Solving Time Domain Helmholtz Wave Equation With Mod-FDM

Jung, Baek Ho; Sarkar, Tapan K.

doi:10.2528/pier07102802

Cited by 7 publications

(12 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further analysis shows that by eliminating the lowest-order cross partial derivative term in the truncation error (Ref. [6], 218-220), we may derive the normalized, 2nd-order accurate, discrete Helmholtz operatorL FD2-9 (Equation (10), Ref. [1]) as:…”

Section: Normalized Discrete Fd Helmholtz Operatorsmentioning

confidence: 99%

“…On the green lines the Neumann's boundary condition (NBC) is applied whereas on the red lines the transparent boundary condition (TBC) is implemented. For points on the NBC lines, LFE equations are modified by reflecting the exterior node back onto its mirrored, interior node [Equations (5)- (6). Ref.…”

Section: Numerical Verification Of Clf Computation Of the Two-dimensimentioning

confidence: 99%

“…From these FourierBessel coefficients we derived FD-like, compact nine-point stencils for the 2D Helmholtz equation. We show that CLF is capable of advancing existing FD-FD methods [5][6][7][8][9] by reducing the sampling density to just a little more than two points per wavelength, which is theoretical limit for spatial sampling.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

View full text Add to dashboard Cite

Abstract-The method of connected local fields (CLF), developed for computing numerical solutions of the two-dimensional (2-D) Helmholtz equation, is capable of advancing existing frequency-domain finitedifference (FD-FD) methods by reducing the spatial sampling density nearly to the theoretical limit of two points per wavelength. In this paper, we show that the core theory of CLF is the result of applying the uniqueness theorem to local EM waves. Furthermore, the mathematical process for computing the local field expansion (LFE) coefficients from eight adjacent points on a square is similar to that in the theory of discrete Fourier transform. We also present a theoretical analysis of both the local and global errors in the theory of connected local fields and provide closed-form expressions for these errors.

show abstract

Section: Normalized Discrete Fd Helmholtz Operatorsmentioning

confidence: 99%

Section: Numerical Verification Of Clf Computation Of the Two-dimensimentioning

confidence: 99%

See 1 more Smart Citation

Theoretical Foundation for the Method of Connected Local Fields

Mu¹,

Chang²

2011

PIER

View full text Add to dashboard Cite

show abstract

“…This MOD methodology has been successfully implemented in a FDTD formulation [10][11][12][13][14] and in integral equations dealing with skin effects in conductors, and propagation in non-dispersive dielectric and in a dispersive media [15][16][17]. The basic idea here is that we fit the fields, the permittivity and permeability with a series of orthogonal associate Laguerre basis functions in the time domain.…”

Section: Introductionmentioning

confidence: 99%

Transient Wave Propagation in a General Dispersive Media Using the Laguerre Functions in a Marching-on-in-Degree (Mod) Methodology

Jung¹,

Mei²,

Sarkar³

2011

PIER

Self Cite

View full text Add to dashboard Cite

Abstract-The objective of this paper is to illustrate how the marching-on-in-degree (MOD) method can be used for efficient and accurate solution of transient problems in a general dispersive media using the finite difference time-domain (FDTD) technique. Traditional FDTD methods when solving transient problems in a general dispersive media have disadvantages because they need to approximate the time domain derivatives by finite differences and the time domain convolutions by using finite summations. Here we provide an alternate procedure for transient wave propagation in a general dispersive medium where the two issues related to finite difference approximation in time and the time consuming convolution operations are handled analytically using the properties of the associate Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the permittivity and permeability with a series of orthogonal associate Laguerre basis functions in the time domain. In this way, the time variable can not only be decoupled analytically from the temporal variations but that the final computational form of the equations is transformed from FDTD to a FD formulation in the differential equations after a Galerkin testing. Numerical results are presented for transient wave propagation in general dispersive materials which use for example, a Debye, Drude, or Lorentz models.

show abstract

“…Due to the needs of TD solutions, many efforts have been applied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Typical TD approaches include using fast Fourier transform (FFT) or analytical time transform (ATT) [16,17] to directly inverse FD solutions into TD, finite difference time domain (FDTD) [18], TD integral approaches [19] and TD uniform geometrical theory of diffractions (TD-UTD) [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A Discrete Time Electromagnetic Formulization and Its Applications

Tuan¹,

Chou²

2008

PIER

View full text Add to dashboard Cite

Abstract-This paper presents a formulization of time domain (TD) discrete electromagnetic (EM) solution to provide an effective analysis over a variety of EM problems. This procedure first represents the time responses of EM fields in terms of a set of selected basis functions. Their coefficients are then employed to create matrix-form Maxwell's equations with forms analogous to frequency domain (FD) Maxwell's equations, which allows one to formulate TD solutions via utilizing their corresponding FD solutions that are existing and generally much mature. This work provides general characteristics with parts previously described in the discrete-time EM theory [20,21] and, most importantly, provides rigorous theoretical derivations in formulating the TD solutions.

show abstract

Solving Time Domain Helmholtz Wave Equation With Mod-FDM

Cited by 7 publications

References 27 publications

Theoretical Foundation for the Method of Connected Local Fields

Theoretical Foundation for the Method of Connected Local Fields

Transient Wave Propagation in a General Dispersive Media Using the Laguerre Functions in a Marching-on-in-Degree (Mod) Methodology

A Discrete Time Electromagnetic Formulization and Its Applications

Contact Info

Product

Resources

About