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A measurement system capable of in situ measurements of formation permeability is described. The measurement method relies upon imaging the distribution of magnetic permeability fluid injected into a wellbore system through mutual inductance measurements between pairs of coils and relating the change in distribution of this fluid over time to a direct measurement of formation phase permeability. Analysis of the mutual inductance measurement method shows a unique response to distributions of magnetic permeability for various coil spacings and insensitivity to other confounding electrical parameters. The lower bound of measurement variance for this system is modeled for a continuum of coil spacings and radii of investigation for a perturbation in magnetic permeability. [ABSTRACT FROM AUTHOR]

This paper presents an algebraic technique for generating arbitrary-order divergence-conforming bases for curvilinear triangular cells. The bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions. Koornwinder–Dubiner polynomials are chosen as the general function set. Basic constraints are presented to obtain divergence-conforming bases, and additional constraints are presented to further enforce the bases to be Nédélec. Results from a variety of problems are given to show that the bases exhibit high-order convergence and also produce systems that are relatively well conditioned compared to other basis sets. [ABSTRACT FROM AUTHOR]

Objective: To improve peripheral nerve repair, new techniques to increase the speed of regeneration are required. Studies have shown that the electrical stimulation can enhance nerve regeneration; however, stimulation parameters that regulate the growth increases are unknown. The objective of this study was to examine dorsal root ganglion (DRG) neurite extension, directionality, and density after using methods to specifically control ac electrical field intensity and frequency exposure. Methods: Chick DRG explants were exposed to 20-Hz, 200-Hz, 1-MHz, and 20-MHz sinusoidal electric field of 17.86 V/m, and tissue parameters were measured. Results: Results show that neurite extension and directionality were influenced by frequency; however, the ratio of support cell emigration with respect to neurite extension from the DRG body was not. These results were further verified through finite-element modeling of intracellular calcium, which show that higher frequencies have minimal effect on intracellular calcium. Conclusion: In conclusion, these results demonstrate that 1) directional growth of neurites within EFs can be achieved, 2) high-frequency stimulation in megahertz does not enhance or impair the neurite growth, and 3) low-frequency stimulation affects the growth and directionality. Significance: The significance of this study is the direct comparison of neurite extension after high stimulation frequencies (megahertz) with typical low-frequency fields (20 and 200 Hz), and modeling the results with finite-element modeling. [ABSTRACT FROM AUTHOR]

A new surface integral equation formulation for scattering from perfectly conducting objects is presented. The formulation is developed by adding a constraint on the normal component of the magnetic field to the augmented electric field integral equation (AEFIE) and extracting the static charge solution. The resulting AEFIEnH-S formulation is discretized using the method of moments with Rao–Wilton–Glisson (RWG) source functions and Buffa–Christiansen (BC) test functions. An iterative diagonal matrix scaling algorithm is used to improve the conditioning of the discrete system. Numerical examples demonstrate that the AEFIEnH-S is stable and accurate as the frequency is reduced for closed, open, and multiscale multiply connected geometries. The formulation relies only on diagonal preconditioning, it accurately models the near electric, near magnetic, and far fields, it does not require frequency scaling of the unknowns, and it does not incorporate any type of Helmholtz decomposition. [ABSTRACT FROM PUBLISHER]

A well-conditioned, high-order Nyström discretization of a volume integral equation for quasi-magnetostatic, time-harmonic eddy current analysis of magnetic-conducting materials is presented. Good conditioning is contingent on augmenting the system with a charge neutrality constraint. Two forms of the continuity constraint are discussed. An iterative diagonal preconditioning scheme is applied to greatly improve the condition number. Results are presented for canonical problems and the TEAM Workshop Problem 7. [ABSTRACT FROM PUBLISHER]

A new formulation for electromagnetic scattering from perfect electric conductors is presented. The new EFIE-hd formulation is based on the electric field integral equation (EFIE) and incorporates a Helmholtz decomposition (HD) of the current. Instead of using specialized basis functions, the HD is obtained by imposing appropriate surface integral constraints. It is shown that this strategy allows for the use of a locally corrected Nyström discretization method for the resulting formulation. Numerical examples are provided to demonstrate that the EFIE-hd is frequency stable and provides accurate solutions for the electric and magnetic fields at both high and low frequencies for simply connected structures. Examples for multiply connected structures are also provided. [ABSTRACT FROM PUBLISHER]

