Engineering › Electrical and Electronic Engineering

Electromagnetic Simulation and Numerical Methods

Works Count: 37367

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Description

This cluster of papers focuses on the development and analysis of Finite-Difference Time-Domain (FDTD) methods for simulating electromagnetic wave propagation. It includes research on Discontinuous Galerkin methods, Perfectly Matched Layers, stability and dispersion analysis, high-order schemes, and unconditionally stable algorithms for time-domain simulations of Maxwell's equations in complex media.

Keywords

Finite-Difference Time-Domain; Electromagnetics; Discontinuous Galerkin; Perfectly Matched Layer; Stability Analysis; Dispersion Analysis; High-Order Methods; Unconditionally Stable Schemes; Time-Domain Simulation; Maxwell's Equations

Computational Electromagnetics: The Finite-Difference Time-Domain Method

2005-01-01

Allen Taflove , Susan C. Hagness , M. Piket-May

Electromagnetic Simulation Using the FDTD Method

2000-01-01

Dennis M. Sullivan

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Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method

1998-01-01

Allen Taflove

A Survey of the Finite-Difference Time-Domain Literature, by Kurt L. Shlager, Lockheed-Martin Missiles and Space Company, Sunnyvale, CA and John B. Schneider, Washington State University. High-Order Methods, by Eli Turkel, … A Survey of the Finite-Difference Time-Domain Literature, by Kurt L. Shlager, Lockheed-Martin Missiles and Space Company, Sunnyvale, CA and John B. Schneider, Washington State University. High-Order Methods, by Eli Turkel, Tel Aviv University, Israel. Time-Domain Analysis Using Multiresolution Expansions, by Linda P. B. Katehi, University of Michigan, Ann Arbor James F. Harvey, U.S. Army Research Office, Research Triangle Park, NC and Emmanouil Tentzeris, Georgia Institute of Technology, Atlanta. Explicit Time-Domain Solutions of Maxwell's Equations via Generalized Grids, by Stephen D. Gedney, University of Kentucky, Lexington J. Alan Roden, Georgia Tech Research Institute, Atlanta Niel K. Madsen, Lawrence-Livermore National Laboratory, CA and Alireza H. Mohammadian, William F. Hall, Vijaya Shankar, and Christopher M. Rowell, Rockwell Science Center, Thousand Oaks, CA. The Perfectly Matched Layer Absorbing Medium, by Stephen D. Gedney, University of Kentucky, Lexington. Analysis of Periodic Structures, by James G. Maloney and Morris P. Kesler, Georgia Tech Research Institute, Atlanta. Modeling of Antennas, by James G. Maloney, Georgia Tech Research Institute, Atlanta and Glenn S. Smith, Georgia Institute of Technology, Atlanta. High-Speed Electronic Circuits with Active and Nonlinear Components, by Bijan Houshmand, Jet Propulsion Laboratory, CA Tatsuo Itoh, UCLA and Melinda Piket-May, University of Colorado, Boulder. Physics-Based Modeling of Millimeter-Wave Devices, by Samir M. El-Ghazaly, Arizona State University, Tempe. Microcavity Resonators, by Susan C. Hagness, University of Wisconsin, Madison. FDTD in Bioelectromagnetics: Safety Assessment and Medical Applications, by Om. P. Gandhi, University of Utah, Salt Lake City. Imaging and Inverse Problems, by Weng C. Chew, University of Illinois, Urbana-Champaign.

Numerical techniques for microwave and millimeter-wave passive structures

1989-01-01

T. Itoh

The Finite Element Method (J. Davies). Integral Equation Technique (J. Mosig). Planar Circuit Analysis (K. Gupta & M. Abouzahra). Spectral Domain Approach (T. Uwaro & T. Itoh). The Method of … The Finite Element Method (J. Davies). Integral Equation Technique (J. Mosig). Planar Circuit Analysis (K. Gupta & M. Abouzahra). Spectral Domain Approach (T. Uwaro & T. Itoh). The Method of Lines (R. Pregla & W. Pascher). The Waveguide Model for the Analysis of Microstrip Discontinuities (I. Wolff). The Transmission Line Matrix (TLM) Method (W. Hoefer). The Mode--Matching Method (Y. Shih). Generalized Scattering Matrix Technique (T. Itoh). Transverse Resonance Technique (R. Sorrentino). Index.

Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations

2003-01-01

Willem Hundsdorfer , J.G. Verwer

Absorbing boundaries for wave propagation problems

1986-04-01

Ronnie Kosloff , Dan Kosloff

An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation

2007-09-01

Dimitri Komatitsch , Roland Martin

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves … The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.

Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations

1981-11-01

Gerrit Mur

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 … 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.

A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

1994-09-01

Weng Cho Chew , William H. Weedon

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 … 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.

Non-reflecting boundary conditions

1991-05-01

Dan Givoli

A perfectly matched layer for the absorption of electromagnetic waves

1994-10-01

Jean-Pierre Bérenger

Nonreflecting boundary conditions for Euler equation calculations

1990-12-01

Michael B. Giles

We present a unified theory for the construction of steady-state and unsteady nonreflecting boundary conditions for the Euler equations. These allow calculatios to be performed on truncated domains without the … We present a unified theory for the construction of steady-state and unsteady nonreflecting boundary conditions for the Euler equations. These allow calculatios to be performed on truncated domains without the generation of spurious nonphysical reflections at the far-field boundaries.

An object-oriented electromagnetic PIC code

1995-05-01

John Verboncoeur , A. B. Langdon , N. T. Gladd

Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves

1996-09-01

Jean-Pierre Bérenger

Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

1981-06-01

A. Jameson , Wolfgang M. Schmidt , Eli Turkel

A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an … A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media

2001-01-01

Francis Collino , Chrysoula Tsogka

We present and analyze a perfectly matched, absorbing layer model for the velocity‐stress formulation of elastodynamics. The principal idea of this method consists of introducing an absorbing layer in which … We present and analyze a perfectly matched, absorbing layer model for the velocity‐stress formulation of elastodynamics. The principal idea of this method consists of introducing an absorbing layer in which we decompose each component of the unknown into two auxiliary components: a component orthogonal to the boundary and a component parallel to it. A system of equations governing these new unknowns then is constructed. A damping term finally is introduced for the component orthogonal to the boundary. This layer model has the property of generating no reflection at the interface between the free medium and the artificial absorbing medium. In practice, both the boundary condition introduced at the outer boundary of the layer and the dispersion resulting from the numerical scheme produce a small reflection which can be controlled even with very thin layers. As we will show with several experiments, this model gives very satisfactory results; namely, the reflection coefficient, even in the case of heterogeneous, anisotropic media, is about 1% for a layer thickness of five space discretization steps.

Nodal High-Order Methods on Unstructured Grids

2002-09-01

Jan S. Hesthaven , Tim Warburton

An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices

1996-12-01

Stephen D. Gedney

A perfectly matched layer (PML) absorbing material composed of a uniaxial anisotropic material is presented for the truncation of finite-difference time-domain (FDTD) lattices. It is shown that the uniaxial PML … A perfectly matched layer (PML) absorbing material composed of a uniaxial anisotropic material is presented for the truncation of finite-difference time-domain (FDTD) lattices. It is shown that the uniaxial PML material formulation is mathematically equivalent to the perfectly matched layer method published by Berenger (see J. Computat. Phys., Oct. 1994). However, unlike Berenger's technique, the uniaxial PML absorbing medium presented in this paper is based on a Maxwellian formulation. Numerical examples demonstrate that the FDTD implementation of the uniaxial PML medium is stable, equal in effectiveness as compared to Berenger's PML medium, while being more computationally efficient.

The Application of Preconditioning in Viscous Flows

1993-04-01

Yun-Jeong Choi , Charles Merkle

A comparison of different propagation schemes for the time dependent Schrödinger equation

1991-05-01

Claude Leforestier , Rob H. Bisseling , C. Cerjan +7 more

Radiation boundary conditions for acoustic and elastic wave calculations

1979-05-01

Björn Engquist , Andrew J. Majda

A Symmetrical Condensed Node for the TLM Method

1987-04-01

P.B. Johns

A new symmetrical condensed node is developed for the analysis of electromagnetic waves by the transmission-line modeling (TLM) method of numerical analysis.The new node has the advantage of condensing the … A new symmetrical condensed node is developed for the analysis of electromagnetic waves by the transmission-line modeling (TLM) method of numerical analysis.The new node has the advantage of condensing the field components to one point in space at the node and removes the disadvantage of asymmetry in existing condensed nodes.

