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In this article, a nonconformal and nonoverlapping domain decomposition method (DDM) based on surface integral equation (SIE) is proposed for the electromagnetic (EM) scattering or radiation of multiscale metallic targets. To reduce the unknown amount of the conventional SIE for multiscale EM simulation, we apply curved triangular elements and higher order hierarchical vector (HOHV) basis functions to the SIE. Next, to increase the flexibility of geometrical modeling and accelerate the convergence of the presented SIE system for electrically large and multiscale metallic targets, a DDM scheme is further developed to employ a discontinuous Galerkin (DG) approach to glue conformal/nonconformal surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution, and half edge-based HOHV basis functions are introduced to model the current associated with nonconformal surface elements. Meanwhile, the basis expansion and recombination (BER) technique is introduced to significantly accelerate the matrix-filling and improve the efficiency. The flexibility of basis order selection is further enhanced by the hierarchical characteristic of HOHV bases. Finally, several numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of the proposed HO-DG-DDM. [ABSTRACT FROM AUTHOR]

In this communication, we present flexible and efficient solutions of large-scale electromagnetic scattering problems using the parallel discontinuous Galerkin (DG) surface integral equation (SIE) method. A simplified formulation of the conventional DG is used by removing the interior penalty term, thereby avoiding computational burden of the contour integral in the conventional DG. It is demonstrated numerically that the simplification causes convergence deficiency and changes the accuracy convergence rate of the solution for objects with sharp corners. The former is overcome by constructing preconditioners using the near-field matrix of the whole region, and the latter is proved to have a neglectable influence on the accuracy of the final solutions as long as normal mesh density requirement is satisfied. The wellscaling ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is incorporated into the DG domain decomposition framework to reduce the complexity of the solution and strength its capability for large-scale problems, with the distribution of the nearfield-related calculation adjusted to adapt the nonuniform meshes for a better workload balance. Numerical results are included to validate the accuracy and demonstrate the scalability and versatility of the proposed method. In addition, we demonstrated the effectiveness of our algorithm by solving a high-definition complicated aircraft model with inlets and exhausts involving over one billion unknowns. [ABSTRACT FROM AUTHOR]

A nonconformal and nonoverlapping domain decomposition method (DDM) based on hybrid volume and surface integral equation (VSIE) is presented for modeling complex thin dielectric/perfect electric conductor (PEC) composite targets. To reduce the unknown amount of the conventional volume integral equation (VIE) for thin dielectric bulks, the improved simplified prism vector (ISPV) basis function is developed. By using the basis function, the volume integrals can be simplified into surface integrals or line integrals, which significantly reduce the simulation time. Prism grids can also avoid the overmeshing problem for thin dielectrics. Moreover, they can be perfectly matched to the triangular meshes widely used in surface integral equation (SIE) hence assures a simple and robust VSIE implementation. Next, in order to increase the flexibility of geometrical modeling and accelerate the convergence of the presented VSIE system for electrically large and multiscale composite targets, a DDM is further developed. In this DDM scheme, discontinuous Galerkin approaches are, respectively, employed for VIE and SIE, accounting for conformal/nonconformal volume grids and surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution. Finally, some numerical results are considered and analyzed to show the validity, efficiency, and applicability of the presented scheme. [ABSTRACT FROM AUTHOR]

A time-domain discontinuous Galerkin Poggio–Miller–Chang–Harrington–Wu integral equation method, which is based on marching-on-in-degree (MOD) scheme, is proposed to simulate electromagnetic pulse (EMP) responses of arbitrarily shaped dielectric objects, where half Rao–Wilton–Glisson basis functions are chosen as the spatial basis ones. Both electric and magnetic current continuities between adjacent elements are guaranteed by introducing additional interior penalty terms. Therefore, three-dimensional dielectric structures with either conformal or nonconformal meshes can be treated. Meanwhile, the weighted Laguerre polynomials are chosen as the temporal basis functions and implemented for the MOD scheme, and stable EMP responses can be captured. Since our method is based on the surface integral equation with the objects’ surface meshed, the number of unknowns are significantly reduced in comparison with that of the volume integral equation method. Some numerical examples are presented to validate both stability and accuracy of the developed algorithm. [ABSTRACT FROM AUTHOR]

A discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree (MOD) scheme for simulating transient responses of perfect electric conductor objects is proposed in this letter. With the help of half-Rao–Wilton–Glisson spatial basis functions, we can simulate transient scattering responses of three-dimensional structures with either conformal or nonconformal meshes. The weighted Laguerre polynomials are chosen as temporal basis functions and implemented for the MOD scheme. Under such circumstances, the developed algorithm eliminates late-time instabilities and the limitation of Courant–Friedrichs–Lewy criteria. In addition, we adopt a fast-Fourier-transform-based blocking scheme to accelerate the temporal convolution of the MOD procedure. Some numerical examples are given to validate its stability and accuracy. [ABSTRACT FROM AUTHOR]

A discontinuous Galerkin (DG) augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full-wave solution of multiscale targets. The conventional surface integral equation-based DG method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low-frequency breakdown. By augmenting the DG-EFIE with current continuity equation, the proposed scheme can alleviate the low-frequency breakdown. In the augmented system, the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including Rao–Wilton–Glisson (RWG) and half RWG basis functions. Since the half RWG basis is not divergence conforming, line charge degrees of freedom on the adjoining edges are introduced in this paper. It is observed that the resulting linear system is well conditioned at low frequencies, which leads to a rapid convergence over wide frequency band. Numerical examples demonstrate the accuracy and efficiency of the augmented system. [ABSTRACT FROM AUTHOR]