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A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

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Chinese Physics B 2014年第12期23卷 166-176页

作者：刘亚文陈亦望张品刘宗信 National Key Laboratory on Electromagnetic Environment and Electro-optical Engineering PLA University of Science and Technology

A higher-order finite-difference time-domain（HO-FDTD） in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain（FDTD） and the multiresolution time-domain（MRTD） schemes with respect to memory requirements and CPU time. Moreover, the Berenger＇s perfectly matched layer（PML） is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.

关键词： higher-order finite-difference time-domain spherical coordinates stability numerical dispersion perfectly matched layer

A Well-Posed and Discretely Stable perfectly matched layer for Elastic Wave Equations in Second Order Formulation

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Communications in Computational Physics 2012年第5期11卷 1643-1672页

作者： Kenneth Duru Gunilla Kreiss Division of Scientific Computing Department of Information TechnologyUppsala UniversityBox 337SE-75105 UppsalaSweden

We present a well-posed and discretely stable perfectly matched layer for the anisotropic(and isotropic)elastic wave equations without first re-writing the governing equations as a first order *** new model is derived by the complex coordinate stretching *** standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensures the decay of eigen-modes for all relevant *** buttress the stability properties and the robustness of the proposed model,numerical experiments are presented for anisotropic elastic wave *** model is approximated with a stable node-centered finite difference scheme that is second order accurate both in time and space.

关键词： perfectly matched layer well-posedness stability hyperbolicity elastic waves

An Optimized perfectly matched layer for the Schrödinger Equation

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Communications in Computational Physics 2011年第1期9卷 147-179页

作者： Anna Nissen Gunilla Kreiss Department of Information Technology Uppsala UniversityP.O.Box 337SE-75105 UppsalaSweden.

We derive a perfectly matched layer(PML)for the Schrödinger equation using a modal *** derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is *** computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case,with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.

关键词： Schrödinger equation perfectly matched layer

Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

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Acta Seismologica Sinica(English Edition) 2007年第6期20卷 684-695页

作者：李宁谢礼立翟长海 School of Civil Engineering Harbin Institute of Technology

The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.

关键词： perfectly matched layer multi-transmitting formula, elastodynamic wave, artificial boundary,hybrid finite element

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Finite Element Analysis in Combination with perfectly matched layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials

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Applied Mathematics 2013年第5期4卷 64-71页

作者： Dbich Karim Sylvain Ballandras Thierry Laroche Karl Wagner Jean-Michel Brice Xavier Perois TDK Sophia AntipolisFrance Institut Femto-st BesanconFrance TDK MunichGermany

The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The perfectly matched layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators.

关键词： Finite Element Method perfectly matched layer Surface Acoustic Wave Piezoelcetric Numerical Modeling

Analysis and FDTD Simulation of a perfectly matched layer for the Drude Metamaterial

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Annals of Applied Mathematics 2022年第2期38卷 159-182页

作者： Jichun Li Li Zhu Department of Mathematical Sciences University of Nevada Las VegasNevada 89154-4020USA

In this paper,we are concerned about the stability analysis for a perfectly matched layer(PML)recently developed by Becache et al.[5]for simulating wave propagation in the Drude *** PML is proved to be stable originally in[6]through a modal *** we establish its stability by the energy method.A FDTD scheme is developed and *** simulations illustrate the stability of the PML model and its effectiveness in absorbing outgoing waves in the Drude medium.

关键词： Maxwell’s equations perfectly matched layer FDTD method

perfectlymatched layer withMixed Spectral Elements for the Propagation of LinearizedWaterWaves

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Communications in Computational Physics 2012年第2期11卷 285-302页

作者： Gary Cohen Sebastien Imperiale INRIA Domaine de VoluceauRocquencourt-BP 10578153 Le Chesnay CedexFrance

After setting a mixed formulation for the propagation of linearized water waves problem,we define its spectral element ***,in order to take into account unbounded domains,we construct absorbing perfectly matched layer for the *** approximate these perfectly matched layer by mixed spectral elements and show their stability using the“frozen coefficient”***,numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions.

关键词： Linearized water waves perfectly matched layer mixed finite elements

Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by perfectly matched layers

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Numerical Mathematics(Theory,Methods and Applications) 2022年第2期15卷 387-414页

作者： Yu Du Jiwei Zhang Department of Mathematics Xiangtan UniversityHunan 411105China School of Mathematics and Statistics Hubei Key Laboratory of Computational ScienceWuhan UniversityWuhan 430072China

We consider the computation of a nonlocal Helmholtz equation by using perfectly matched layer(PML).We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal operator of integral *** that,we give stability estimates of some weighted-average values of the nonlocal Helmholtz solution and prove that(i)the weighted-average value of the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the weighted-average value of the nonlocal Helmholtz solution itself decays exponentially outside some *** for a typical kernel functionγ_(1)(s)=1/2 e^(−|s|),we obtain the Green’s function of the nonlocal Helmholtz equation,and use the Green’s function to further prove that(i)the nonlocal PML solution decays exponentially in PML layers in one case;(ii)in the other case,the nonlocal Helmholtz solution itself decays exponentially outside some *** on our theoretical analysis,the truncated nonlocal problems are discussed and an asymptotic compatibility scheme is also introduced to solve the resulting truncated ***,numerical examples are provided to verify the effectiveness and validation of our nonlocal PML strategy and theoretical findings.

关键词： Nonlocal wave propagation Helmholtz equation perfectly matched layer asymptotic compatibility scheme Green’s function

Stability of perfectly matched layers for Time Fractional Schrödinger Equation

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Engineering（科研） 2023年第1期15卷 1-12页

作者： Tingting Zhang Xiangkun Li School of Mathematics and Statistics Shandong Normal University Jinan China

It is an important issue to numerically solve the time fractional Schrödinger equation on unbounded domains, which models the dynamics of optical solitons propagating via optical fibers. The perfectly matched layer approach is applied to truncate the unbounded physical domain, and obtain an initial boundary value problem on a bounded computational domain, which can be efficiently solved by the finite difference method. The stability of the reduced initial boundary value problem is rigorously analyzed. Some numerical results are presented to illustrate the accuracy and feasibility of the perfectly matched layer approach. According to these examples, the absorption parameters and the width of the absorption layer will affect the absorption effect. The larger the absorption width, the better the absorption effect. There is an optimal absorption parameter, the absorption effect is the best.

关键词： Time Fractional Schrödinger Equation perfectly matched layer Stability