The Transmission-Line Matrix Method--Theory and Applications

1985-10-01

W.J.R. Hoefer

This paper presents an overview of the transmission-line matrix (TLM) method of analysis, describing its historical background from Huygens's principle to modem computer formulations. The basic algorithm for simulating wave … This paper presents an overview of the transmission-line matrix (TLM) method of analysis, describing its historical background from Huygens's principle to modem computer formulations. The basic algorithm for simulating wave propagation in two- and three-dimensional transmission-live networks is derived. The introduction of boundaries, dielectric and magnetic materials, losses, and anisotropy are discussed in detail. Furthermore, the various sources of error and the limitations of the method are given, and methods for error correction or reduction, as well as improvements of numerical efficiency, are discussed. Finally, some typical applications to microwave problems are presented.

Numerical solution of partial differential equations by the finite element method

1988-10-01

Claes Johnson

Professor Johnson presents an easily accessible introduction to one of the most important methods used to solve partial differential equations. The bulk of the text focuses on linear problems, however … Professor Johnson presents an easily accessible introduction to one of the most important methods used to solve partial differential equations. The bulk of the text focuses on linear problems, however a chapter extending the development of non-linear problems is also included, as is one on finite element methods for integral equations. Throughout the text the author has included applications to important problems in mathematics and physics, and has endeavored to keep the mathematics as simple as possible while still presenting significant results.

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Radiation boundary conditions for wave‐like equations

1980-11-01

A. Bayliss , Eli Turkel

Abstract In the numerical computation of hyperbolic equations it is not practical to use infinite domains. Instead, one truncates the domain with an artificial boundary. In this study we construct … Abstract In the numerical computation of hyperbolic equations it is not practical to use infinite domains. Instead, one truncates the domain with an artificial boundary. In this study we construct a sequence of radiating boundary conditions for wave‐like equations. We prove that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O( r −m−1/2 ) for the m ‐th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature and utility of the boundary conditions.

Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions

1991-10-01

Philippe R. Spalart , Robert Moser , Michael M. Rogers

The application of high‐order differencing to the scalar wave equation

1986-01-01

M. A. Dablain

The second‐order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high‐order approximations … The second‐order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high‐order approximations for these derivatives. A one‐dimensional model is used to illustrate the relative accuracy of [Formula: see text] central‐difference schemes. For comparison, [Formula: see text] pseudospectral schemes are used as an additional measure of performance. The results indicate that [Formula: see text] differencing can achieve similar accuracy as the [Formula: see text] spectral scheme. For practical illustration, a two‐dimensional form of the [Formula: see text] algorithm is used to compute the exploding reflector response of a salt‐dome model and compared with a fine‐grid [Formula: see text] result. Transmissive sponge‐like boundary conditions are also examined and shown to be effective.

DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method

2007-06-14

Bálint Aradi , B. Hourahine , Thomas Frauenheim

A new Fortran 95 implementation of the DFTB (density functional-based tight binding) method has been developed, where the sparsity of the DFTB system of equations has been exploited. Conventional dense … A new Fortran 95 implementation of the DFTB (density functional-based tight binding) method has been developed, where the sparsity of the DFTB system of equations has been exploited. Conventional dense algebra is used only to evaluate the eigenproblems of the system and long-range Coulombic terms, but drop-in O(N) or O(N2) modules are planned to replace the small code sections that these entail. The developed sparse storage structure is discussed in detail, and a short overview of other features of the new code is given.

Time-Splitting Methods for Elastic Models Using Forward Time Schemes

2002-08-01

Louis J. Wicker , William C. Skamarock

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with … Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward–backward scheme for integrating high-frequency acoustic and gravity modes to create stable split-explicit schemes for integrating the compressible Navier–Stokes equations. The time-split methods facilitate the use of both centered and upwind-biased discretizations for the advection terms, allow for larger time steps, and produce more accurate solutions than existing approaches. The time-split Crowley scheme illustrates a methodology for combining any pure forward-in-time advection schemes with an explicit time-splitting method. Based on both linear and nonlinear tests, the third-order Runge–Kutta-based time-splitting scheme appears to offer the best combination of efficiency and simplicity for integrating compressible nonhydrostatic atmospheric models.

