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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]

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]

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 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 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 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 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]

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 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.

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.

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.