid FEM, the boundary integral is only used on the aperture to enforce the radiation condition by employing the standard free space Green's function. The boundary integral truncation of the FEM volume domain, although necessary for rigor, is also the cause of substantial increase in CPU complexity. In this paper, we concentrate on fast integral methods for speeding-up the computation of these boundary integrals during the execution of the iterative solver. We consider both the adaptive integral method (AIM) and the fast multipole method (FMM) to reduce the complexity of boundary integral computation down to []( N α ) with α <1.5. CPU and memory estimates are given when the AIM and FMM accelerations are employed as compared to the standard []( N 2 ) algorithms. In addition, several examples are included to demonstrate the practicality and application of these fast hybrid methods to planar finite and infinite arrays, frequency selective surfaces, and arrays on curved platforms. Copyright © 2000 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35033/1/347_ftp.pd

Accuracy and Conditioning of Surface-Source Based Near-Field to Far-Field Transformations

The conditioning and accuracy of various inverse surface-source formulations are investigated. First, the normal systems of equations are discussed. Second, different implementations of the zero-field condition are analyzed regarding their effect on solution accuracy, conditioning, and source ambiguity. The weighting of the Love-current side constraint is investigated in order to provide an accurate problem-independent methodology. The transformation results for simulated and measured near-field data show a comparable behavior regarding accuracy and conditioning for most of the formulations. Advantages of the Love-current solutions are found only in diagnostic capabilities. Regardless of this, the Love side constraint is a computationally costly way to influence the iterative solver threshold, which is more conveniently controlled with the appropriate type of normal equation. The solution behavior of the inverse surface-source formulations is mostly influenced by the choice of the reconstruction surface. A spherical Huygens surface leads to the best conditioning, whereas the most accurate solutions are found with a tight, possibly convex hull around the antenna under test.Comment: 15 pages, 13 figures, 4 tables, accepted for publication in IEEE Transactions on Antennas and Propagatio

Directly connected hybrid finite element-boundary integral-ray-optical models

The hybrid finite element-boundary integral-uniform geometrical theory of diffraction method with acceleration by the multi-level fast multi-pole method is extended in a way that allows the application of the hybrid method to problems, where the finite element-boundary integral-multi-level fast multi-pole method parts of the model can be directly connected to uniform geometrical theory of diffraction regions. This becomes possible by an appropriate utilization of Huygens' principle, together with the fact that the regions exterior to the introduced Huygens surface is free of any fields and can thus be filled with arbitrary materials. As such, the appropriate materials are chosen in order to obtain simple enough bodies, which can be treated by the uniform geometrical theory of diffraction. Since some of the boundary integral basis functions typically touch flat parts of these bodies, the image principle is employed for the accurate evaluation of the corresponding boundary integrals. Numerical results for radiation and scattering problems are presented and compared to reference numerical data. The obtained results prove the feasibility of the procedure and considerable computation time and memory savings