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A perfectly matched anisotropic absorber for use as an absorbing boundary condition

1995-01-01

Zachary S. Sacks , D.M. Kingsland , Robert Lee +1 more

An alternative formulation of the "perfectly matched layer" mesh truncation scheme is introduced. The present scheme is based on using a layer of diagonally anisotropic material to absorb outgoing waves … An alternative formulation of the "perfectly matched layer" mesh truncation scheme is introduced. The present scheme is based on using a layer of diagonally anisotropic material to absorb outgoing waves from the computation domain. The material properties can be chosen such that the interface between the absorbing material and free space is reflection-less for all frequencies, polarizations, and angles of incidence. This approach does not involve a modification of Maxwell's equations and is easy to implement in codes that allow the use of anisotropic material properties.

TIME DOMAIN ELECTROMAGNETIC FIELD COMPUTATION WITH FINITE DIFFERENCE METHODS

1996-07-01

T. WEILAND

The solution of Maxwell's equations in the time domain has now been in use for almost three decades and has had great success in many different applications. The main attraction … The solution of Maxwell's equations in the time domain has now been in use for almost three decades and has had great success in many different applications. The main attraction of the time domain approach, originating in a paper by Yee (1966), is its simplicity. Compared with conventional frequency domain methods it takes only marginal effort to write a computer code for solving a simple scattering problem. However, when applying the time domain approach in a general way to arbitrarily complex problems, many seemingly simple additional problems add up. We describe a theoretical framework for solving Maxwell's equations in integral form, resulting in a set of matrix equations, each of which is the discrete analogue to one of the original Maxwell equations. This approach is called Finite Integration Theory and was first developed for frequency domain problems starting about two decades ago. The key point in this formulation is that it can be applied to static, harmonic and time dependent fields, mainly because it is nothing but a computer-compatible reformulation of Maxwell's equations in integral form. When specialised to time domain fields, the method actualy contains Yee's algorithm as a subset. Further additions include lossy materials and fields of moving charges, even including fully relativistic analysis. For amny practical problems the pure time domain algorithm is not sufficient. For instance a waveguide transition analysis requires knowledge of the incoming and outgoing mode patterns for proper excitation in the time domain. This is a typical example where both frequency and time domian analysis are essential and only the combinatin yields the successful result. Typical engineers may wonder why at all one should apply time domain analysis to basically monochromatic field problems. The answer is simple: it is much faster, needs less computer memory, is more general nad typically more accurate. Speed-up factors of over 200 have been reached for realistic problems in filter and waveguide design. The small core space requirement makes time domain methods applicable on desktop computers using milions of cells, and six unknowns per cell—a dimension that has not yet been reached by frequency domain approaches. This enormous amount of mesh cells is absolutely neceesary when complex structures or structures with spacial dimensions of many wavelengths are to be studied. Our personal recod so far is a waveguide problem in which we used 72,000,000 unknowns.

A frequency-dependent finite-difference time-domain formulation for dispersive materials

1990-01-01

R. Luebbers , F. Hunsberger , Karl S. Kunz +2 more

The traditional finite-difference time-domain (FDTD) formulation is extended to include a discrete time-domain convolution, which is efficiently evaluated using recursion. The accuracy of the extension is demonstrated by computing the … The traditional finite-difference time-domain (FDTD) formulation is extended to include a discrete time-domain convolution, which is efficiently evaluated using recursion. The accuracy of the extension is demonstrated by computing the reflection coefficient at an air-water interface over a wide frequency band including the effects of the frequency-dependent permittivity of water. Extension to frequency-dependent permeability and to three dimensions is straightforward. The frequency dependent FDTD formulation allows computation of electromagnetic interaction with virtually any material and geometry (subject only to computer resource limitations) with pulse excitation. Materials that are highly dispersive, such as snow, ice, plasma, and radar-absorbing material, can be considered efficiently by using this formulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents

1989-07-01

Oszkár Bíró , Kurt Preis

Various magnetic vector potential formulations for the eddy-current problem are reviewed. The uniqueness of the vector potential is given special attention. The aim is to develop a numerically stable finite-element … Various magnetic vector potential formulations for the eddy-current problem are reviewed. The uniqueness of the vector potential is given special attention. The aim is to develop a numerically stable finite-element scheme that performs well at low and high frequencies, does not require an unduly high number of degrees of freedom, and is capable of treating multiple connected conductors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Higher order interpolatory vector bases for computational electromagnetics

