一种基于正弦变换的三维泊松方程并行求解算法

发布时间：2018-11-06 14:57

【摘要】：泊松方程的数值解法在许多物理或者工程问题上得到广泛应用,但是由于大部分三维泊松方程的离散化格式不具有明显的并行性,实际中使用整体迭代的思想,这使得计算效率和稳定性受到了限制。摒弃了传统数值解法中整体迭代的思想,结合离散正弦变换理论(DST),基于27点四阶差分格式,将三维泊松方程求解算法在算法级进行修改和并行优化,把整个求解问题转化成多个独立的问题进行求解,稳定性和并行性能得到大幅提升。对于确定的离散化形式,可以使用同一套参数解决不同的泊松方程,大大提高了编程效率。基于共享存储并行模型实现了该算法,实验结果显示,对于给出的实例,新算法具有较好的加速效果,计算结果精度误差约为10e-5,在可接受范围内,并且计算精度随着维数的升高具有一定提升。
[Abstract]:The numerical solution of Poisson equation is widely used in many physical or engineering problems. However, because most of the discretization schemes of the three-dimensional Poisson equation do not have obvious parallelism, the idea of global iteration is used in practice. This limits the computational efficiency and stability. In this paper, the idea of global iteration in traditional numerical solution is abandoned. Based on the 27 point fourth-order difference scheme, the three-dimension Poisson equation solving algorithm is modified and optimized in parallel with the discrete sinusoidal transform theory (DST), which is based on the 27-point fourth-order difference scheme. The stability and parallel performance are greatly improved by transforming the whole problem into a number of independent problems. For the definite discretization form, the same set of parameters can be used to solve different Poisson equations, which greatly improves the programming efficiency. The algorithm is implemented based on the shared memory parallel model. The experimental results show that the new algorithm has a good acceleration effect for the given example, and the accuracy error of the calculation results is about 10e-5, which is within the acceptable range. And the accuracy of calculation increases with the increase of dimension.
【作者单位】：国防科技大学计算机学院;海军海洋水文气象中心;国防科技大学海洋科学与工程研究院;
【基金】：国家自然科学基金(41375113)
【分类号】：O246

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