A fast method for estimating discrete field values in early engineering design
A fast method for estimating discrete field values in early engineering design
复制标题
早期工程设计中估计离散场值的快速方法
DOI：
10.1145/218013.218096
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
J. Zagajac
中科院分区：
文献类型：
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作者：
J. Zagajac
在工程设计中所做的大部分分析都涉及到偏微分方程（PDE）的解，这些偏微分方程受初值或边值条件的约束;通常这些问题被称为“场问题”。有限元法和有限差分法（FEM，FDM）是主要的求解技术，但在设计的早期阶段使用这些方法往往过于昂贵或繁琐。我们需要的是一种快速的方法来计算在几个关键点，使用简单和强大的几何工具的字段值的估计。本文介绍了这样一种方法。它是基于一个古老的技术-通过随机（蒙特卡罗）采样集成偏微分方程-这是通过使用射线表示加速。在第一阶段（预处理），域（通常是一个机械部件）进行相干采样，以产生一个射线代表。第二阶段涉及到通常的随机采样的字段，这是现在通过利用射线代表的半离散字符增强。该方法是相对不敏感的形状的复杂性进行分析，它具有可调的精度。以拉普拉斯方程为例，说明了它的原理和优点。
Much of the analysis done in engineering design involves the solution of partial differential equations (PDEs) that are subject to initial-value or boundary-value conditions; generically these are called "field problems." Finite-element and finite-difference methods (FEM, FDM) are the predominant solution techniques, but these are often too expensive or too tedious to use in the early phases of design. What's needed is a fast method to compute estimates of field values at a few critical points that uses simple and robust geometric tools. This paper describes such a method. It is based on an old technique-integrating PDEs through stochastic (Monte Carlo) sampling-that is accelerated through the use of ray representations. In the first (pre-processing) stage, the domain (generally a mechanical part) is coherently sampled to produce a ray-rep. The second stage involves the usual stochastic sampling of the field, which is now enhanced by exploiting the semi-discrete character of ray-reps. The method is relatively insensitive to the complexity of the shape being analyzed, and it has adjustable precision. Its mechanics and advantages are illustrated by using Laplace's equation as an example.