On the Accuracy of Spectral Element Method in Electromagnetic Scattering Problems

Abstract

Abstract-Spectral element method (SEM), which is known of its high accuracy, has been recently applied in solving electromagnetic problems governed by Maxwell's equations. This paper investigates the accuracy of SEM in twodimensional, frequency-domain electromagnetic scattering problems where Helmholtz equation acts as the governing partial differential equation (PDE). As experience in meshing a problem in finite element method is important to obtain accurate results, the choice of elements in SEM, on the other hand, is important too. The aspect ratio in this paper is taken into account while studying the accuracy in a single element by utilizing the Green's function. In addition, the scalar field scattered by a circular cylinder placed in front of an incident plane wave is solved after truncating the domain by perfectly matched layer. Numerical results show that one should carefully discretize the problem and keeping the aspect ratio close to unity as much as possible to guarantee accurate results.Index Terms-Aspect ratio, electromagnetic scattering, PML SEM. I. INTRODUCTIONIt is more an art experience than a science to know how to optimally place and size the mesh in finite element method (FEM). In fact, experience taught us to have more elements in the physical domain where functions change rapidly and less elements where low gradient is expected. Mesh generation may take several trials before achieving a good mesh [1]. On the other hand, the complexity in the physical domain itself may add additional limitations to mesh generation.In FEM, ranges of the aspect ratio have been investigated extensively and for wide variety of problems. As an example, but not restricted to, M. Picasso [2] proposed an adaptive algorithm for solving the Strokes problem with finite elements and meshes with high aspect ratio. In that paper, the effect of aspect ratio on the results is discussed in details and some examples were illustrated for a non-acceptable mesh that can deteriorate accuracy. V. Prachittham et al. [3] presented a two-dimensional adaptive method with large aspect ratio finite elements for the numerical simulation of mixed electroosmotic microflows. In their work, the refinement/ coarsening criterion is based on a posteriori error estimates. On the other side, spectral element method (SEM) which is known for its high degree of accuracy and lower CPU time and less memory requirement, when compared Manuscript received December 20, 2013; revised March 20, 2014 with other numerical methods, has the flexibility of using larger elemental aspect ratio without significant deterioration in accuracy. S. Dong et al. [4] proposed a parallel SEM for dynamic three-dimensional nonlinear elasticity problems that provides a tolerant large elemental aspect ratio employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics. D. Rh. Gwynllyw et al. [5] proposed an iterative method for moving SEM applied to the journal bearing problem where they inve...

On the application of the spectral element method in electromagnetic problems involving domain decomposition

“…One is scattering type and the other is radiating type. The utilized numerical method in this study is SEM, which is known for its high accuracy [11,33,[36][37][38][39][40][41]. It is important to note that the proposed technique is not restricted to SEM as the finite difference method (FDM) or FEM can also be utilized.…”

“…The PML region is discretized into rectangular elements so that each element has an aspect ratio close to unity in order to reduce the deterioration in the accuracy due to elemental deformation [38]. For GLL grids, the optimum values of the attenuation factor α recommended in [11] are utilized in this work.…”

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

“…Inspired by the concepts of "perfectly matched layer" and "domain truncation" in SEM, the position at a tenth of the outer radius of PM is defined as the zero SMP [20,21]. Such a selection method can not only guarantee that MF is fully calculated, but also saves a lot of computation time and cost [22].…”

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“…Besides a significant work is done in literature where many numerical approximation schemes like finite element method (FEM), finite difference method (FDM), and spectral element method (SEM) are developed. Among these, SEM is found to have more accuracy and less computational cost [15][16][17][18]. SEM could be used for simulations related to wireless relay networks or waveguides.…”