PPKE ITK PhD and MPhil Thesis Classes

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48 2. MAPPING THE NUMERICAL SIMULATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 2.00E+09 1.50E+09 1.00E+09 5.00E+08 million cell iteration/s 0E+00 SPE 1 SPE 2 SPE 4 SPE 8 Performance (A) Performance (B) Figure 2.11: Performance comparison of one and multiple SPEs almost 24% more than if the nonlinearity is partitioned into four parts (B) as seen in Figure 2.11. The performance depends not only on the number of segments, but also on the number of SPEs as in the linear case. So if the number of SPEs increases, the performance of the simulations increases in the same way. 2.1.1.3 Performance comparisons The performance of the implementation on the Cell architecture was tested by running the global maximum finder template on a 256×256 image for 16 iterations. The achievable performance of the Cell using different number of SPEs is compared to the performance of the Intel Core 2 Duo T7200 2GHz scalar processor and the linear and nonlinear Falcon Emulated Digital CNN-UM architecture. The results are shown in Figure 2.4. Comparison of the performance of the single SPE solution to a high performance microprocessor in the linear case showed that about 6 times speedup can be achieved. By using all the 8 SPEs about 35 times speedup can be achieved. Compared to emulated digital architectures one SPE
2.2 Ocean model and its implementation 49 Table 2.1: Comparison of different CNN implementations: 2GHz CORE 2 DUO processor, Emulated Digital CNN running on Cell processors and on Virtex 5 SX240T FPGA, and Q-EYE with analog VLSI chip CNN Implementations Parameters Core 2 Duo Q-Eye FPGA CELL (8 SPEs) Speed (linear template, µs) 4092.6 250 737.2 111.8 Speed (nonlinear template, µs) 84691.4 - 737.2 197.33 Power (W) 65 0.1 20 85 Area (mm 2 ) 143 - 389 253 (CNN cell array size: 176×144, 16 forward Euler iterations) can outperform a single Falcon Emulated Digital CNN-UM core implemented on XC5VSX240T Xilinx FPGA. When using nonlinear templates the performance advantage of the Cell architecture is much higher. In a single SPE configuration 64 times speedup can be achieved while using 8 SPEs the performance is 429 times higher. Typical computing time of one template operation along with area and power requirements of the different architectures are summarized on Table 2.1. Let us mention that solution of a given computational problem can be much faster implemented in a Cell architecture then on FPGA. 2.2 Ocean model and its implementation Several studies proved the effectiveness of the CNN-UM solution of different PDEs [15] [16]. But the results cannot be used in real life implementations due to the limitations of the analog CNN-UM chips such as low precision, temperature sensitivity or the application of non-linear templates. Some previous results show that emulated digital architectures can be very efficiently used in the computation of the CNN dynamics [45] [28] and in the solution of PDEs [46] [47] [30]. Using the CNN simulation kernel described in the previous sections helped to solve Navier-Stokes PDE on the Cell architecture.
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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
Page 18 and 19: xii LIST OF ABBREVIATIONS FPE Falco
Page 21 and 22: Chapter 1 Introduction Due to the r
Page 23 and 24: 3 can be represented in arbitrary t
Page 25 and 26: 1.1 Cellular Neural/Nonlinear Netwo
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Page 33 and 34: 1.4 Field Programmable Gate Arrays
Page 47 and 48: 1.5 IBM Cell Broadband Engine Archi
Page 55 and 56: Chapter 2 Mapping the Numerical Sim
Page 57 and 58: 2.1 Introduction 37 18 Load instruc
Page 59 and 60: 2.1 Introduction 39 Instruction his
Page 61 and 62: 2.1 Introduction 41 2E+07 1E+07 9E+
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Page 65 and 66: 2.1 Introduction 45 6 4.5 3 Speedup
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Page 73 and 74: 2.3 Computational Fluid Flow Simula
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Page 91 and 92: 3.2 Numerical Solutions of the PDEs
Page 93 and 94: 3.3 Testing Methodology 73 In fixed
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Page 99 and 100: 3.5 Results 79 in the L2 cache of t
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4. IMPLEMENTING A GLOBAL ANALOGIC P
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110 5. SUMMARY OF NEW SCIENTIFIC RE
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References The author’s journal p
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5.2 Application of the results 123
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