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浅水波模式半拉格朗日方法的并行研究
PARALLELIZATION OF THE SEMI-LAGRANGIAN SHALLOW-WATER MODEL USING MPI TECHNIQUES
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摘要: 该文研究的问题是分布式并行计算机消息传递方式下半拉格朗日并行算法, 重点研究二维浅水波并行模式中有关子区域过渡带(HALO)的问题和有关求解赫姆霍兹方程的并行算法。进行了一系列的对比试验, 研究在不同分辨率下模式的并行效率的问题。结果表明:采用分区域并行计算的方法, 可得到较好的并行效率。模式中使用半拉格朗日方法处理平流项是有利的, 在分辨率高时, 可有效地提高计算速度。Abstract: Parallelization of the semi-Lagrangian shallow-water model using Message Passing Interface (MPI) techniques was introduced. A detailed description of the 2-dimension semi-Lagrangian shallow-water model was made, and the model was successfully parallelized and implemented on the IBM SP2 computer, which is a distributed memory scalable parallel system.A semi-implicit semi-Lagrangian scheme, Ritchie scheme (nointerpolation), was introduced and adopted to deal with the advection term in the model, and the parallelization of the model was done by the method of standard Domain Partitioning Techniques (DPT). Special attention was paid to two key points: HALO and the parallel algorithm of Helmhotz Equation, in which the Odd-Even scheme was used. A number of comparative experiments were carried out to test the computation efficiency of serial and parallel model with different schemes.The experimental results show that higher parallel efficiency can be resulted in by the adoption of DPT. In the case of high resolution, the parallelization of semi-implicit semi-Lagrangian scheme is very efficient to cope with the advection term in the shallow-water model, and raises the computaion rate and the parallel efficiency.
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Key words:
- Semi-Lagrangian scheme;
- Parallel algorithm;
- HALO;
- Odd-Even scheme;
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图 1 三时间层半拉格朗日格式示意图
(实曲线CA为流体质点的实际轨迹。长虚线CA′为一般内插格式的近似轨迹,实直线CE为RITCHIE非内插格式的近似轨迹。D,E位于格点上。B为CA′的中点。质点在tn +Δt时位于xm。αm为质点在Δt时间所走的距离)
图 2 格点在结点上的分布示意图和HALO示意图 (在某一个结点上的格点分布)
(灰框代表本结点的HALO,是周围结点需要与本结点交换数据的格点。4条长直线所框的点为本结点的内点。本文idx和idy取为2)
图 4 (a) RITCHIE模式在不同分辨率和不同结点数下单结点的计算时间
(每一结点数从左到右分辨率依次为200,150,100,75,50 km); (b) 并行加速比; (c) 并行效率; (d) 不同分辨率不同结点数下计算量倍数的比较 (计算时间的倍数指以分辨率为200 km时的计算时间为1。结点数由上而下为1,2,4,8,16,24)
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