# A perfectly matched layer for the absorption of electromagnetic waves

01 Oct 1994-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 114, Iss: 2, pp 185-200

TL;DR: Numerical experiments and numerical comparisons show that the PML technique works better than the others in all cases; using it allows to obtain a higher accuracy in some problems and a release of computational requirements in some others.

About: This article is published in Journal of Computational Physics.The article was published on 1994-10-01. It has received 9875 citations till now. The article focuses on the topics: Perfectly matched layer.

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TL;DR: This work shows how electromagnetic fields can be redirected at will and proposes a design strategy that has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

Abstract: Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields-electric displacement field D, magnetic induction field B, and Poynting vector B-are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

7,811 citations

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01 Jan 2002TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.

Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

5,791 citations

### Additional excerpts

...See, for example, [1], [21], [28], [117], [123], [176], [197], [230]....

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TL;DR: This work fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%.

Abstract: We present the design for an absorbing metamaterial (MM) with near unity absorbance A(omega). Our structure consists of two MM resonators that couple separately to electric and magnetic fields so as to absorb all incident radiation within a single unit cell layer. We fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%. Unlike conventional absorbers, our MM consists solely of metallic elements. The substrate can therefore be optimized for other parameters of interest. We experimentally demonstrate a peak A(omega) greater than 88% at 11.5 GHz.

5,550 citations

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TL;DR: A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates that allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies.

Abstract: A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.

1,660 citations

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TL;DR: By comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces and the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.

Abstract: A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.

1,629 citations

### Cites background from "A perfectly matched layer for the a..."

...This wave wrapping can be avoided by implementing an absorbing boundary condition known as a perfectly matched layer sPMLd.(27,28) This is a thin absorbing layer that encloses the computational domain and is governed by a nonphysical set of equations, causing anisotropic attenuation....

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##### References

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Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.

14,070 citations

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TL;DR: This work develops a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries that not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.

Abstract: In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries. These boundary conditions not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.

2,648 citations

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TL;DR: In this paper, highly absorbing boundary conditions for two-dimensional time-domain electromagnetic field equations are presented for both two-and three-dimensional configurations and numerical results are given that clearly exhibit the accuracy and limits of applicability of these boundary conditions.

Abstract: When time-domain electromagnetic-field equations are solved using finite-difference techniques in unbounded space, there must be a method limiting the domain in which the field is computed. This is achieved by truncating the mesh and using absorbing boundary conditions at its artificial boundaries to simulate the unbounded surroundings. This paper presents highly absorbing boundary conditions for electromagnetic-field equations that can be used for both two-and three-dimensional configurations. Numerical results are given that clearly exhibit the accuracy and limits of applicability of highly absorbing boundary conditions. A simplified, but equally accurate, absorbing condition is derived for two- dimensional time-domain electromagnetic-field problems.

2,553 citations

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TL;DR: In this article, a finite-difference time-domain (FD-TD) method is proposed to compute the near total fields within a rectangular volume which fully encloses the object and then an electromagnetic-field equivalence principle is invoked at a virtual surface of this rectangular volume to transform the tangential near scattered fields to the far field.

Abstract: The finite-difference time-domain (FD-TD) method is proposed as a means of accurately computing electromagnetic scattering by arbitrary-shaped extremely complex metal or dielectric objects excited by an external plane wave. In the proposed method, one first uses the FD-TD method to compute the near total fields within a rectangular volume which fully encloses the object. Then, an electromagnetic-field equivalence principle is invoked at a virtual surface of this rectangular volume to transform the tangential near scattered fields to the far field. To verify the feasibility of this method, the surface currents, near scattered fields, far scattered fields, and radar cross section of two canonical two-dimensional objects are presented. For these cases, it is shown that the FD-TD method provides magnitude of current and field predictions which are within ± 2.5 percent and further phase values within ± 30 of values predicted by the method of moments ( MOM) at virtually every point including in shadow regions.

513 citations

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TL;DR: In this paper, a theorie des approximations par differences des conditions aux limites absorbantes for l'equation d'ondes scalaire a plusieurs dimensions d'espace is proposed.

Abstract: On developpe une theorie des approximations par differences des conditions aux limites absorbantes pour l'equation d'ondes scalaire a plusieurs dimensions d'espace

487 citations