Conference Paper

Implementation of three-dimensional FPGA-based FDTD solvers: an architectural overview

EM Photonics, Inc.
DOI: 10.1109/FPGA.2003.1227265 Conference: Field-Programmable Custom Computing Machines, 2003. FCCM 2003. 11th Annual IEEE Symposium on
Source: DBLP

ABSTRACT Maxwell's equations, which govern electromagnetic propagation, are a system of coupled, differential equations. As such, they can be represented in difference form, thus allowing their numerical solution. By implementing both the temporal and spatial derivatives of Maxwell's equations in difference form, we arrive at one of the most common computational electromagnetic algorithms, the Finite-Difference Time-Domain (FDTD) method (Yee, 1966). In this technique, the region of interest is sampled to generate a grid of points, hereafter referred to as a mesh. The discretized form of Maxwell's equations is then solved at each point in the mesh to determine the associated electromagnetic fields. In this extended abstract, we present an architecture that overcomes the previous limitations. We begin with a high-level description of the computational flow of this architecture.

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Available from: Mark Mirotznik, Jan 16, 2014
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    • "The analysis is applied to rectangular cavity scheme, in this context the PDE solution model could be reduced to equation 9 and should be changed to a frequency domain to reduce the model size. And now the main objective of the models comparison will be: • The numerical comparison between the results given by the generalization of the equation 5 and 6 (FDTD) with the theoritical method for the Rectangular Cavity in time, making not only a comparison between a sequential process, but for parallelized scheme too [4] [5]. • And to do the same analysis for the frequency domain. "
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    ABSTRACT: PDEs in some cases require analysis not only for the analytical approach, but for any other particular numerical approach. An equation represented by vectorial operators (i.e. curl or divergence) such as Maxwell equation for example, requires a multi dimensional analysis and its model increase in some critical ways so that analytical models (i.e Fourier Expansion) [6] would be a slow strategy to frightening the Maxwell equation solution taking into account any computational implementation contextless
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    ABSTRACT: The Finite-Difference Time-Domain (FDTD) method has been used extensively for several years to analyze planar microstrip circuits. This paper presents a 3-D FDTD field compute engine design on an Virtex-4 FPGA, which is used to analyze discontinuities in planar microstrip circuits. The hardware design presented here does not grow on resources, as the problem size scales up. The paper also presents a mathematical formulation to compute the theoretical speed-up of the design. Gated clocking techniques have been used to reduce the power consumption. Details of the implemen-tation along with the results are presented, which shows that with a careful design a speed-up over a standalone PC and a lower power consumption is achieved.
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    ABSTRACT: Computational fluids dynamics(CFD) has evolved more than thirty years to simulate fluids physics by solving Navier-Stokes equations, or its simple variants, like Euler and linearized Euler equations. Most problems have to be computed on supercomputers or clusters and spend more than weeks to get solutions, or still impossible to get solutions based on nowadays computer system. Here the authors summarize the basic elements of CFD, and explore the feasibility of its implementation based on the expeditious developing FPGA techniques. The govern equations of CFD are a system of coupled differential equations, generally have first- and second-order spatial and temporal differential terms. Numerous numerical methods have been applied to represent these terms and solve the equations. One of the most commonly used methods is representing interested areas as a mesh, and approximates differential terms by the finite difference method. Hereafter the associated fluids dynamics are simulated on the corresponding finite difference equations on the mesh. Essentially to say, this method only includes operations of the multiplication and addition, even
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