1997-03-01

Roberto D. Graglia , Donald R. Wilton , Andrew F. Peterson

Low-order vector basis functions compatible with the Nedelec (1980) representations are widely used for electromagnetic field problems. Higher-order functions are receiving wider application, but their development is hampered by the … Low-order vector basis functions compatible with the Nedelec (1980) representations are widely used for electromagnetic field problems. Higher-order functions are receiving wider application, but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases. In this paper, fully interpolatory higher order vector basis functions of the Nedelec type are defined in a unified and consistent manner for the most common element shapes. It is shown that these functions can be obtained as the product of zeroth-order Nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties of the vector functions are discussed, and expressions for the vector functions of arbitrary polynomial order are presented. Sample numerical results confirm the faster convergence of the higher order functions.

Meep: A flexible free-software package for electromagnetic simulations by the FDTD method

2009-11-23

Ardavan Oskooi , David Roundy , Mihai Ibanescu +3 more

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A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals

1987-05-01

J.C.F. Telles

Abstract Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. … Abstract Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two‐dimensional, axisymmetric and three‐dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near‐singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self‐adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self‐adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.

The modified nodal approach to network analysis

1975-06-01

Chung-Wen Ho , Albert E. Ruehli , P.A. Brennan

The nodal method has been widely used for formulating circuit equations in computer-aided network analysis and design programs. However, several limitations exist in this method including the inability to process … The nodal method has been widely used for formulating circuit equations in computer-aided network analysis and design programs. However, several limitations exist in this method including the inability to process voltage sources and current-dependent circuit elements in a simple and efficient manner. A modified nodal analysis (MNA) method is proposed here which retains the simplicity and other advantages of nodal analysis while removing its limitations. A simple and effective pivoting scheme is also given. Numerical examples are used to compare the MNA method with the tableau method. Favorable results are observed for the MNA method in terms of the dimension, number of nonzeros, and fill-ins for comparable circuit matrices.

Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media

1966-05-01

K.S. Yee

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 … 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.

Finite elements in computational electromagnetism

2002-01-01

Ralf Hiptmair

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement … This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.

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A new FDTD algorithm based on alternating-direction implicit method

1999-01-01

Takefumi Namiki

In this paper, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on an alternating-direction implicit method. … In this paper, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on an alternating-direction implicit method. It is shown that the new algorithm is quite stable both analytically and numerically even when the CFL condition is not satisfied. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than conventional FDTD schemes in terms of computer resources such as central-processing-unit time. Numerical formulations are presented and simulation results are compared to those using the conventional FDTD method.

Higher-Order Numerical Methods for Transient Wave Equations

2002-01-01

Gary Cohen

Electromagnetic waves in stratified media

1963-12-01

J. Heading

Finite Element Method Electromagnetics

1998-01-01

John L. Volakis , Arindam Chatterjee , Leo C. Kempel

Absorbing boundary conditions for acoustic and elastic wave equations

1977-12-01

R. W. Clayton , Björn Engquist

abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in … abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

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Convolution PML (CPML): An efficient FDTD implementation of the CFS–PML for arbitrary media

2000-12-05

Judith Roden , Stephen D. Gedney

A novel implementation of perfectly matched layer (PML) media is presented for the termination of FDTD lattices. The implementation is based on the stretched coordinate form of the PML, a … A novel implementation of perfectly matched layer (PML) media is presented for the termination of FDTD lattices. The implementation is based on the stretched coordinate form of the PML, a recursive convolution, and the use of complex frequency, shifted (CFS) PML parameters. The method, referred to here as the convolutional PML (CPML), offers a number of advantages over the traditional implementations of the PML. Specifically, the application of the CPML is completely independent of the host medium. Thus, no modifications are necessary when applying it to inhomogeneous, lossy, anisotropic, dispersive, or nonlinear media. Secondly, it is shown that the CFS–PML is highly absorptive of evanescent modes and can provide significant memory savings when computing the wave interaction of elongated structures, sharp corners, or low-frequency excitations. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 334–339, 2000.

