Efficient Implementation of the UPML in the Generalized Finite-Difference Time-Domain Method

Bernard, Laurent; Torrado, Ruben Rodriguez; Pichon, Lionel

doi:10.1109/tmag.2010.2045357

Cited by 14 publications

(7 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mechanism of LSTM is based on the following equations (2)- (8). The specific computation process within equations (2)-(8) is as follows: the initial state and the sequence in the first time step is used to calculate the first output and update the cell states.…”

Section: (B)mentioning

confidence: 99%

“…The important sequence information is involved in the cell state. For each time step t, the layer 'store' or 'forget' information from the cell state [24]- [30], as described in the equations (2)- (8). step t, while denotes the Hadamard product.…”

Section: (B)mentioning

confidence: 99%

“…Perfectly matched layer (PML), as the most widely-used ABC, has been developed in various application scenarios, thanks to its high tolerance to frequency and its excellent absorption capability over a broad scope of angles [4], [5]. Also, PML has been widely reported in various application of electromagnetic modeling, including convolutional PML (CPML) [6] and uniaxial PML (UPML) [7], [8]. But, the PML size has to be augmented to decrease the residue error for better absorption performance over wide range angles and broad frequency band.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enhanced PML Based on the Long Short Term Memory Network for the FDTD Method

Yao

Jiang

2020

IEEE Access

View full text Add to dashboard Cite

This paper proposes a new absorbing boundary condition (ABC) computation approach based on the deep learning technique. Benefited from the sequence dependence feature, the Long Short-Term Memory (LSTM) network is employed to replace the conventional perfectly matched layer (PML) ABC for the Finite-Difference Time-Domain (FDTD) solving process. The newly proposed LSTM based PML model is trained by the electromagnetic field data on the interface of the conventional PML. Different from the conventional PML, the newly proposed model only needs one cell layer as the boundary. Hence, the newly proposed method conveniently reduces both the algorithm's complexity and the area of computation domain of FDTD. Additionally, the newly proposed LSTM based PML model can achieve higher accuracy than the conventional artificial neural network (ANN) based PML, thanks to the sequence dependence feature of the LSTM networks. Numerical examples have illustrated the capability and the accuracy of the proposed LSTM model. The results illustrate that the new method can be compatibly embedded into the FDTD solving process with the high accuracy.

show abstract

Section: (B)mentioning

confidence: 99%

Section: (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Enhanced PML Based on the Long Short Term Memory Network for the FDTD Method

Yao

Jiang

2020

IEEE Access

View full text Add to dashboard Cite

show abstract

“…For such problems, and especially for FDTD method, an absorbing boundary condition (ABC) should be used with the aim to complete the interior numerical scheme and to simulate the expression of the lattice to infinity. The perfect matched layer (PML) introduced by Bérenger is a effective ABC to terminate domains employing free space, lossy, dispersive, inhomogeneous, anisotropic, and nonlinear media . In particular, the innovation of the PML is that plane waves of arbitrary incidence, polarization, and frequency are matched at the boundary.…”

Section: Fdtd Dispersive Modelingmentioning

confidence: 99%

“…The perfect matched layer (PML) introduced by B erenger is a effective ABC to terminate domains employing free space, lossy, dispersive, status solidi physica a www.advancedsciencenews.com www.pss-a.com inhomogeneous, anisotropic, and nonlinear media. [85][86][87] In particular, the innovation of the PML is that plane waves of arbitrary incidence, polarization, and frequency are matched at the boundary. Lots of papers appeared to validate PML technique and among the various implementations of PMLs the uniaxial anisotropic PML (UPML), presented by Gedney, [88] appears very attractive in view of the fact that Maxwell's equations maintain their familiar physical form as well as its application to the FDTD method is more computationally efficient and ideal for parallel computation.…”

Section: Upml Boundary Conditionsmentioning

confidence: 99%

Fractional‐Calculus‐Based Electromagnetic Tool to Study Pulse Propagation in Arbitrary Dispersive Dielectrics

Mescia

Bia

Caratelli

2018

Physica Status Solidi (a)

View full text Add to dashboard Cite

Fractional calculus is a fruitful field of research in science and engineering. The concept of fractional exponents is an outgrowth of exponents with integer value. In the same way, fractional order of integration is a generalization of the mathematical operations of differentiation and integration to arbitrary, general, noninteger order. Although it better models the higher complexity by nature, it is still fairly easy to physically represent its meaning. However, taking in consideration that the study of fractional calculus theory opens the mind to entirely new branches of thought, in this feature article the authors illustrate as such concept can be an interesting and useful tools in electromagnetic theory to solve specific electromagnetic problems regarding the wave propagation and radiation in arbitrary dispersive dielectric materials. In particular, time fractional Maxwell's equations for media with power‐law frequency dispersions are illustrated focusing the attention on the mathematical and computational topics. Moreover, practical examples highlighting their usefulness for understanding a variety of electromagnetic phenomena are provided.

show abstract

Implementation of uniaxial perfectly matched layer based on hexahedron element in discontinuous Galerkin time domain

Xiao

Wei

2021

IET Microwaves Antenna & Prop

View full text Add to dashboard Cite

The uniaxial perfectly matched layer (UPML), an important link in the numerical calculation of the discontinuous Galerkin time domain (DGTD), truncates the size of the computational domain and absorbs the outward-travelling waves. In traditional DGTD, tetrahedral meshes are used to divide the computational domain. These meshes are also used in UPML. As the scope of the computational domain is wide, many meshes will be generated after the UPML division wraps the external part of the domain, thereby resulting in inefficient computation. The use of a UPML in DGTD form based on hexahedral meshes is proposed. The internal propagation and UPML regions are divided by a tetrahedral element and a hexahedral element, respectively. Among the relevant numerical examples given, a few cases are analysed to demonstrate the feasibility of the proposed method: the high efficiency of the UPML with hexahedral mesh, attenuation of electromagnetic waves inside the UPML, and relative error of the electric field values at the observation points.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

show abstract

Efficient Implementation of the UPML in the Generalized Finite-Difference Time-Domain Method

Cited by 14 publications

References 4 publications

Enhanced PML Based on the Long Short Term Memory Network for the FDTD Method

Enhanced PML Based on the Long Short Term Memory Network for the FDTD Method

Fractional‐Calculus‐Based Electromagnetic Tool to Study Pulse Propagation in Arbitrary Dispersive Dielectrics

Implementation of uniaxial perfectly matched layer based on hexahedron element in discontinuous Galerkin time domain

Contact Info

Product

Resources

About