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52 2. MAPPING THE NUMERICAL SIMULATIONS OF PARTIAL DIFFERENTIAL EQUATIONS open, the grid size is 128×128 and the grid resolution is 8km. The simulation timestep is 6s and 360 iterations are computed. The results are shown in Figure 2.2. Experimental results of the average iteration time are summarized on Table 2.3. Table 2.2: The initial state, and the results of the simulation after a couple of iteration steps. Where the x- and y-axis models 1024km width ocean (1 untit is equal to 2.048km).
2.3 Computational Fluid Flow Simulation on Body Fitted Mesh Geometry with IBM Cell Broadband Engine and FPGA Architecture 53 Table 2.3: Comparison of different CNN ocean model implementations: 2GHz CORE 2 DUO processor, Emulated Digital CNN running on Cell processors CNN Implementations Parameters Core 2 Duo CELL (8 SPEs) Iteration time ( ms) 8.2 1.11 Computation time of a 354.2 47.52 72 hour simulation (s) Power (W) 65 85 Area (mm 2 ) 143 253 (CNN cell array size: 128×128, 1 iteration) 2.3 Computational Fluid Flow Simulation on Body Fitted Mesh Geometry with IBM Cell Broadband Engine and FPGA Architecture 2.3.1 Introduction In the paper of Kocsárdi et. al the authors applied the finite volume Lax-Friedrich [53, 54] scheme for solving 2D Euler equations over uniformly spaced rectangular meshes [55]. However, most real life applications of CFD require handling more complex geometries, bounded by curved surfaces. A popular and often an efficient solution to this problem is to perform the computation over non-uniform, logically structured grids. Technically, this idea can be exploited either by employing body fitted grids or by performing the computation in a curvilinear coordinate frame following the curvature of the boundaries. Although in the latter approach the standard 2D scheme over Cartesian geometry can be put to work, it is computationally much more demanding than the former one, due to the expensive operations related to coordinate transformation. There is a number of reasons why we have chosen the IBM Cell multiprocessor system as the restricted (bounded) architecture, namely, its high computing performance, the double-precision floating point number support, the support of the standard multiprocessing libraries, such as OpenMP or MPI and the freely available software development kit.
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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
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+
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 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
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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
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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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