Finite difference time domain methods for the Chern–Simons–Schrödinger equations

2025-06-21

Jeongho Kim , Bora Moon | Journal of Computational and Applied Mathematics

Higher-order FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation

2025-06-21

Y. S. Li , Haijun Wu | Journal of Scientific Computing

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Energy-Stable Finite Element Approximation of the Landau–Lifshitz–Bloch Equation Below the Curie Temperature

2025-06-21

Agus L. Soenjaya | Journal of Scientific Computing

Abstract The Landau–Lifshitz–Bloch (LLB) equation is a micromagnetic model which describes the time evolution of the magnetisation vector field in a ferromagnet at elevated temperatures. In this work, we develop … Abstract The Landau–Lifshitz–Bloch (LLB) equation is a micromagnetic model which describes the time evolution of the magnetisation vector field in a ferromagnet at elevated temperatures. In this work, we develop an energy-stable finite element scheme for solving the LLB equation in the regime below the Curie temperature. In this setting, the LLB equation takes the form of a vector-valued quasilinear PDE with a singular term. To overcome the challenges associated with this singular term, we adopt a ‘regularise-then-discretise’ strategy. Specifically, we introduce a regularised version of the equation whose solution converges to that of the original LLB equation. We then design an energy-stable, fully discrete Galerkin finite element method based on implicit Euler time discretisation to solve the regularised problem. Under suitable regularity assumptions on the exact solution, we prove that the scheme converges at an optimal rate. Numerical experiments are presented to corroborate the theoretical results.

Accurate generation of a Gaussian beam in the HIE-FDTD method

2025-06-20

Nan Qin , Chunhui Mou , Juan Chen +3 more | Optics Express

An effective interface formulation for electromagnetic shielding using the A-formulation in 3D

2025-06-20

Markus Schöbinger , Michael Leumüller , Karl Hollaus | COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

Purpose The purpose of this paper is to present an effective material approach to simulate electromagnetic shields using the A-Formulation in a fully 3D setting with nonlinear materials in the … Purpose The purpose of this paper is to present an effective material approach to simulate electromagnetic shields using the A-Formulation in a fully 3D setting with nonlinear materials in the frequency domain. It allows to treat the shield as an interface in the finite element mesh so that only the magnetic vector potential in the surrounding air has to be considered for the solution. Design/methodology/approach The jump of the tangential components of the potential across the interface is controlled by an effective material parameter based on a suitable cell problem. This parameter can be efficiently interpolated from a precomputed look-up table. Findings The method is able to consider curved shields and holes. A numerical example shows an excellent agreement of the presented method compared to a reference solution both in a global and a local sense. Originality/value A novel effective material approach based on numerical solutions of a suitable nonlinear cell problem is presented.

Optimal DG Placement Using Realistic Method

2025-06-19

Ekkati Manoj , Bantupavani Lalitha , Mohammad Almas +1 more | CRC Press eBooks

Field–potential finite-difference time-domain (FiPo FDTD) technique for computational electromagnetics

2025-06-16

Laleh Avazpour , Samuel Belling , M. L. King +2 more | Journal of Computational Electronics

FDTD (Finite Difference Time Domain) Method

2025-06-16

Kotaro Kajikawa , Takayuki Okamoto | CRC Press eBooks

Radial Perfectly Matched Layers and Infinite Elements for the Anisotropic Wave Equation

2025-06-16

Martin Halla , Maryna Kachanovska , Markus Wess | SIAM Journal on Mathematical Analysis

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BOUNDED TIME INVERSE SCATTERING FOR SEMILINEAR DIRAC EQUATION

2025-06-13

Y. Yi | Inverse Problems

Abstract In this paper, we present the first uniqueness result on the bounded time inverse scattering problem for a semilinear Dirac equation with smooth nonlinearity $F(x, z)$ where $(x, z)\in … Abstract In this paper, we present the first uniqueness result on the bounded time inverse scattering problem for a semilinear Dirac equation with smooth nonlinearity $F(x, z)$ where $(x, z)\in \mathbb{R}^3\times \mathbb{C}^4$ and $x$ is the spatial variable. We show that the solution map, which sends initial data at time 0 to the solution at time $T$, uniquely determines $F(x, z)$ on $x \in \mathbb{R}^3$ and $|z| \leq M$, where $M$ is a constant depend on the solution map, under the assumption that $\partial_z F(x, 0)$ and $\partial^2_z F(x, 0)$ are known. In the proof, we construct a sequence of collisions approaching the initial timeline to simulate a boundary collision. This technique enables us to overcome the difficulties of this hyperbolic system without assumptions on the nonlinearity structure.

