PPKE ITK PhD and MPhil Thesis Classes

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64 2. MAPPING THE NUMERICAL SIMULATIONS OF PARTIAL DIFFERENTIAL EQUATIONS coordinate transformations. The number of slices, multipliers and block-RAMs of the arithmetic unit can be seen in Figure (2.15)-(2.17) respectively. 2.00E+05 1.50E+05 1.00E+05 5.00E+04 Number of slices 0E+00 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 Precision Figure 2.15: Number of slices in the arithmetic unit To show the efficiency of our solution a complex test case was used, in which a Mach 3 flow around a cylinder was computed. The direction of the flow is from left to right and the speed of the flow at the left boundary is 3-times the speed of sound constantly. The solution contains a symmetrical bow shock flow around the cylinder. Therefore, only the upper half of the region should be simulated. This problem was solved on a 128 × 256 grid, which was bent over the cylinder using 2ms timestep. Result of the computation after 1s of simulation time is shown in Figure 2.18. The experimental results of the average computation time are compared to a Intel Core2Duo microprocessor is shown on Table 2.4. The Cell based solution is 35 times faster compared to that of a high performance microprocessor, even using a single SPE during the computation. Utilizing all the 16 SPEs of the IBM CellBlade the computation can be carried out two orders of magnitude faster, while the FPGA solution is three order of magnitude
2.3 Computational Fluid Flow Simulation on Body Fitted Mesh Geometry with IBM Cell Broadband Engine and FPGA Architecture 65 3000 2250 1500 750 Number of Multipliers 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 Precision (bit) Figure 2.16: Number of multipliers in the arithmetic unit faster. The power dissipation and the area of the architectures are in the same range. 2.3.3 Conclusion Complex spatio-temproral dynamical problems are analyzed by a topographic array processor. A CNN simulation kernel was implemented on the Cell architecture and was optimized according to the special requirements of the IBM Cell processor. By using this kernel both linear and nonlinear CNN arrays can be simulated. Based on the basic CNN simulation kernel a framework was developed to compare the optimal mapping of the simulation of a complex spatio-temporal dynamics on Xilinx Virtex FPGA and on IBM Cell architecture. The framework has been tested by the acceleration of a computational fluid dynamics (CFD) simulation. During the implementation the goal was to reach the highest possible computational performance. The governing equations of two dimensional compressible Newtonian flows on body fitted mesh geometry were solved by using different kind of Xilinx Virtex 5 FPGAs and by using the IBM QS22 and LS22 systems. The Falcon proces-
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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
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+
Page 63 and 64: 2.1 Introduction 43 Main memory 8 t
Page 65 and 66: 2.1 Introduction 45 6 4.5 3 Speedup
Page 67 and 68: 2.1 Introduction 47 2.50E+07 1.88E+
Page 69 and 70: 2.2 Ocean model and its implementat
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Page 73 and 74: 2.3 Computational Fluid Flow Simula
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Page 89 and 90: Chapter 3 Investigating the Precisi
Page 91 and 92: 3.2 Numerical Solutions of the PDEs
Page 93 and 94: 3.3 Testing Methodology 73 In fixed
Page 95 and 96: 3.4 Properties of the Arithmetic Un
Page 97 and 98: 3.4 Properties of the Arithmetic Un
Page 99 and 100: 3.5 Results 79 in the L2 cache of t
Page 101 and 102: 3.5 Results 81 1E-02 1E-03 Error 1E
Page 103 and 104: 3.5 Results 83 arithmetic unit requ
Page 105: 3.6 Conclusion 85 point and the 40
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114 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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