Conference Paper

Progress on radiation boundary conditions for electromagnetic finite element analysis

Univ. Stellenbosch, Matieland
DOI: 10.1109/ICEAA.2007.4387463 Conference: Electromagnetics in Advanced Applications, 2007. ICEAA 2007. International Conference on
Source: IEEE Xplore

ABSTRACT Recent progress on three types of radiation boundary conditions (RBCs) for the finite element method (FEM) is presented. The following RBCs are discussed: a rigorous implementation of the 2nd order Bayliss-Turkel type for vector FEM; an implementation of a spherical perfectly matched layer (PML); and infinite elements. The performance of the 2nd order absorbing boundary condition (ABC) and the spherical PML are compared, both with each other and with the standard 1st order ABC. Implementation issues are addressed. Current work on infinite elements for terminating tetrahedral meshes is outlined.

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    ABSTRACT: The finite element method (FEM) is commonly used for electromagnetic radiation and scattering analysis. When an infinite, free space exterior domain needs to be incorporated into the method, a radiation boundary condition must be enforced. An approach which has received considerable attention, is to employ approximate conditions, known as absorbing boundary conditions (ABCs), that preserve the sparsity of the original FEM system upon discretization. In the case of time-harmonic analysis based on the vector wave equation in three dimensions, the symmetric, spherical Bayliss-Turkel-type ABCs of first- and second-orders are well-established. The second-order version is expected to be more accurate, however when using the standard curl-conforming approach to FEM discretization, an implementation difficulty is encountered, relating to successive derivatives being required of the nonconforming field components. This issue is addressed here by introducing a scheme where the nonconforming first-order derivatives are projected onto a suitably conforming auxiliary field, of which another derivative can then be taken instead. Additional computational costs are minimal and the scheme retains the symmetry of the standard formulation. Numerical results demonstrate the superior performance of the rigorously implemented second-order ABC over its first-order counterpart
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    ABSTRACT: The implementation and evaluation of a spherical perfectly matched layer (PML) within a Cartesian finite element method context using standard curl-conforming elements is presented in this paper. Results are compared to the long-standing 1st order absorbing boundary condition (ABC) and a new, rigorous implementation of a 2nd order ABC for curl-conforming elements. The 4 and 8 layer spherical PMLs are shown to offer very attractive levels of absorption, with reflections on the order of -60 to -70dB demonstrated. Numerical tests show that the guidelines for Cartesian PML absorbers, in terms of maximum conductivity, also carry over to the spherical PML. The 2nd order ABC is also shown to offer very good performance. Finally, coding issues for both the spherical PML and the analytical ABCs are briefly addressed
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