Multilevel Methods for $p$-Adaptive Finite Element Analysis of Electromagnetic Scattering

Aghabarati, Ali; Webb, J.P.

doi:10.1109/tap.2013.2277713

Cited by 11 publications

(2 citation statements)

References 30 publications

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“…Although only one DDM has been tested, it is likely that ASP/AMG could be used with other DDMs, including those that permit non-matching meshes. Another development under consideration is the extension of the method to higher order, hierarchical elements by incorporating -type multiplicative Schwartz methods [21].…”

Section: Discussionmentioning

confidence: 99%

Algebraic Multigrid Combined With Domain Decomposition for the Finite Element Analysis of Large Scattering Problems

Aghabarati

Webb

2015

IEEE Trans. Antennas Propagat.

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In the finite element analysis of electromagnetic scattering, a recent algebraic multigrid method (Aghabarati and Webb, "An Algebraic Multigrid Method for the Finite Element Analysis of Large Scattering Problems," IEEE Trans. Antennas Propag., vol. 61, no, 2, pp. 809-817, Feb. 2013) has been shown to be an efficient way to solve the large, sparse matrix equation. However, the effectiveness of the method decreases as the electrical size of the problem increases. This limitation is overcome by combining it with a domain decomposition method (DDM). Exact solution on each domain is not needed: a single W-cycle of the multigrid method is sufficient. Results are presented for scattering of plane waves by conducting and dielectric objects, with dimensions ranging from 3 wavelengths to 20 wavelengths.Index Terms-Finite element analysis, iterative methods, microwave propagation, multigrid methods, sparse matrices.

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Section: Discussionmentioning

confidence: 99%

Algebraic Multigrid Combined With Domain Decomposition for the Finite Element Analysis of Large Scattering Problems

Aghabarati

Webb

2015

IEEE Trans. Antennas Propagat.

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“…The smoother in the V cycle is realized by some simple stationary method, e.g., a symmetric Gauss-Seidel iteration. Details are given in [9] and [10], see [11] for a recent improvement.…”

Section: Prototype Iterative Solvermentioning

confidence: 99%

A New Low-Frequency Stable Potential Formulation for the Finite-Element Simulation of Electromagnetic Fields

2015

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The finite-element formulation proposed in this paper is for the frequency domain and covers the entire range from static/stationary fields to wave propagation. It does not involve any frequency-dependent thresholds, leads to complex symmetric system matrices and unique solutions, and applies to the most general structures, comprising both lossy and lossless regions. Compared with non-stabilized methods, e.g., the electric field formulation, the price to be paid is one extra scalar potential in the lossy region. Numerical examples demonstrate that the proposed method is well-suited for direct and iterative solvers, and remains stable in the static case.Index Terms-Electromagnetic fields, finite-element (FE) method, low-frequency (LF) stable, Maxwell equations, potential formulation.

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Progress in frequency selective surface-based smart electromagnetic structures: A critical review

Panwar

Lee

2017

Aerospace Science and Technology

172

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Multilevel Methods for $p$-Adaptive Finite Element Analysis of Electromagnetic Scattering

Cited by 11 publications

References 30 publications

Algebraic Multigrid Combined With Domain Decomposition for the Finite Element Analysis of Large Scattering Problems

Algebraic Multigrid Combined With Domain Decomposition for the Finite Element Analysis of Large Scattering Problems

A New Low-Frequency Stable Potential Formulation for the Finite-Element Simulation of Electromagnetic Fields

Progress in frequency selective surface-based smart electromagnetic structures: A critical review

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