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118 5. SUMMARY OF NEW SCIENTIFIC RESULTS 5.2 Application of the results 5.2.1 Application of the Fluid Flow Simulation Simulation of compressible and incompressible fluids is one of the most exciting areas of the solution of PDEs because these equations appear in many important applications in aerodynamics, meteorology, and oceanography. Modeling ocean currents plays a very important role both in medium- term weather forecasting and global climate simulations. In general, ocean models describe the response of the variable density ocean to atmospheric momentum and heat forcing. In the simplest barotropic ocean model a region of the oceans water column is vertically integrated to obtain one value for the vertically different horizontal currents. The more accurate models use several horizontal layers to describe the motion in the deeper regions of the ocean. Such a model is the Princeton Ocean Model (POM), being a sigma coordinate model in which the vertical coordinate is scaled on the water column depth. Computational Fluid Dynamics (CFD) is the scientific modeling the temporal evolution of gas and fluid flows by exploiting the enormous processing power of computer technology. Simulation of fluid flow over complex shaped objects currently requires several weeks of computing time on high performance supercomputers. The developed CFD simulation architecture, implemented on FPGA, is several order of magnitude faster than todays microprocessors. 5.2.2 Examining the accuracy of the results In real life engineering application double precision floating point numbers are used for computations to avoid issues of roundoff error. However it is worth to examine the required precision, if the computing resources, power dissipation or size is limited or the computation should be carried out in real time. The speed of the partial differential equation solver architecture implemented on FPGA can be greatly increase, if we decrease the precision of the solver architecture, consequently more processing unit can be implemented on the same area. This thesis is useful if we want to investigate the limitation of a real time computation. I have examined a simplified advection equation solver architecture, where the analytic
5.2 Application of the results 119 solution is known. With the minimal modification of such problems (which has analytic solution), the computed precision is remaining probably acceptable with a similar problem, which has no analytic solution. 5.2.3 The importance of Global Analogic Programming Unit In order to provide high flexibility in CNN computations, it is interesting how we can reach large performance by connecting locally a lot of simple and relatively low-speed parallel processing elements, which are organized in a regular array. The large variety of configurable parameters of this architecture (such as stateand template-precision, size of templates, number of rows and columns of processing elements, number of layers, size of pictures, etc.) allows us to arrange an implementation, which is best suited to the target application (e.g. image/video processing). So far, without the GAPU extension, when solving different types of PDEs, a single set of CNN template operations has been implemented on the host PC: by downloading the image onto the FPGA board (across a quite slow parallel port), computing the transient, and finally uploading the result back to the host computer where logical, arithmetic and program organizing steps were executed. Reconfigurable CNN-UM implementation on FPGAs may also mean a possible breakthrough point towards industrial applications, due to their simplicity, high computing power, minimal cost, and fast prototyping.
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An Optimal Mapping of Numerical Sim
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Acknowledgements It is not so hard
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Contents 1 Introduction 1 1.1 Cellu
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CONTENTS iii 4.3.3 Operating Steps
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vi LIST OF FIGURES 2.4 Performance
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List of Tables 2.1 Comparison of di
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xii LIST OF ABBREVIATIONS FPE Falco
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Chapter 1 Introduction Due to the r
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3 can be represented in arbitrary t
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1.1 Cellular Neural/Nonlinear Netwo
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1.2 Cellular Neural/Nonlinear Netwo
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1.3 CNN-UM Implementations 9 the Lo
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1.3 CNN-UM Implementations 11 modif
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1.4 Field Programmable Gate Arrays
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1.5 IBM Cell Broadband Engine Archi
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Chapter 2 Mapping the Numerical Sim
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2.1 Introduction 37 18 Load instruc
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2.1 Introduction 39 Instruction his
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2.1 Introduction 41 2E+07 1E+07 9E+
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2.1 Introduction 43 Main memory 8 t
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2.1 Introduction 45 6 4.5 3 Speedup
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2.1 Introduction 47 2.50E+07 1.88E+
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2.2 Ocean model and its implementat
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2.2 Ocean model and its implementat
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2.3 Computational Fluid Flow Simula
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