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A reduction of the ultradiscrete modified KdV equation and its finite order solutions

2025-06-13

Juho Halonen | Journal of Physics A Mathematical and Theoretical

Abstract In this paper we will perform a reduction on the ultradiscrete modified Korteweg–De Vries equation. We will then describe the form of the solutions of the reduction in detail. … Abstract In this paper we will perform a reduction on the ultradiscrete modified Korteweg–De Vries equation. We will then describe the form of the solutions of the reduction in detail. We will also show that with certain parameter values the equation acquired from the reduction possesses only finite order solutions while with other parameter values the equation possesses infinite order solutions. Finally, we will pose a conjecture about the ultradiscrete Painlevé I equation.

Numerical and Analytical Methods for Complex Electromagnetic Media

2025-06-01

Numerical method and analysis for fluid-structure model on unbounded domains

2025-06-01

Hongwei Li , Xinyue Chen | Applied Numerical Mathematics

A Bernstein-B ’ezier finite element method with perfectly matched layer for refraction and diffraction of waves in coastal regions

2025-06-01

Saloua El Marri , Abdellah El Kacimi , Nabil El Moçayd +1 more | Journal of Computational Science

Fast simulation of EM telemetry in vertical drilling: A semi-analytical finite-element method with virtual layering technique

2025-06-01

Hao Liang , Changchun Yin , Yang Su +4 more | Petroleum Science

Tunable unidirectional large-area surface magnetoplasmons in a stratified waveguide

2025-05-29

Qian Shen , Yun You , Zhengming Tang +2 more | Optics Express

Application of FDTD for Accurate Scattering From Stratified Media With/Without Target

2025-05-28

Chao Yang , Zhong Hua Tang , Haiyan Xie +3 more | Microwave and Optical Technology Letters

ABSTRACT Interactions of electromagnetic waves with stratified media, with or without a target, are fundamental in many fields. However, existing finite‐difference time‐domain (FDTD) method faces significant challenges in accurately modeling … ABSTRACT Interactions of electromagnetic waves with stratified media, with or without a target, are fundamental in many fields. However, existing finite‐difference time‐domain (FDTD) method faces significant challenges in accurately modeling total internal reflection (TIR), frustrated total internal reflection (FTIR), and the composite structures of stratified media and targets. To address this issue, this paper employs the generalized total‐field/scattered‐field (G‐TF/SF) method to address 3D electromagnetic scattering from stratified media, both with and without a target. Numerical simulations validate the effectiveness of the G‐TF/SF method. Key findings demonstrate that the G‐TF/SF method effectively mitigates edge effects in numerical simulations, accurately handles TIR and FTIR phenomena, and is well‐suited for applications involving composite scattering from targets within stratified media.

Monic Chebyshev's First Derivative Pseudo-Galerkin Method for Solving Linear and Non-Linear IBVPS: Real-Life and Physical Applications

2025-05-28

Hager Alaa-Eldeen , Gaitha M. Alzabeedy , Weam G. Alharbi +3 more | Fractals

On the Relationship Between the Pole Condition, Absorbing Boundary Conditions, and Perfectly Matched Layers

2025-05-28

Martin J. Gander , Achim Schädle | SIAM Journal on Numerical Analysis

Analysis of Complete Radiation Boundary Conditions for Maxwell’s Equations

2025-05-28

Seungil Kim | SIAM Journal on Numerical Analysis

Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation Methods for PDEs with Time Delay

2025-05-26

Bankim C. Mandal , Deeksha Tomer

Abstract We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs) … Abstract We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs) incorporating time delay. Time delay phenomena frequently arise in various real-world systems, making their accurate modeling and simulation crucial for understanding and prediction. We consider a series of model problems, ranging from Parabolic, Hyperbolic to Neutral PDEs with time delay and apply the iterative techniques DNWR and NNWR for solving in parallel. We present the theoretical foundation, numerical implementation, and comparative performance analysis of these two methods. Through numerical experiments and simulations, we explore their convergence properties, computational efficiency, and applicability to various types of PDEs with time delay.

