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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]

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 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 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 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]

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]