The Parallel Models of Coronal Polarization Brightness Calculation

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The Parallel Models of Coronal Polarization
Brightness Calculation

• Jiang Wenqian

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Outline

• Introduction
• pB Calculation Formula
• Serial pB Calculation Process
• Parallel pB Calculation Models
• Conclusion

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Part ?. Introduction

• Space weather forecast needs an accurate solar
  wind model for the solar atmosphere and the
  interplanetary space. The global model of corona
  and heliosphere is the basis of numerical space
  weather forecast, and the observation basis of
  explaining various relevant relations.
• Meanwhile, three-dimensional numerical
  Magnetohydrodynamics (MHD) simulation is one of
  the most common numerical methods to study corona
  and solar wind.

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Part ?. Introduction

• Besides, calculating and converting the generated
  coronal electron density to the coronal
  polarization brightness (pB) is the key method of
  comparing with observation results, and is
  important to validate the MHD models.
• Due to the massive data and the complexity of the
  pB model, the computation will cost too much time
  to visualize the pB data in nearly real time
  while using a single CPU (or core).

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Part ?. Introduction

• According to the characteristic of CPU/GPU
  computing environment, we analyze the pB
  conversion algorithm, implement two parallel
  models of pB calculation with MPI and CUDA, and
  compares the two models efficiency.

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Part ?. pB Calculation Formula

• pB is derived from electron-scattered photosphere
  radiation. It can be used in the inversion of
  coronal electron density and to validate
  numerical models. Taking limb darkening into
  account, pB calculation formula of a small
  coronal volume element is shown as followed
• 
  (1)
• 
  (2)
• 
  (3)

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Part ?. pB Calculation Formula

• The polarization brightness image for comparing
  with the observation of coronagraph can be
  generated through integrating the electron
  density along the line of sight.
• Density integral Process of pB Calculation

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Part ?. Serial pB Calculation Process

• The steps of the serial model of pB calculation
  on CPU with the experimental data are shown as
  below.
• The
  serial process of pB calculation

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Part ?. Serial pB Calculation Process

• According to the serial process of pB calculation
  above, we implement it under the environment of
  G95 on Linux and Visual Studio 2005 on Windows XP
  respectively.
• With being measured the time cost of each step,
  it is found that the most time-consuming part of
  the whole program is the calculation of pB
  values, accounting for 98.05 and 99.05 of the
  total time cost respectively.

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Part ?. Serial pB Calculation Process

• Therefore, in order to improve the performance to
  meet the command of getting coronal polarization
  brightness in nearly real-time, we should
  optimize the calculation part of pB values.
• As the density integration of each point over
  solar limb along the line of sight is
  independent, the parallel computation method is
  very suitable for pB calculation.

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Part ?. Parallel pB Calculation Models

• Currently, parallelized MHD numerical calculation
  is mainly based on MPI.
• With the development of high performance
  computation, using GPU architecture to solve
  intensive computation shows obvious advantages.
• Based on this situation, it will be an efficient
  parallel solution to implement the parallel MHD
  numerical calculation using GPU.
• We implement two parallel models based on MPI and
  CUDA respectively.

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Part ?. Parallel pB Calculation Models

• Experiment Environment
• Experimental Data
• 424282(r, ?, f) density data(den)
• 321321481(x , y, z) cartesian coordinate grid
• 321321 pB values will be generated.
• Hardware
• Intel(R) Xeon(R) CPU, E5405 _at_ 2.00GHz(8 CPUs)
• 1GB memory
• NVIDIA Quadro FX 4600 GPU, 760MB Global Memory
  GDDR3 SDRAM graphics card
• (It owns G80 kernel architecture, 12 MPs and
  128 SPs )

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Part ?. Parallel pB Calculation Models

• Experiment Environment
• Compiling Environment
• CUDA-based parallel model
• Visual Studio 2005 on Windows XP
• CUDA 1.1 SDK
• MPI-based parallel model
• G95 on Linux
• MPICH2

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Part ?. Parallel pB Calculation Models

• MPI-based Parallelized Implementation
• In the MPI environment, how the experiment
  decomposes computing domain into sub-domains is
  shown as bellow.

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Part ?. Parallel pB Calculation Models

• MPI-based Parallelized Implementation

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Part ?. Parallel pB Calculation Models

• MPI-based Parallelized Implementation
• The final result shows that MPI-based parallel
  model reaches a speedup of 5.8. As the experiment
  is implemented under the platform with 8 CPU
  cores, the speed-up ratio of the result is closed
  to its theoretical value.
• Meanwhile, it is revealed that the MPI-based
  parallel solution for the experiment has balanced
  the utilization ratio of processors and the
  communication between processors.

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Part ?. Parallel pB Calculation Models

• CUDA-based Parallelized Implementation
• According to pB serial calculation process and
  the CUDA architecture, we should put the
  calculation part into the Kernel function to
  implement the parallel program.
• Since the calculation of density interpolation
  and the cumulative sum involved in every pB value
  are independent, we can use multi-threads to
  process the pB value calculation in the CUDA, and
  each thread calculates one pB value.

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Part ?. Parallel pB Calculation Models

• CUDA-based Parallelized Implementation
• However, the pB values to be calculated is much
  larger than the available thread number of GPU,
  so each thread should calculate multiple pB
  values. According to experimental conditions, the
  thread number is setting to 256 for each block so
  as to maximize the use of computing resources.
• The block number depends on the ratio of pB
  number and thread number. In addition, since the
  access time of global memory is large, we can put
  some independent data to the shared memory to
  reduce data access time.

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Part ?. Parallel pB Calculation Models

• CUDA-based Parallelized Implementation
• The size of data put into shared memory is about
  7KB, less than 16KB provided by GPU, so the
  parallel solution is feasible.
• Moreover, the data-length array is read-only and
  its using frequency is very high, so the
  optimized strategy that the data-length array is
  migrated from shared memory into constant memory
  is adopted to further improve its access
  efficiency.
• The CUDA-based parallel calculation process is
  shown as bellow.

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Part ?. Parallel pB Calculation Models
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Part ?. Parallel pB Calculation Models

• Experiment results
• The pB calculation time of two models is shown in
  Table 1.
• Table 1. The pB calculation time of serial models
  and parallel
• models and their speed-up ratio

MPI (G95) CUDA (Visual Studio 2005)
pB calculation time of serial models(s) 32.403 48.938
pB calculation time of parallel models(s) 5.053 1.536
Speed-up ratio 6.41 31.86
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Part ?. Parallel pB Calculation Models

• Experiment results
• The total performance of two models is as shown
  in Table 2.
• Table 2. The total running-time of two parallel
  models and the speed-up ratios
• compared with their serial models

MPI (G95)(s) CUDA (Visual Studio 2005)(s) The speed-up ratio of running-time
Serial models 33.05 49.406 0.67
Parallel models 5.70 2.004 2.84
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Part ?. Parallel pB Calculation Models

• Experiment results
• Finally, we draw the coronal polarization
  brightness image shown as bellow with using
  calculated data.

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Conclusion

• Under the same environment, pB calculation time
  of MPI-based parallel model costs 5.053 seconds
  while the serial model costs 32.403 seconds. The
  models speedup is 6.41.
• The pB calculation time of CUDA-based parallel
  model costs 1.536 seconds while the serial model
  costs 48.936 seconds. The models speedup is
  31.86.
• The total running-time of CUDA-based model is
  2.84 times than that of MPI-based model.

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Conclusion

• It finds that the CUDA-based parallel model is
  more suitable for pB calculation, and it provides
  a better solution for post-processing and
  visualizing the MHD numerical calculation
  results.

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• Thank you!!!