N. V. Nair

A GMR-Based Eddy Current System for NDE of Aircraft Structures

Onsite real-time nondestructive evaluation of aircraft using eddy current techniques has gained significance in the past few years. In this paper, emphasis is placed on developing a flexible and a fast real-time inspection system using giant magnetoresistive (GMR) field sensors. Experimental signals are compared with finite-element model (FEM) model simulations and signals acquired using traditional data acquisition methods. Several advantages of the improved design are discussed

Stability Properties of the Time Domain Electric Field Integral Equation Using a Separable Approximation for the Convolution With the Retarded Potential

The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers and (ii) understanding the stability properties of the electric field integral equation. As is well known, time domain electric field integral equation solvers have been notoriously difficult to stabilize. Research into methods for understanding and prescribing remedies have been on the uptick. The most recent of these efforts are (i) Lubich quadrature and (ii) exact integration. In this paper, we re-examine the solution to this equation using (i) the undifferentiated form of the time domain electric field integral equation (TDEFIE) and (ii) a separable approximation to the spatio-temporal convolution. The proposed scheme can be constructed such that the spatial integrand over the source and observer domains is smooth and integrable. As several numerical results will demonstrate, the proposed scheme yields stable results for long simulation times and a variety of targets, both of which have proven extremely challenging in the past.

Generalized Method of Moments: A Novel Discretization Technique for Integral Equations

Typical method of moments solution of integral equations for electromagnetics relies on defining basis functions that are tightly coupled to the underlying tessellation. This limits the types of functions (or combinations thereof) that can be used for scattering analysis. In this paper, we introduce a framework that permits seamless inclusion of multiple functions within the approximation space. While the proposed scheme can be used in a mesh-less framework, the work presented herein focuses on implementing these ideas in an existing mesh topology. A number of results are presented that demonstrate approximation properties of this method, comparison of scattering data with other numerical and analytical methods and several advantages of the proposed method; including the low frequency stability of the resulting discrete system, its ability to mix different orders and types of basis functions and finally, its applicability to non-conformal tessellations.

Further Development of Vector Generalized Finite Element Method and Its Hybridization With Boundary Integrals

Recently, vector generalized finite element method (VGFEM) was introduced for the solution of the vector Helmholtz equation, and its applicability was validated for canonical problems. VGFEM uses a local Helmholtz decomposition to construct basis functions in overlapping local domains of some canonical shape. While using a canonical shape for local domains adds flexibility to the method, one needs to provide information regarding boundaries of domains/inhomogeneities. The need for surface information proves to be a bottleneck in using the method for a larger class of problems. This paper is targeted towards overcoming these deficiencies; here, we will introduce the modifications to this method that permit interfacing with arbitrarily shaped local domains (to facilitate interfacing with existing meshing software), integrate this method with boundary integrals and provide a framework for studying dispersion. As will be apparent, the hybridization of the method with boundary integrals is not a simple adaptation of existing methods onto the VGFEM framework. Likewise, dispersion analysis is nontrivial due to the overlapping nature of VGFEM basis functions. A range of practical problems has been analyzed within the presented framework and results are compared either against measurements or existing FEM data to validate the presented methodology.

Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies.

In this paper, we present a novel framework for discretizing integral equations--specifically, those used for analyzing scattering from dielectric bodies. The candidate integral equations chosen for the analysis are the well-known Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and the Müller equations. Discrete solutions to these equations are typically obtained by representing the spatial variation of the currents using the Rao-Wilton-Glisson (RWG) basis functions or their higher order equivalents. In this paper, we propose a framework for defining basis functions that departs significantly from those of RWG functions in that approximation functions can be chosen independent of continuity constraints. We will show that using this framework together with a quasi-Helmholtz type representation has a number of benefits. Namely, (i) it shows excellent convergence, (ii) it permits inclusion of different orders of polynomials or different functions as basis functions without imposition of additional constraints, (iii) the method can easily handle nonconformal meshes, and (iv) the method is well conditioned at all frequencies. These features will be demonstrated via a number of numerical experiments.

The Generalized Method of Moments for Electromagnetic Boundary Integral Equations

The generalized method of moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on GMM for electromagnetics was confined to geometries modeled by piecewise flat tessellations and suffered from spurious internal line charges. In the present article, we redesign the GMM scheme and demonstrate its ability to model scattering from PEC scatterers composed of mixtures of smooth and non-smooth geometrical features. Furthermore, we demonstrate that because the partition of unity provides both functional and effective geometrical continuity between patches, GMM permits mixtures of local geometry descriptions and approximation function spaces with significantly more freedom than traditional moment methods.

A Wavelet Based Signal Processing Technique for Image Enhancement in Terahertz Imaging Data

Terahertz imaging is a relatively new technique for sub‐surface imaging using radiations in the spectral range between 0.1 to 10 THz. The technique has been used to image artificially induced inserts simulating disbonds in metal‐foam interfaces and has shown significant promise as a possible non destructive evaluation technique for evaluating the bonding quality of foam. The data in these cases is obtained by scanning across a surface on top of the foam coated on metal structures and collecting the time signal in a window of interest at each point in the scan plane. Proper data processing and visualization techniques become critical in being able to detect the disbonds and delaminations that, additionally, become convoluted due to the wide variety of artifacts and support structures that occur on the metal substrates. In this work we discuss a wavelet based signal enhancement algorithm that provides an effective scheme for visualizing the imaging data and provides a very high contrast between disbonded areas and normal substrate. The technique also shows promise as a first step towards automatic detection and classification of the disbonds. Some preliminary results, obtained on data collected using simulated disbonds that demonstrate the usefulness of the algorithm will be presented.

A Higher Order Space-Time Galerkin Scheme for Time Domain Integral Equations

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter methods efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

Generalized method of moments: A boundary integral framework for adaptive analysis of acoustic scattering

Boundary integral equations (BIEs) find applications in problems ranging from sonar to medical diagnostics. The two ingredients of the BIE solution technique are (1) representation of the domain and (2) design of approximation spaces to represent physical quantities on the domain. These, in concert, affect accuracy and convergence of the simulation. This paper presents a framework that permits the development of a scheme for refinement (of size and order) in both geometry and function representations. Further, this permits flexibility in the types of basis functions that can be used. Capabilities of the proposed framework are shown via a number of numerical examples.

A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This letter provides a systematic prescription for the application of the rules for weakly singular integrals on higher order surfaces. Here, we present implementation details and several demonstrative results that compare the accuracy and convergence of the integration rules.