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首页> 外文期刊>Journal of Computational Physics >Spatial filter averaging approach of probabilistic method to linear second-order partial differential equations of the parabolic type
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Spatial filter averaging approach of probabilistic method to linear second-order partial differential equations of the parabolic type

机译：抛物线型线性二阶偏微分方程概率方法的空间滤波平均方法

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摘要

A backward-in-time probabilistic method with spatial filter averaging is presented to solve linear second-order partial differential equations of the parabolic type. An advantage of this methodology is that while forward methods are subject to region with loss of density of particles and hence loss of spatial resolution of the solution, the solution given by backward methods is given on any desired grid. However, traditional backward time probabilistic method using Monte Carlo averaging are computationally expensive. We prove a convergence result and present several examples. The method leads to important improvement in computational efficiency and is expected to perform well to solve high dimensional problems where a solution is needed on a large grid.
机译：为了解决抛物线型线性二阶偏微分方程，提出了一种具有空间滤波平均的倒数概率方法。该方法的一个优点是，尽管前向方法会遇到粒子密度降低从而导致解决方案空间分辨率降低的区域，但后向方法给出的解决方案会在任何所需的网格上给出。然而，使用蒙特卡洛平均的传统后向时间概率方法在计算上是昂贵的。我们证明了收敛的结果并给出了几个例子。该方法导致计算效率的重要提高，并有望在解决大型网格上需要解决的高维问题时表现出色。

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