Alex Heldring

Nonconforming Discretization of the Electric-Field Integral Equation for Closed Perfectly Conducting Objects

Galerkin implementations of the method of moments (MoM) of the electric-field integral equation (EFIE) have been traditionally carried out with divergence-conforming sets. The normal-continuity constraint across edges gives rise to cumbersome implementations around junctions for composite objects and to less accurate implementations of the combined field integral equation (CFIE) for closed sharp-edged conductors. We present a new MoM-discretization of the EFIE for closed conductors based on the nonconforming monopolar-RWG set, with no continuity across edges. This new approach, which we call “even-surface odd-volumetric monopolar-RWG discretization of the EFIE”, makes use of a hierarchical rearrangement of the monopolar-RWG current space in terms of the divergence-conforming RWG set and the new nonconforming “odd monopolar-RWG” set. In the matrix element generation, we carry out a volumetric testing over a set of tetrahedral elements attached to the surface triangulation inside the object in order to make the hyper-singular Kernel contributions numerically manageable. We show for several closed sharp-edged objects that the proposed EFIE-implementation shows improved accuracy with respect to the RWG-discretization and the recently proposed volumetric monopolar-RWG discretization of the EFIE. Also, the new formulation becomes free from the electric-field low-frequency breakdown after rearranging the monopolar-RWG basis functions in terms of the solenoidal, Loop, and the nonsolenoidal, Star and “odd monopolar-RWG”, components.

On the Convergence of the ACA Algorithm for Radiation and Scattering Problems

The adaptive cross approximation (ACA) algorithm, when used to accelerate the numerical solution of integral equations for radiation and scattering problems, sometimes suffers from inaccuracies. These inaccuracies occur when the ACA convergence criterion, which is based on an approximation of the residual relative error, is prematurely satisfied. This paper identifies the two sources of this problem and proposes adaptations of the algorithm that remedy them.

Volumetric Testing Parallel to the Boundary Surface for a Nonconforming Discretization of the Electric-Field Integral Equation

The volumetric monopolar-RWG discretization of the electric-field integral equation (EFIE) imposes no continuity constraint across edges in the surface discretization around a closed conductor. The current is expanded with the monopolar-RWG set and the electric field is tested over a set of tetrahedral elements attached to the boundary surface. This scheme is facet-oriented and therefore, well suited for the scattering analysis of nonconformal meshes or composite objects. The observed accuracy, though, is only competitive with respect to the RWG-discretization for a restricted range of heights of the tetrahedral elements. In this communication, we introduce a novel implementation of the volumetric monopolar-RWG discretization of the EFIE with testing over a set of wedges. We show with RCS and near-field results that this scheme offers improved accuracy for a wider range of heights than the approach with tetrahedral testing. The application of the wedge testing to the even-surface odd-volumetric monopolar-RWG discretization of the EFIE, edge-oriented and therefore less versatile, shows similar accuracy as with tetrahedral testing, which is a sign of robustness.

Discretization of the EFIE in Method of Moments without continuity of the normal current component across edges

The discretization in Method of Moments (MoM) of the Electric-Field Integral Equation (EFIE) is traditionally carried out by preserving the continuity of the normal component in the expansion of the current across the edges arising from the discretization. This allows the cancellation of the hyper-singular Kernel contributions arising from the discretization of the EFIE. Divergence-conforming sets, like the RWG set, appear then as suitable choices to generate successful MoM-EFIE implementations. In this paper, we present a novel MoM-discretization of the EFIE with the non-conforming monopolar-RWG basis functions, with jump discontinuities in the expanded normal component of the current. We show with RCS results that the new EFIE implementation shows good agreement with the traditional normal-continuous RWG-implementation.

Regularization of the 2D TE-EFIE for homogeneous objects discretized by the Method of Moments with discontinuous basis functions

The discretization of the Electric-Field Integral Equation (EFIE) by the Method of Moments (MoM) for a transversal electric (TE) illuminating wave impinging on an infinitely long cylinder (2D-object) is traditionally carried out with continuous piecewise linear basis functions. In this paper, we present a novel discretization of the TE-EFIE formulation for the scattering analysis of homogeneous, perfectly conducting 2D-objects based on the expansion of the currents around the line-boundary through discontinuous piecewise linear or piecewise constant basis functions. We show for several infinitely long cylinders, with smooth or sharp-edged sections, the good accuracy of the proposed approach in the computation of far-field and near-field quantities, such as RCS and currents, with respect to the observed accuracy in conventional continuous piecewise linear discretizations.

Multilevel field interpolation algorithm for large PEC objects

A multilevel field interpolation algorithm (MLFIA) that allows for numerically efficient evaluation of fields produced by given current distributions is presented. The algorithm is based on a source domain decomposition that permits a fast matrix-vector multiplication within the iterative solution that reduces the computational complexity and the memory requirements to O(NlogN). Its implementation is composed of the computation of the field evaluated at a set of evaluation points within the observation domain, application of a phase extraction, interpolation of the fields, and finally a phase-restoration. The algorithm is applied to the analysis of 1-D/2-D large PEC objects discretized by the method of moments.

Simultaneously improving the efficiency and compression of the adaptive cross approximation algorithm

This paper proposes an adaptation of the conventional ACA algorithm for block-wise impedance matrix compression, yielding a substantial speed-up as well as a higher compression rate. The recently published stochastic Frobenius norm estimation is complemented with a new approach to allow applying it to blocks that represent touching regions. The stochastic method is then combined with SVD recompression to simultaneously eliminate the stochastic uncertainty and optimize the compression rate.

Fast direct solution of the combined field integral equation

The Method of Moments for electromagnetic scattering and radiation problems is often used in conjunction with the EFIE because the EFIE allows the analysis of open surfaces. For electrically large closed surfaces, the CFIE is often much more efficient because it yields a well conditioned impedance matrix. This is particularly important when an iterative solution method is used. This paper compares the EFIE and the CFIE for a novel fast direct (non-iterative) solution method, the Multiscale Compressed Block Decomposition method.

On the accuracy of the adaptive cross approximation algorithm

This contribution identifies an often ignored source of uncertainty in the accuracy of the adaptive cross approximation algorithm, and proposes a combination of adaptations that reduce this uncertainty with negligible additional computational cost.

Volumetric testing with wedges for a nonconforming discretization of the Electric-Field Integral Equation

The discretization in Method of Moments (MoM) of the Electric-Field Integral Equation (EFIE) is traditionally carried out with divergence-conforming sets of basis functions, like the RWG set. This enforces the normal continuity of the current across the edges arising from the discretization and makes the quasi-singular Kernel contributions numerically manageable. However, these MoM-implementations of the EFIE show little flexibility when handling nonconformal meshes, normally arising from from the juxtaposition or interconnection of independent meshes in the modular design of composite objects. A nonconforming discretization of the EFIE is possible if the testing procedure is carried out over volumetric elements attached to the surface triangulation, inside the body. In this paper, we present a new nonconforming discretization of the EFIE, where wedges attached to the source triangles are used as testing volumetric elements.