Reducing solution time in monochromatic FDTD waveguide simulations

Prescott, D.T.; Shuley, N.V.

doi:10.1109/22.297823

Cited by 14 publications

(8 citation statements)

References 3 publications

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“…This can be observed in Fig. 5, where the reflection from the second-order Higdon ABC (17) has been calculated for a number of mesh discretizations. One can see that as the mesh discretization ratio is increased ( ) that the reflection function for this ABC approaches the optimal level of performance, displaying zeros for the desired angles of incidence.…”

Section: Abc Optimizationmentioning

confidence: 83%

“…One can see that there is a slight discrepancy in the results where the reflection is less than 10 . This is acceptable since numerical error will occur in the FDTD simulation owing to accumulating computational roundoff and the oscillatory nature of monochromatic FDTD simulations [17]. A much-improved performance (greater than one order) is obtained for this ABC over that achieved by the secondorder Trefethen and Halpern ABC (see Fig.…”

Section: Trefethen and Halpern's Second-order Abcmentioning

confidence: 93%

“…The weightings required to implement the box scheme discretization of Higdon's second-order ABC are as follows, with all other weightings being zero: (17) where (18) The reflection function has been obtained for this ABC using both the FDTD simulation and the numerical formulation procedure for two configurations of the Higdon ABC with the variables and (18) chosen, such that the theoretical angles of complete absorption are: a) and b) and . Fig.…”

Section: Trefethen and Halpern's Second-order Abcmentioning

confidence: 99%

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Reflection analysis of FDTD boundary conditions. I. Time-space absorbing boundaries

Prescott

1997

IEEE Trans. Microwave Theory Techn.

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Time-space absorbing-boundary conditions (ABC's) are employed to truncate finite-difference time-domain (FDTD) computational domains and are predominantly used because of their simplicity. Their implementation requires only the calculation of a boundary-field value as a function of the local fields and their recent time history. A general method is described, which enables highly accurate calculation of the reflection properties of these boundary conditions for plane-wave incidence. A number of commonly used time-space ABC's are studied, and the technique is verified by way of FDTD simulation. It is demonstrated that the performance of time-space ABC's is substantially degraded by the influence of the finite-mesh discretizations. A technique is described, which enables these discretization inaccuracies to be overcome by correctly choosing the relevant ABC weighting parameters, thus enabling the various boundary conditions to perform precisely as desired. Solutions for these weighting parameters are provided for a number of common boundary conditions such that their absorption characteristics may be precisely configured to suit any level of mesh discretization. As a consequence, a performance equivalence is established amongst all time-space ABC's of the same order.

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Section: Abc Optimizationmentioning

confidence: 83%

Section: Trefethen and Halpern's Second-order Abcmentioning

confidence: 93%

Section: Trefethen and Halpern's Second-order Abcmentioning

confidence: 99%

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Reflection analysis of FDTD boundary conditions. I. Time-space absorbing boundaries

Prescott

1997

IEEE Trans. Microwave Theory Techn.

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“…Here, we employ the Hanning window function to alter the rising slope of the excitation from zero to steady state. This modified excitation has less of its spectrum located below the cutoff frequency and can arrive at steady state with minimal transient interference [5]. The monochromatic excitation for the dominant TElo mode in a rectangular waveguide, modified by the Hanning window, is given by where T , the rise time, is chosen to be 10 cycles of the excitation frequency, fin, z and x are transverse coordinates (y is longitudinal) in the waveguide, W is the larger dimension of the cross-section, and U(t) is the Heaviside function.…”

Section: Methodology 21 Excitation Choicementioning

confidence: 99%

“…2, let C = K/V2, and G = Vj/V3, with I$ calculated on the second line at P3. Then, we obtain from (4), (5) and ( …”

Section: Calculating the Bourndary Reflectionmentioning

confidence: 99%

A simple method to correct the reflection error of absorbing boundary condition in the FDTD analysis of waveguides

Lin

Naishadham²

1998 IEEE MTT-S International Microwave Symposium Digest (Cat. No.98CH36192)

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The recent progress in absorbing boundary conditions (ABCs), especially Berenger's perfectly matched layer (PML), promises to be very attractive for microwave circuit and packaging full-wave analysis using the FDTD method. However, in waveguides, multimodal and dispersive waves exist, which makes it difficult to minimize the error from absorbing boundary reflection. Several studies have shown that no single ABC, including the PML, is effective in absorbing energy having widely varying transverse distributions and group velocities. The possibility of excitation of evanescent modes by input spectral content below the cutoff frequency complicates the design of the ABC. In this paper, an efficient and simple method, the geometry rearrangement technique (GRT), is implemented to minimize the boundary truncation error in a waveguide. Numerical illustration of the propagation constant in a rectangular waveguide, terminated with Mur's first-order ABC, demonstrates the effectiveness of GRT in correcting the ABC-induced reflection error for waveguide problems.

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A new finite element‐FDTD‐boundary integral equation technique with biconjugate gradient solver for modeling electromagnetic problems in the frequency domain

Rogier

Zutter

2003

Radio Science

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[1] A new hybrid formalism in the frequency domain is presented, based on a combination of the boundary integral equation (BIE) technique, the finite element (FE) method and the finite difference time domain (FDTD) algorithm. An FE method and FDTD are used to describe the inhomogeneous parts of the simulation domain, whereas large homogeneous portions of the simulation space are modeled with a BIE. To solve the global matrix system efficiently, a biconjugate gradient solver is used. To calculate the matrix-vector products in each iteration step of the solution process, the system matrix is required for the FE and the BIE subregions. For FDTD subregions, we will either construct a system matrix or we will calculate matrix-vector products directly relying on FDTD. Guidelines will be given to choose the most efficient approach for each FDTD subdomain. To illustrate the efficiency of the new method and to compare the new approach with other (hybrid) methods, three representative configurations are studied.

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Reducing solution time in monochromatic FDTD waveguide simulations

Cited by 14 publications

References 3 publications

Reflection analysis of FDTD boundary conditions. I. Time-space absorbing boundaries

Reflection analysis of FDTD boundary conditions. I. Time-space absorbing boundaries

A simple method to correct the reflection error of absorbing boundary condition in the FDTD analysis of waveguides

A new finite element‐FDTD‐boundary integral equation technique with biconjugate gradient solver for modeling electromagnetic problems in the frequency domain

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