Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing

Francés, Jorge; Bleda, Sergio; Álvarez, Mariela L.; Martínez-Guardiola, Francisco J.; Márquez, Andrés; Neipp, Cristian

doi:10.1117/1.oe.53.1.011005

Cited by 13 publications

(19 citation statements)

References 53 publications

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“…It is worthwhile to note that finite-difference schemes have an exponentially growing cost in terms of grid size, so enlarging the grid size has a dramatic impact on the time simulation costs. More information regarding the stability, convergence, and computational optimization can be found in [15,[22][23][24]27]. The SF-FDTD leapfrog algorithm used for updating field equations uses Eqs.…”

Section: A Fundamentals Of the Sf-fdtd Methodsmentioning

confidence: 99%

“…However, it encounters difficulties in analyzing periodic media under oblique incidence. This issue is addressed by the split-field FDTD (SF-FDTD) method [22], which has lately been extended, for example, to one-dimensionally (1D) periodic structures made of anisotropic media [23,24] and to two-dimensionally (2D) periodic components made of dispersive [25,26] or anisotropic [27] materials. Recently, SF-FDTD has also been extended to nonlinear media in two dimensions [28,29].…”

Section: Introductionmentioning

confidence: 99%

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Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures

et al. 2015

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The split-field finite-difference time-domain method is extended to second-harmonic generation in twodimensionally periodic structures. Making use of the full coefficient-tensor formalism, a coupled nonlinear system of equations, which must be solved at each update of the electromagnetic field, is developed. The accuracy of the method is verified by comparing the results to well-known one-dimensional problems. The results for L-shaped arrays are compared with results obtained with the Fourier modal method.

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Section: A Fundamentals Of the Sf-fdtd Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures

et al. 2015

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“…These factors make mandatory the application of acceleration strategies in order to reduce the time simulation costs. Regarding this aspect, some works related with GPU computing and FDTD in the field of Electromagnetics have been developed [11][12][13]. For FDTD and GPU computing applied to vibration problems there are some contributions related with seismology [14] and also for vibroacoustics [15].…”

Section: Introductionmentioning

confidence: 99%

Multi-GPU and multi-CPU accelerated FDTD scheme for vibroacoustic applications

Francés

Otero

Bleda

et al. 2015

Computer Physics Communications

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a b s t r a c tThe Finite-Difference Time-Domain (FDTD) method is applied to the analysis of vibroacoustic problems and to study the propagation of longitudinal and transversal waves in a stratified media. The potential of the scheme and the relevance of each acceleration strategy for massively computations in FDTD are demonstrated in this work. In this paper, we propose two new specific implementations of the bidimensional scheme of the FDTD method using multi-CPU and multi-GPU, respectively. In the first implementation, an open source message passing interface (OMPI) has been included in order to massively exploit the resources of a biprocessor station with two Intel Xeon processors. Moreover, regarding CPU code version, the streaming SIMD extensions (SSE) and also the advanced vectorial extensions (AVX) have been included with shared memory approaches that take advantage of the multi-core platforms. On the other hand, the second implementation called the multi-GPU code version is based on Peer-to-Peer communications available in CUDA on two GPUs (NVIDIA GTX 670). Subsequently, this paper presents an accurate analysis of the influence of the different code versions including shared memory approaches, vector instructions and multi-processors (both CPU and GPU) and compares them in order to delimit the degree of improvement of using distributed solutions based on multi-CPU and multi-GPU. The performance of both approaches was analysed and it has been demonstrated that the addition of shared memory schemes to CPU computing improves substantially the performance of vector instructions enlarging the simulation sizes that use efficiently the cache memory of CPUs. In this case GPU computing is slightly twice times faster than the fine tuned CPU version in both cases one and two nodes. However, for massively computations explicit vector instructions do not worth it since the memory bandwidth is the limiting factor and the performance tends to be the same than the sequential version with auto-vectorisation and also shared memory approach. In this scenario GPU computing is the best option since it provides a homogeneous behaviour. More specifically, the speedup of GPU computing achieves an upper limit of 12 for both one and two GPUs, whereas the performance reaches peak values of 80 GFlops and 146 GFlops for the performance for one GPU and two GPUs respectively. Finally, the method is applied to an earth crust profile in order to demonstrate the potential of our approach and the necessity of applying acceleration strategies in these type of applications.

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“…In order to achieve this reduction parallel strategies have been considered. 11,20,21 Basically, the auto-vectorisation performed by the compiler and OpenMP have been considered. For enabling properly the auto-vectorisation an efficient memory alignment, a correct loop count and proper structures were considered.…”

Section: One-dimensional Nonlinear Coated Binary Gratingmentioning

confidence: 99%

Efficient split field FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

et al. 2016

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In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one-and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finitedifference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.

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Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing

Cited by 13 publications

References 53 publications

Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures

Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures

Multi-GPU and multi-CPU accelerated FDTD scheme for vibroacoustic applications

Efficient split field FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

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