Zero reflection coefficient in discretized PML

Juntunen, J.; Kantartzis, Nikolaos V.; Tsiboukis, T.D.

doi:10.1109/7260.916328

Cited by 8 publications

(8 citation statements)

References 8 publications

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“…Assuming the collapsing stencil differencing scheme described in the previous paragraph, the discretized derivatives in the parabolic equation can be written (15) ( 16) where, because of the Dirichlet conditions, is the -element vector of field values in (11). The differencing coefficient matrices and are parametrized by the number of upper diagonals in the matrix representation of the interior scheme, , before collapse, and the overall order of the large-stencil family from which all the schemes are drawn.…”

Section: A System Evolution Equationsmentioning

confidence: 99%

“…The differencing coefficient matrices and are parametrized by the number of upper diagonals in the matrix representation of the interior scheme, , before collapse, and the overall order of the large-stencil family from which all the schemes are drawn. The next step in discretizing the right-hand side of the parabolic equation is to properly scale the derivatives created in (15) and (16) by their variable coefficients. Multiplication by a diagonal matrix with the appropriate coefficient values on the diagonal achieves this end.…”

Section: A System Evolution Equationsmentioning

confidence: 99%

“…The simplicity of small-stencil schemes is a benefit when analyzing their characteristics, but may hamper computational efficiency on implementation because of their poor dispersive performance. In the case of the FDTD method in electromagnetics, low-order simplicity has allowed the derivation of the analytic form of a discrete reflection coefficient [15] that accounts for the influence of both spatial discretization and the time-advance scheme. A similar result has been obtained for the parabolic equation [8] using second-order finite elements.…”

Section: Introductionmentioning

confidence: 99%

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Dispersive Waves and PML Performance for Large-Stencil Differencing in the Parabolic Equation

Keefe¹

2012

IEEE Trans. Antennas Propagat.

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The discrete reflection/absorption performance of perfectly matched layer (PML) boundary conditions is a function of the field discretization scheme throughout the computational domain and the form of the complex coordinate extension that characterizes the PML region. Most previous work analyzing PML reflection performance has assumed use of low-order (second-or fourth-), small-stencil (three-or five-point) spatial discretizations whose dispersion is poor outside a narrow low-wavenumber band. Large-stencil differencing schemes, regardless of order, are easily created with physically realistic, wide-band dispersive characteristics, but the effect their adoption has on PML performance has not been analyzed previously. In the context of a semi-discrete approximation to the parabolic/paraxial equation, this work derives the analytic form of the discrete PML reflection coefficient for an arbitrary-order/arbitrary-stencil interior differencing scheme coupled to an arbitrary-order/arbitrary-stencil PML region. This result is then used to show that the absorption performance of the PML regions is largely insensitive to changes in interior differencing. As a consequence, the benefits of superior dispersion characteristics provided by use of large-stencil differencing in the interior physical domain can be had without incurring discrete reflection penalties at the PML.Index Terms-Absorbing boundary condition, atmospheric propagation, finite difference methods, numerical dispersion, parabolic wave equation, perfectly matched layer.

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Section: A System Evolution Equationsmentioning

confidence: 99%

Section: A System Evolution Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dispersive Waves and PML Performance for Large-Stencil Differencing in the Parabolic Equation

Keefe¹

2012

IEEE Trans. Antennas Propagat.

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“…Through similar manipulations, one can obtain 8where , and . Next, (8) are combined together to yield (9) Analogously, (5) and (9) lead to (10) The magnetic-field time-marching formula, at , is (11) which, after some algebra, becomes…”

Section: Analysis Of the One-cell Uniaxial Pmlmentioning

confidence: 99%

“…Among them [6] and [7] develop a rigorous set of algorithms for the design of improved PMLs, whereas in [8], the absorber's governing reflection mechanism is thoroughly explored. Finally, in a recent paper [9], the Berenger's scheme is adequately optimized to yield zero reflection for isolated pairs of frequency and angles of incidence.…”

Section: Introductionmentioning

confidence: 99%

Performance optimization of the PML absorber in lossy media via closed-form expressions of the reflection coefficient

2003

Self Cite

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A robust closed-form expression of the reflection coefficient concerning the discrete uniaxial finite-difference time-domain/perfectly matched layer (FDTD/PML) for the termination of lossy materials is presented in this paper. The novel formulation introduces an advanced procedure in the optimized derivation of layer conductivities involving medium parameters, spatial or temporal increments, and excitation frequencies. Numerical results indicate that the proposed technique greatly diminishes artificial reflections and therefore achieves a significant accuracy.

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Perfectly matched layers for Maxwell’s equations in second order formulation

Sjögreen

Petersson

2005

Journal of Computational Physics

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We consider the two-dimensional MaxwellÕs equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ''small-cell'' time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the parameters of the PML can be chosen to make the discrete solution of the PML equations converge to the solution of MaxwellÕs equations on the unbounded domain, as the grid size goes to zero. Several numerical examples are given.

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Zero reflection coefficient in discretized PML

Cited by 8 publications

References 8 publications

Dispersive Waves and PML Performance for Large-Stencil Differencing in the Parabolic Equation

Dispersive Waves and PML Performance for Large-Stencil Differencing in the Parabolic Equation

Performance optimization of the PML absorber in lossy media via closed-form expressions of the reflection coefficient

Perfectly matched layers for Maxwell’s equations in second order formulation

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