Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems

Geranmayeh, Amir; Ackermann, Wolfgang; Weiland, Thomas

doi:10.1016/j.apnum.2008.12.026

Cited by 16 publications

(16 citation statements)

References 35 publications

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“…Enforcing the boundary condition J = n × H, which sets the total (incident plus scattered) magnetic field tangential to the exterior surface conformal to S equal to the unknown induced surface current density J(r,t), finally results in the time-domain magnetic field integral equation (MFIE) [1][2][3][4][5][6][7]. Taking the existing curl operator into the integral and extracting the Cauchy principal value afterwards, the MFIE can be represented by…”

Section: Formulationsmentioning

confidence: 99%

“…for the time integration and interpolation provides a stable scheme [1]. Due to the presence of the retarded time τ in (1), the necessary knowledge of past solution requires an interpolation between known past solution samples using the subdomain time evolution function (3), which results in the expression , , ,…”

Section: Formulationsmentioning

confidence: 99%

“…Note that cancelation of the first term in (4) can also be integrated into the numerical solution procedure of the time-domain electric field integral equation (EFIE), using the formulation Fig. 1 (b) and (c) illustrate the x-directed transient induced surface current density at the center of the top face of a perfectly conducting cube, 0.2 m on a side illuminated by an x-polarized Gaussian plane-wave propagating along the zdirection with a full-width half maximum of 0.7071 m. The cube is discretized into 3072 triangular patches with M = 4608 common edges and the applied MFIE is solved by the MOT schemes with time step size Δt = 10.3 min{R mk }/c purely using adaptive numerical quadratures and Duffy's transformation for singularity cancellation [1] or alternatively the analytic space integration (7). The values are compared with high-resolution finite integration technique (FIT) results.…”

Section: =Lnmentioning

confidence: 99%

“…Time-domain surface integral equations, which are prefectly suited for the analysis of electromagnetic wave scattering from three-dimensional objects, are numerically solved using the time-domain boundary element methods [1][2][3][4][5][6][7]. Depending on the choice of time discretization approaches, several categories of integral solvers have been attained.…”

Section: Introductionmentioning

confidence: 99%

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1/R²-Kernel cancelation in classical marching-on-in-time schemes

Geranmayeh

Ackermann

Weiland

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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Cancelation of 1/R 2 -associated integrals in the numerical solution procedure of the time-domain magnetic field integral equations are explained to halve the computational costs of the classical marching-on-in-time (MOT) schemes in which the delay time is approximated by the barycentric electric distance of the subdomain patches. The new technique improves the accuracy of the MOT as the resulting interpolation coefficients for the calculation of the impedance matrices became independent of the electrical distance of surface elements. Additionally, the analytical closed-form expressions for the evaluation of the remaining 1/R 3 -associated integrals allow the fast computation of the retarded matrices on demand. The applicability of the scheme to large-scale wave scattering problems is investigated.

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Section: Formulationsmentioning

confidence: 99%

Section: Formulationsmentioning

confidence: 99%

Section: =Lnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

1/R²-Kernel cancelation in classical marching-on-in-time schemes

Geranmayeh

Ackermann

Weiland

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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“…[3]). The stability of the MOT algorithm hinges on both the accurate evaluation of the interaction integrals [4]- [7] and the choice of temporal discretization scheme [8]- [11]. Space-time Galerkin schemes have been found to produce good results in terms of stability, accuracy and extensibility to higher order in both space and time [10], [12]- [14].…”

Section: Introductionmentioning

confidence: 99%

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

Beghein

Cools

Andriulli

2015

IEEE Trans. Antennas Propagat.

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Abstract-The marching-on-in-time solution of the time domain electric field integral equation (TD-EFIE) has traditionally suffered from a number of issues, including the emergence of spurious static currents (DC instability) and ill-conditioning at large time steps (low frequencies). In this contribution, a spacetime Galerkin discretization of the TD-EFIE is proposed, which separates the loop and star components of both the equation and the unknown. Judiciously integrating or differentiating these components with respect to time leads to an equation which is free from DC instability. By choosing the correct temporal basis and testing functions for each of the components, a stable marchingon-in-time system is obtained. Furthermore, the scaling of these basis and testing functions ensure that the system remains wellconditioned for large time steps. The loop-star decomposition is performed using quasi-Helmholtz projectors in order to avoid the explicit transformation to the unstable bases of loops and stars (or trees), and to avoid the search for global loops, which is a computationally expensive operation.Index Terms-time domain, electric field integral equation, DC instability, low frequency breakdown.

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A time‐domain equivalence principle and its marching‐on‐in‐degree solution

Shi

Wang

Chen

2014

Micro & Optical Tech Letters

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sensor without the needed for a calibration tag and any background subtraction technique, which is impractical in most real situations. Now the sensor is heated with an air flow coming from a heat gun up to the maximum temperature and its response is measured while it cools down to room temperature. Three measurements are obtained simultaneously: the sensor response (|S 21 |), the value R NTC2 and V 0 . The real temperature at the NTC can be calculated from R NTC2 using (2). As a second example, Figures 8(a) and 8(b) present the measured |S 21 | at a distance sensor-reader of 40 cm. Figure 8(c) shows the detected f r as a function of temperature (obtained from NTC 2 ) after Lorentzian approximation is applied. As can be observed, the sensor can measure a range of temperature between 29 and 62 C, which in the proposed design means an f r range between 3.

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Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems

Cited by 16 publications

References 35 publications

1/R²-Kernel cancelation in classical marching-on-in-time schemes

1/R²-Kernel cancelation in classical marching-on-in-time schemes

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

A time‐domain equivalence principle and its marching‐on‐in‐degree solution

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Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems

Cited by 16 publications

References 35 publications

1/R2-Kernel cancelation in classical marching-on-in-time schemes

1/R2-Kernel cancelation in classical marching-on-in-time schemes

A DC Stable and Large-Time Step Well-Balanced TD-EFIE Based on Quasi-Helmholtz Projectors

A time‐domain equivalence principle and its marching‐on‐in‐degree solution

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1/R²-Kernel cancelation in classical marching-on-in-time schemes

1/R²-Kernel cancelation in classical marching-on-in-time schemes