Different types of local global solution (LOGOS) modes have been proposed to develop fast direct solvers for electromagnetic wave problems. While radiating LOGOS modes are suitable for high frequency problems, this paper focuses on the localizing LOGOS modes, which are suitable for low-to-mid frequency problems. Factorizations relying on non-overlapped, localizing LOGOS (NL-LOGOS) modes are provably error controllable, but fail to provide acceptable asymptotic computational efficiencies. Factorizations using overlapped, localizing LOGOS (OL-LOGOS) modes provide improved asymptotic computational performance, but have been observed to suffer from significant overhead and, in some cases, poorer error control. This paper describes a new procedure for obtaining the OL-LOGOS modes. It is observed that the asymptotic efficiency is similar to previously reported OL-LOGOS schemes while providing stable error control for standard problem formulations. The overhead associated with computing the OL-LOGOS modes is also reduced significantly. [ABSTRACT FROM PUBLISHER]

Local-global solution (LOGOS) modes provide a computationally efficient framework for developing fast, direct solution methods for electromagnetic simulations. LOGOS modes provide a single basis for which both electromagnetic operators and their inverses are sparse with a controllable accuracy. For fixed-frequency modeling with h-refinement, efficient application of this observation is shown to provide efficient factorization algorithms for both integral equation and finite element methods. In addition to providing fast, direct solutions, the LOGOS framework is also shown to provide a new strategy for modular electromagnetic analysis. The possibility of developing efficient direct solution strategies at high frequencies using the LOGOS framework is also discussed. [ABSTRACT FROM AUTHOR]

An algorithm is presented for the sparse pseudo inversion of discrete forms of the plane wave transform. The starting point for the sparse pseudo inverse is a new sparse representation of the discrete plane wave transform (DPWT). While other sparse representations of the DPWT exist, the sparse representation developed here is shown to be amenable to sparse factorization. This feature is used to develop an efficient, error-controlled pseudo-inverse of the DPWT. Representative numerical examples are provided to illustrate the general properties of the proposed algorithms. Areas for additional work are identified, and potential applications of the results are discussed. [ABSTRACT FROM AUTHOR]

The details of a Galerkin discretization scheme for a modified form of the electric field integral equation are outlined for smooth, three-dimensional, perfectly conducting scatterers. Limitations of the divergence conforming finite-element bases in pit- serving the self-stabilizing properties of the electric field integral equation operator are indicated. A numerically efficient alternative is outlined which relies on an operator-based Helmholtz decomposition. The condition number of the resulting matrix equation is demonstrated to be frequency independent for scattering from a perfectly conducting sphere at various frequencies. [ABSTRACT FROM AUTHOR]

The properties of different forms of the combined field integral equation (CFIE) formulation of electromagnetic scattering from convex, perfect electrically conducting geometries are considered. Several difficulties encountered in the numerical implementation of the traditional CFIEs of electromagnetic scattering theory are discussed. An alternate form of the CFIE is introduced which is free of many of the deficiencies of traditional formulations for smooth, convex geometries. The improved numerical properties of the new formulation are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

The physical and analytical properties of a stabilized form of the electric field integral equation are discussed for closed and open perfectly conducting geometries. It is demonstrated that the modified equation provides a well-conditioned formulation for smooth geometries in both the high- and low-frequency limits; an instability remains near the edges of open geometries, requiring future consideration. The surface Helmholtz decomposition is used to illustrate the mechanism of the stabilization procedure, and the relevance of this mechanism to the numerical discretization of the equation is outlined. [ABSTRACT FROM AUTHOR]

Focuses on well conditioned multilevel fast multipole algorithm formulation for closed perfect electric conductor targets in the vicinity of a half space. Application of the algorithm to the problem of scattering; Overview of the use of a modified electric-field integral equation for the purpose.

