Conference Paper
Implementation of threedimensional FPGAbased FDTD solvers: an architectural overview
EM Photonics, Inc.
DOI: 10.1109/FPGA.2003.1227265 Conference: FieldProgrammable Custom Computing Machines, 2003. FCCM 2003. 11th Annual IEEE Symposium on Source: DBLP

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ABSTRACT: Modeling, simulation and optimization using com puting tools are the core approach nowadays in science com plementary to experiment and theory. Computational Fluid Dynamics (CFD) has evolved many years ago to simulate fluid physics by solving NavierStokes equations, or its simple variants, Euler equations. However, most problems spend many hours to get solutions even with expensive supercomputers or clusters. The long computation time required for fluid dynamics simulations has lead the industry to look for some alternatives. Field Programmable Gate Arrays (FPGAs) are becoming more and more attractive for high precision scientific computations. FPGA holds the potential to alleviate this situations. It is possible for an FPGA to configure hundreds of multipliers working concurrently. In this paper, the authors explain the design on implementing the onedimensional Euler equations in hardware. Two designs with single and double floatingpoint arithmetic are developed in an FPGA. Synthesis results show that a single floatingpoint arithmetic design is consumed less area and memory usage, also operating at higher frequency. However, doubleprecision design is crucial for give a better accuracy of the result. I. INTRODUCTION01/2011;  [Show abstract] [Hide abstract]
ABSTRACT: Computational fluids dynamics(CFD) has evolved more than thirty years to simulate fluids physics by solving NavierStokes 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 firstand secondorder 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 in the case with very complex geometry boundaries. Moreover, the coefficients which appear in the govern equations usually are constants. One of our threedimensional computational case representing by the mesh including 1 million cells is programmed by Fortran90 and parallel computed on 40 Opteron 2.2GHz cpus with gigabyte interconnection, and costs around 36 cpu hours and 23 communication hours to get fluids dynamics. The computing is definitely not executed realtime. It will has problem when we try to apply sensors, actuators and the flow control theory together to adjust flow fields dynamically. The reference model in the controller is described by aforementioned partial differential equations and requiring vast computation resource. That is one reason why most current flow control applications can only operated openlooped. The authors always feel it is weird that we are using so expensive hardware, generally including several to hundreds cpus with gigabyte switching technology(e.g. Myrinet), which is usually depreciated or outdated quickly, and so complex softwares, like TCP/IP stack and parallel languages(.e.g. high performance fortran, unified parallel C) or protocol(.e.g. message passage interface), and the only cumbersome task is exchange data between cpus and the multiplication with constants. Not to mention that with even so expensive computing infrastructures, the fluids problems can be solved is still very limitive. FPGA holds potentials to alleviate the situations. Firstly, nowadays it is possible to FPGA to configure hundreds of multiplier working concurrently. That 2 Xun Huang et al. means for small computation mesh, every cell can be assigned a multiplier and all operations in every iteration can be finished at the same cycle. For big computation meshes, neighbor cells can be grouped together and the blockstructured finite difference method can be applied. The multiplication is executed serial inside the block, and parallel between blocks. It resembles the philosophy employed in supercomputers. But the cost for communications can be reduced greatly due to the complex and extensive interconnection levels(e.g. 7 layers in the ISO/OSI network model) are bypassed totally. Secondly, the computation structure is only consisted of multiplier, adder and necessary interfaces with peripheral memory or PC. The design and producing costs for this regular structured FPGA should be lower than that of cpus. By the way, the operation costs can be reduced greatly because implementations based on FPGA should consume less power than its corresponding cpu. Finally, we have to admit that current resources which FPGA holds are still too trivial to complex CFD computations. But even with this limiting capacities, computation speedup have gotten in some previous endeavors in [1][2]. The performance of FPGAbased CFD solver is decided by the availability of gates to the implementations of multipliers, rather than by main clock frequency. Until now in the semiconductor industry, the increase of the density is roughly double than the speed in every 18 months(Moore's Law). According to that trend, we predict that FPGAbased CFD solvers can prevail computerbased solvers in 20 years. With an inserted reconfigurable FPGA board on the PC bus, fluids physical scientist can do CFD experiments easily and promptly, and a standalone FPGA board can act as a realtime estimator for flow control applications. To the best of authors'knowledge, FPGA's applications for CFD are never talked before, although the NavierStokes equations is similar with the Maxwell's equations in the format. The authors hope to shed a light on the topic and communicate between ASIC engineers and CFD scientists. Next research may utilize the offtheshelf commercial FPGA evaluation board to get benchmarks for linearized Euler equations in small computation domain, and try to construct a realtime flow controller for the model predictive control system.
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