Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation

Kuzuoğlu, Mustafa; Mittra, R.

doi:10.1109/8.558662

Cited by 97 publications

(44 citation statements)

References 26 publications

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“…For PML-based methods the error is controlled by the functional form of the complex coordinate mapping (the absorbing function), the thickness of the layer that surrounds the computational domain, and the number of elements used to discretise it. Unfortunately, the optimisation of these parameters in order to obtain the best numerical solution for a given computational effort is non-trivial and often highly problem-dependent [18,20,21,22,23,24]. Recently, Bermúdez et al [25] proposed a novel unbounded absorbing function which ensures that (in the continuous setting) spurious reflections off the boundary of the computational domain are completely suppressed for planar waves governed by the 2D Helmholtz equation.…”

Section: Introductionmentioning

confidence: 99%

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Cimpeanu

Martinsson

Heil

2015

Journal of Computational Physics

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This paper presents a parameter-free perfectly matched layer (PML) method for the finite-element-based solution of the Helmholtz equation. We employ one of Bermúdez et al.'s unbounded absorbing functions for the complex coordinate mapping underlying the PML. With this choice, the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost (characterised by the number of elements in the bulk and the PML regions) is the thickness of the perfectly matched layer, δ PML . We show that, for the case of planar waves, the absorbing function performs best for PMLs whose thickness is much smaller than the wavelength. We then perform extensive numerical experiments to explore its performance for non-planar waves, considering domain shapes with smooth and polygonal boundaries, different solution types (smooth and singular), and a wide range of wavenumbers, k, to identify an optimal range for the normalised PML thickness, kδ PML , such that, within this range, the error introduced by the presence of the PML is consistently small and insensitive to change. This implies that if the PML thickness is chosen from within this range * Corresponding author URL: http://www3.imperial.ac.uk/people/radu.cimpeanu11 (Radu Cimpeanu), http://www.maths.manchester.ac.uk/~mheil/ (Matthias Heil) Preprint submitted to Journal of Computational PhysicsMay 4, 2015 no further PML optimisation is required, i.e. the method is parameter-free. We characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh.

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Section: Introductionmentioning

confidence: 99%

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Cimpeanu

Martinsson

Heil

2015

Journal of Computational Physics

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“…The amount of reflection in this case depends on the conductivity contrast between adjacent strips and increases for larger contrasts (an analogous issue exists for a ρ as well as for PML models on discrete grids [22]). To minimize reflections, it is therefore desirable to adopt a tapered profile for σ ρ ðρÞ, such as σ ρ ðρÞ ¼ ðσ 0 =ϵ 0 Þ× jðρ − ρ 0 Þ=δj p , where σ 0 is the maximum value of the conductivity (in siemens per meter), ϵ is the vacuum permittivity (in farads per meter), δ is the overall absorber thickness, and p represents the degree of the taper [16,19].…”

Section: B Simulations and Backscattering Resultsmentioning

confidence: 99%

“…However, unlike the planar case [Eq, (1)], the resulting medium ceases to be reflectionless, with a reflection coefficient that now depends on the radius of curvature [16]. A truly reflectionless media in a cylindrical surface entails applying a transformation on the radial coordinate ρ (and not simply on the radial metric element) [14].…”

Section: Metamaterials Blueprints For Reflectionless Absorbersmentioning

confidence: 99%

Impedance-matched absorbers and optical pseudo black holes

2011

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We investigate the design of metamaterial blueprints for impedance-matched (reflectionless) absorbers over nonplanar surfaces in connection with optical pseudo black holes. The presence of some fundamental constraints on the existence of reflectionless absorber media at nonplanar surfaces are discussed based on analytical properties of the associated constitutive tensors on the complex ω (angular frequency) plane. In view of such constraints, some new metamaterial blueprints of near-reflectionless absorbers are suggested for integration into optical pseudo black hole devices.

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“…Moreover, the method can be easily extended to 3-D problems. Here we consider the PML formulation in the stretched coordinate space [5] for the 2-D problem. Inside the PML, the fields and satisfy the following modified Maxwell's equations in the frequency domain (1) where is the electric field and is the magnetic flux density in the frequency domain, is a tensor given in Cartesian coordinate by and , are the stretched-coordinate metrics which are defined as (2) In the above equation, is the conductivity, is assumed to be positive real, and is real and 1.…”

Section: Formulationmentioning

confidence: 99%

“…PMLs are often used to implement absorbing boundary conditions (ABCs) in the finite-difference time-domain (FDTD) [1]- [3] and finite-element frequency-domain (FEFD) [4], [5] methods for simulating open-region wave propagation problems. Recently, a PML scheme to truncate finite-element time-domain (FETD) meshes for analyzing 2-D [6] and generally for 3-D [7], [8] open-region electromagnetic scattering and radiation problems has been developed.…”

Section: T He Perfectly Matched Layer (Pml) Introduced Bymentioning

confidence: 99%

Optimization of the Perfectly Matched Layer for the Finite-Element Time-Domain Method

Movahhedi

Abdipour

Ceric

et al. 2007

IEEE Microw. Wireless Compon. Lett.

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Abstract-We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in 2-D vector finite-element time-domain method directly applied to Maxwell's equations. It is shown that the proposed method is highly absorptive to evanescent modes when computing the wave interaction of elongated structures or sharp corners. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived.Index Terms-Absorbing boundary conditions (ABC), finiteelement time-domain (FETD) method, Maxwell's equations, perfectly matched layer (PML).

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Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation

Cited by 97 publications

References 26 publications

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Impedance-matched absorbers and optical pseudo black holes

Optimization of the Perfectly Matched Layer for the Finite-Element Time-Domain Method

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