Presents information on a sigma-delta audio digital-to-analog converter (DAC) for compact disc (CD) and digital versatile disc (DVD) application. Discussion on the chip architecture and design; Discussion on the circuit design issues; Measured results.

Presents a study which examined a combined field approach to scattering from infinite elliptical cylinders using the method multiple interactions (MOMI). Techniques used; Equations; Summary of results.

Provides information on the use of average altimeter waveform models to more adequately account for the effects of surface roughness and subsurface inhomogeneities on the averaged scattered waveform. Description of the models; Information on the radially and vertically distributed media; Evaluation of the model; Details on the parameter estimates.

Presents information on a study which presented an iterative solution for two-dimensional scattering problems derived from a minimally coupled factorization of the Helmholtz equation. Factorization of Helmholtz operator; Conclusion.

In this paper, a technique to convert a locally corrected Nyström discretization into a moment method discretization is detailed. The method is general and does not rely directly on any specific relationship between the basis functions used to compute the local corrections and the basis and test functions used in the moment method. The technique is applied to a quasi-magnetostatic volume integral equation for both interpolatory and algebraically constrained moment method bases. Numerical results for a variety of problems in terms of error convergence, system condition number, and degrees-of-freedom are provided. [ABSTRACT FROM AUTHOR]

The University of Alabama in Huntsville (UAH) in partnership with the National Aeronautics and Space Administration at Marshall Space Flight Center is working to develop a pulsed power facility. The facility, known as Charger-1, is a 1-TW pulsed power machine. The hardware was originally DECADE Module 1 from L-3 Pulsed Sciences Division in San Leandro, CA. The DECADE program enabled the construction of several pulsed-power modules. Together, they were used for high-energy X-ray generation and weapons effects testing. The module at UAH is being outfitted for z-pinch propulsion system and nuclear energy production experiments. Its primary envisioned goal is to support the development of a Pulsed Fission-Fusion propulsion system with experimental data. This document is intended to update the nuclear and pulsed power communities as to the progress of the facility development. An overview of the facility and its status is presented. [ABSTRACT FROM AUTHOR]

During well-logging operations, the depth of a logging tool is usually obtained by measuring the length of the wireline cable that suspends the tool in the well. In some cases, a secondary depth reference is obtained with a casing collar locator (CCL) that detects the collars along the steel casing lining the well. The thicker steel at these collars is detected by measuring the perturbations it causes to the field of a permanent magnet in the CCL logging tool. Due to its simplicity and efficiency, the CCL tool has not seen many changes throughout the years. However, for small, untethered sensor platforms, neither of the above methods is practical. This paper describes the theory, design, construction, and testing of an inductive sensor that detects the gap on the inside of the casing where two pipe joints mate together within a collar. Two identical cylindrical coils along a common axis are connected in a bridge configuration and driven by an ac signal. When one coil is near the gap, its inductance is slightly larger than that of the other, misbalancing the bridge. The sensor was implemented in a wireline tool and tested in a well. The field data show a clear double pulse of ac signal across the bridge each time the tool passes a collar. This sensor is smaller and lighter than CCLs that use permanent magnets, making it suitable for small, untethered sensor platforms. [ABSTRACT FROM PUBLISHER]

This communication presents an algebraic method for constructing arbitrary-order, divergence-conforming basis functions on hexahedral volume elements. The appropriate constraints within and on the boundaries of elements are provided. In particular, the handling of faces where quantities are discontinuous is discussed. The resulting bases are numerically characterized in terms of error convergence and system conditioning for a moment method discretization of the electric field volume integral equation for dielectric scatterers. Results show the accuracy of the proposed method as well as the low system matrix condition number that can be maintained as the basis order and mesh discretization are increased. [ABSTRACT FROM AUTHOR]

A correction to the article "Electric Field-Based Surface Integral Constraints for Helmholtz Decompositions of the Current on a Conductor," that was published in the September 2013 issue is presented.

