Finite Difference Time Domain (FDTD) Simulations Using Graphics Processors

Adams, Samuel D.M.; Payne, Jerry A.; Boppana, Rajendra V.

doi:10.1109/hpcmp-ugc.2007.34

Cited by 63 publications

(35 citation statements)

References 3 publications

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“…Os primeiros trabalhos de paralelização do método FDTD para GPUs tiveram como objetivo mostrar a viabilidade dessa proposta, exigindo um significativo esforço para compreender e adaptar o algoritmo para o pipeline de computação gráfica (usando as linguagens OpenGL, Brook e Cg) [1,9,12]. A partir daí, várias propostas de implementação do método FDTD para GPUs foram avaliadas, explorando ambientes de programação de nível mais alto, como CUDA.…”

Section: Introductionunclassified

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Melhorando o Desempenho Computacional de um Esquema de Diferenças Finitas para as Equações de Maxwell

Veloso

Vigo

Rossetto

2016

Tend. Mat. Apl. Comput.

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Recebido em 30 setembro, 2015 / Aceito em 11 fevereiro, 2016 RESUMO. As equações de Maxwell têm um papel crucial na teoria do eletromagnetismo e suas aplicações. Entretanto, nem sempreé possível resolver essas equações de forma analítica. Por isso, precisamos de métodos numéricos para obter soluções aproximadas das equações de Maxwell. O método FDTD (FiniteDiference Time-Domain), proposto por K. Yee,é amplamente usado devido a sua simplicidade e eficiência. No entanto, esse método apresenta um alto custo computacional. Neste trabalho, propomos uma implementação paralela do método FDTD para execução em GPUs, usando a plataforma CUDA. Nosso objetivoé reduzir o tempo de processamento requerido para viabilizar o uso do método FDTD para a simulação da propagação de ondas eletromagnéticas. Avaliamos o algoritmo proposto considerando condições de contorno de tipo Dirichlet e também condições absorventes. Obtivemos ganhos de desempenho que variam de 7 a 8 vezes, comparando a implementação paralela proposta com uma versão sequencial otimizada. Palavras-chave:Equações de Maxwell, Algoritmo de Yee, Programação Paralela com GPU. INTRODUÇÃOA energia gerada por fontes eletromagnéticas e suas interações com o entorno possuem muitas aplicações, entre as quais podemos citar as tecnologias de comunicação sem fio e alguns tratamentos e diagnósticos usados naárea médica [7,8,16]. O desenvolvimento e aprimoramento dessas aplicações requerem um estudo detalhado sobre a interação do campo eletromagnético e a propagação de ondas eletromagnéticas na região de interesse. Esse estudo toma como base as equações de Maxwell, um sistema de equações em derivadas parciais que descreve a evolução no tempo do campo eletromagnético.

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Section: Introductionunclassified

“…Assim como em outros trabalhos ( [1,2,17]), nosso objetivoé realizar simulações FDTD em tempo razoável para viabilizar o uso desse método na simulação de aplicações reais. Para isso, implementamos duas versões do algoritmo, uma usando condições de contorno de Dirichlet, e outra usando condições de contorno absorventes [3].…”

Section: Introductionunclassified

Melhorando o Desempenho Computacional de um Esquema de Diferenças Finitas para as Equações de Maxwell

Veloso

Vigo

Rossetto

2016

Tend. Mat. Apl. Comput.

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“…Ref. [5] also did not utilize CUDA for their simulations of the three-dimensional Maxwell equations, yielding speedups of over 100 times. The two-dimensional Maxwell equations were simulated in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…GPUs have been used for various finite-difference PDE integrator codes with good results [4][5][6][7][8][9]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Caplan

2013

Computer Physics Communications

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We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPUenabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time and both second-and fourthorder differencing in space. The integrators are written to run on NVIDIA GPUs and are interfaced with MATLAB including built-in visualization and analysis tools. Restrictions:The main restriction for the GPU integrators is the amount of RAM on the GPU as the code is currently only designed for running on a single GPU. Unusual features:Ability to visualize real-time simulations through the interaction of MATLAB and the compiled GPU integrators. Additional comments:Program has a dedicated web site at www.nlsemagic.com. Running time:A three-dimensional run with a grid dimension of 87x87x203 for 3360 time steps (100 non-dimensional time units) takes about one and a half minutes on a GeForce GTX 580 GPU card.

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“…GPUs have been used for various finite-difference scheme codes with good results [73][74][75][76][77][78]. In Ref.…”

Section: Code Parallelism With Graphics Processing Unitsmentioning

confidence: 99%

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

Carretero-González

Caplan

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We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles.Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.Due to the inherent lack of a closed form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size.The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. The codes are combined into a software package called NLSEmagic which is freely distributed on a dedicated website allowing reproducibility of the simulations presented in the study.vi

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Finite Difference Time Domain (FDTD) Simulations Using Graphics Processors

Cited by 63 publications

References 3 publications

Melhorando o Desempenho Computacional de um Esquema de Diferenças Finitas para as Equações de Maxwell

Melhorando o Desempenho Computacional de um Esquema de Diferenças Finitas para as Equações de Maxwell

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

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