A novel interpolation-based method for solving the one-dimensional wave equation on a domain with a moving boundary

2025-05-24

Michiel Lassuyt , Emma Vancayseele , Wouter Deleersnyder +3 more

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A POD-Based Reduced Order Method Applied to Goda Time-Splitting Scheme

2025-05-19

Mejdi Azaïez , Tomás Chacón Rebollo , Fernando Núñez Hernández +1 more

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Numerical Solution of Time-Dependent Schrödinger Equation in 2D Using Method of Particular Solutions with Polynomial Basis Functions

2025-05-15

Thir Dangal , B. Khatri Ghimire , A.R. Lamichhane

The method of particular solutions using polynomial basis functions (MPS-PBF) has been extensively used to solve various types of partial differential equations. Traditional methods employing radial basis functions (RBFs)—such as … The method of particular solutions using polynomial basis functions (MPS-PBF) has been extensively used to solve various types of partial differential equations. Traditional methods employing radial basis functions (RBFs)—such as Gaussian, multiquadric, and Matérn functions—often suffer from accuracy issues due to their dependence on a shape parameter, which is very difficult to select optimally. In this study, we adopt the MPS-PBF to solve the time-dependent Schrödinger equation in two dimensions. By utilizing polynomial basis functions, our approach eliminates the need to determine a shape parameter, thereby simplifying the solution process. Spatial discretization is performed using the MPS-PBF, while temporal discretization is handled via the backward Euler and Crank–Nicolson methods. To address the ill conditioning of the resulting system matrix, we incorporate a multi-scale technique. To validate the efficacy of the proposed scheme, we present four numerical examples and compare the results with known analytical solutions, demonstrating the accuracy and robustness of the scheme.

Closed-Form Evaluation of Potential Integrals in the Boundary Element Method

2025-05-13

Michael Carley

A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented … A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.

Mixed-Dimensional Modeling of Time-Dependent Wave Problems Using the Panasenko Construction

2025-05-13

Hanan Amar , Dan Givoli

A Time-Segmented SAI-Krylov Subspace Approach for Large-Scale Transient Electromagnetic Forward Modeling

2025-05-11

Y. Fan , Kailiang Lu , Juanjuan Li +1 more

After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the … After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimization of linear equation solvers. However, the dominant approach still relies on direct solvers, which require substantial memory and complicate the modeling of electromagnetic responses in large-scale models. This paper proposes a new method for solving large-scale TEM responses, building on previous studies. The TEM response is expressed as a matrix exponential function with an analytic initial field for a step-off source, which can be efficiently solved using the Shift-and-Invert Krylov (SAI-Krylov) subspace method. The Arnoldi algorithm is used to construct the orthogonal basis for the Krylov subspace, and the preconditioned conjugate gradient (PCG) method is applied to solve large-scale linear equations. The paper further explores how dividing the off-time and optimizing parameters for each time interval can enhance computational efficiency. The numerical results show that this parameter optimization strategy reduces the iteration count of the PCG method, improving efficiency by a factor of 5 compared to conventional iterative methods. Additionally, the proposed method outperforms direct solvers for large-scale model calculations. Conventional approaches require numerous matrix factorizations and thousands of back-substitutions, whereas the proposed method only solves about 300 linear equations. The accuracy of the approach is validated using 1D and 3D models, and the propagation characteristics of the TEM field are studied in large-scale models.

A boundary integral equation formulation for transient electromagnetic transmission problems on Lipschitz domains

2025-05-10

Tonatiuh Sánchez-Vizuet

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission … We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the number of unknown densities and to formulate a system of coupled boundary integral equations describing the scattered and transmitted waves. The system is transformed into the Laplace domain where it is proven to be stable and uniquely solvable. The Laplace domain stability estimates are then used to establish the stability and unique solvability of the original time domain problem. Finally, we show how the bounds obtained in both Laplace and time domains can be used to derive error estimates for semi discrete Galerkin discretizations in space and for fully discrete numerical schemes that use Convolution Quadrature for time discretization and a conforming Galerkin method for discretization of the space variables.

Using Physics-Informed Transformers to Solve Nonlinear Partial Differential Equations in Applications of Physics and Modern Engineering

2025-05-01

Adel Ahmed Hassan Kubba , Ragab Mostafa Mohamed Abdelbar | Journal of research in applied mathematics.

A novel implementation of symmetric boundary condition in harmonic and transient analysis of electromagnetic wave propagation

2025-04-29

Durgarao Kamireddy , Sreekanth Karanam , Arup Nandy

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High-order Sparse-PIC methods: analysis and numerical investigations

2024-02-04

Fabrice Deluzet , Clément Guillet , Jacek Narski +1 more

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