This paper presents an algebraic method of generating arbitrary-order basis functions suitable for use in moment methods. The basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions, leading to a matrix representation of the constraint condition. The desired bases are then found through use of the singular value decomposition. Divergence-conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations. Appropriate constraints for enforcing normal continuity at cell boundaries are discussed. A variety of problems are analyzed using the constrained bases, and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order. [ABSTRACT FROM PUBLISHER]

A generalization of the locally corrected Nyström (LCN) discretization method is outlined wherein sparse transformations of the LCN system matrix are obtained via singular- value decompositions of local constraint matrices. The local constraint matrices are used to impose normal continuity of the currents across boundaries shared by mesh elements. Due to the method’s simplicity and flexibility, it is straightforward to develop high-order constrained LCN (CLCN) systems for different formulations and mesh element types. Numerical examples demonstrate the memory savings provided by the CLCN method and its improved accuracy when applied to geometries with sharp edges. It is also shown that the CLCN method maintains the high-order convergence of the LCN method, and it eliminates the need to include line charges in Nyström-based discretizations of formulations that involve the continuity equation. [ABSTRACT FROM PUBLISHER]

A new version of the combined field integral equation (CFIE) is introduced for the formulation of time-harmonic electromagnetic wave interactions with perfect electric conductors (PECs). The new CFIE-hd formulation is obtained by imposing a Helmholtz decomposition of the current via appropriate surface integral equation constraints. Discretization is performed using a locally corrected Nyström method, and the performance of the resulting numerical scheme is examined for several PEC objects. It is observed that the proposed strategy is frequency stable, provides accurate solutions for the electric and magnetic fields from low to moderate frequencies, and eliminates false interior resonances. [ABSTRACT FROM PUBLISHER]

A high-order Nyström discretization of a volume integral equation derived for quasi-magnetostatic, time-harmonic eddy current analysis is presented. The formulation is based on the coupled magnetic field and magnetic vector potential integral equations. Both magnetic and conducting materials are included in the formulation. Analytic results for canonical problems are used to corroborate the high-order convergence of the method. Data for the TEAM Workshop problem 7 are presented. [ABSTRACT FROM PUBLISHER]

Quasi-mixed order prism basis functions for use in Nyström discretizations of volume integral equations are presented. The prism basis function set is easily mixed with other basis function sets such as those defined on hexahedra and tetrahedra. The prism basis functions are applied to solve a magnetostatic volume integral equation for the analysis of magnetic materials. Analytic results for canonical problems are used to corroborate the basis function set and convergence and error data are discussed. [ABSTRACT FROM PUBLISHER]

Local-global solution (LOGOS) modes provide a computationally efficient framework for developing error controllable, fast, direct solution methods for electromagnetic simulations. This communication provides an error control analysis for the non-overlapped localizing LOGOS factorization procedure. The error analysis indicates how to control the error in the factored representation of the system matrix. Numerical examples demonstrate that the proposed error control procedure provides factorizations with controllably small errors for a number of PEC scattering problems while maintaining the efficiency of the LOGOS factorization. [ABSTRACT FROM AUTHOR]

Localizing modes provide an effective basis for developing efficient, error-controlled factorizations of the dense matrices encountered in integral equation formulations of wave phenomena at low to moderate frequencies. An essential component of these factorization algorithms is the numerical determination of the underlying localizing modes. This communication describes the details of an efficient procedure for computing the so-called non-overlapping, localizing modes. The principle component of the procedure is a QR-like factorization of the sparse multilevel data structure used to compress discrete integral operators. Numerical examples demonstrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

A broad-band Huygens surface method requiring only the measurement of the magnetic field for near-field to near-field transformations is presented. The proposed method is valid down to near dc and supports arbitrary shaped Huygens surfaces. The method relies on an augmented-integral equation formulation that is used to predict the electric field on the Huygens surface. The proposed formulation is discretized using a high-order locally corrected Nyström method. The surface magnetic and electric fields can then be used to compute external electric and magnetic fields. The method is validated using electromagnetic fields radiated by a three-phase motor showing excellent results over several Fourier harmonics of the motor fields, including the zeroth harmonic. The method is also validated at high frequency for a dipole antenna array. [ABSTRACT FROM PUBLISHER]