【Hacker News搬运】有限元法八十年（2022）

hackernews

Title: Eighty Years of the Finite Element Method (2022)

有限元法八十年（2022）

Text:

Url: https://link.springer.com/article/10.1007/s11831-022-09740-9

很抱歉，作为一个AI，我无法直接访问或分析外部链接，如Springer链接中的学术文章。不过，我可以提供一般性的指导，说明如何使用JinaReader或其他工具来抓取、分析和总结文章内容，以及如何处理非中文内容。

以下是一个使用JinaReader进行内容抓取、分析和总结的步骤概述：

1. **设置JinaReader**：
   - 首先，您需要安装JinaReader或类似的工具，并设置它以抓取指定链接的内容。

2. **抓取内容**：
   - 使用JinaReader的爬虫功能，指向上述链接以抓取文章内容。

3. **内容预处理**：
   - 一旦抓取到内容，可能需要进行预处理，例如去除HTML标签、广告和其他无关信息。

4. **语言检测**：
   - 如果文章不是中文，您需要使用JinaReader中的语言检测功能来识别文章的语言。

5. **翻译**：
   - 对于非中文内容，您可以使用JinaReader集成的翻译功能，将文章翻译成中文。

6. **内容分析**：
   - 使用JinaReader的自然语言处理（NLP）工具来分析文本，这可能包括关键词提取、主题建模、情感分析等。

7. **内容总结**：
   - 根据分析结果，使用JinaReader的总结功能来生成文章的摘要或总结。

以下是一个简化的代码示例，展示了如何使用伪代码进行上述步骤：

```python
# 伪代码示例

# 设置JinaReader
jina_reader = JinaReader()

# 抓取内容
article_content = jina_reader.crawl("https://link.springer.com/article/10.1007/s11831-022-09740-9")

# 预处理内容
processed_content = jina_reader.preprocess(article_content)

# 语言检测
language = jina_reader.detect_language(processed_content)

# 如果不是中文，则翻译
if language != 'zh':
    translated_content = jina_reader.translate(processed_content, target_language='zh')

# 内容分析
analysis_results = jina_reader.analyze(translated_content)

# 生成总结
summary = jina_reader.summarize(analysis_results)

# 输出总结
print(summary)

请注意，上述代码是伪代码，实际使用时需要根据JinaReader的具体API和功能来实现。如果您需要具体的实现代码，建议参考JinaReader的官方文档或示例代码。

        
## Post by: sandwichsphinx
        
### Comments: 
        
**angry_moose**: I&#x27;ve been a full-time FEM Analyst for 15 years now. It&#x27;s generally a nice article, though in my opinion paints a far rosier picture of the last couple decades than is warranted.<p>Actual, practical use of FEM has been stagnate for quite some time. There have been some nice stability improvements to the numerical algorithms that make highly nonlinear problems a little easier; solvers are more optimized; and hardware is of course dramatically more capable (flash storage has been a godsend).<p>Basically every advanced&#x2F;&quot;next generation&quot; thing the article touts has fallen flat on its face when applied to real problems. They have some nice results on the world&#x27;s simplest &quot;laboratory&quot; problem, but accuracy is abysmal on most real-world problems - e.g. it might give good results on a cylinder in simple tension, but fails horribly when adding bending.<p>There&#x27;s still nothing better, but looking back I&#x27;m pretty surprised I&#x27;m still basically doing things the same way I was as an Engineer 1; and not for lack of trying. I&#x27;ve been on countless development projects that seem promising but just won&#x27;t validate in the real world.<p>Industry focus has been far more on Verification and Validation (ASME V&amp;V 10&#x2F;20&#x2F;40) which has done a lot to point out the various pitfalls and limitations. Academic research and the software vendors haven&#x27;t been particularly keen to revisit the supposedly &quot;solved&quot; problems we&#x27;re finding.
> **angry_moose**: 我；我做了15年的全职有限元分析。它；总的来说，这是一篇不错的文章，尽管在我看来，这篇文章对过去几十年的描绘要乐观得多<p> 有限元法的实际应用已经停滞了相当长的一段时间。对数值算法进行了一些很好的稳定性改进，使高度非线性问题变得更容易；求解器更加优化；当然，硬件的性能要高得多（闪存一直是天赐之物）<p> 基本上每一个高级&“；下一代”；当应用于实际问题时，这篇文章所宣扬的东西已经完全失败了。他们在世界上取得了一些不错的成绩；最简单的&quot；实验室”；这个问题，但在大多数现实世界的问题上，精度都很糟糕——例如，它可能会在简单的张力下对圆柱体产生很好的效果，但在增加弯曲时会严重失败<p> 那里；这仍然没有什么好的，但回想起来，我；我很惊讶；我基本上还是像工程师一样做事；而不是因为缺乏尝试。我；我参与过无数看似有前途但刚刚获胜的开发项目；在现实世界中无法验证<p> 行业重点更多地放在验证和确认（ASME V&amp；V 10x20x20）上，该标准在指出各种陷阱和局限性方面做了很多工作。学术研究和软件供应商避风港；我并不特别热衷于重新审视所谓的&quot；已解决”；我们面临的问题；重新发现。
            
**weinzierl**: I started my career doing FE modeling and analysis with ANSYS and NASTRAN. Sometimes I miss these days. Thinking about how to simplify a real world problem so far that it is solvable with the computational means available was always fun. Then pushing quads around for hours until the mesh was good had an almost meditative effect. But I don&#x27;t feel overwhelmingly eager to learn a new software or language.<p>Much to my surprise, it seems there hasn&#x27;t been much movement there. ANSYS still seems to be the leader for general simulation and multi-physics. NASTRAN still popular. Still no viable open-source solution.<p>The only new player seems to be COMSOL. Has anyone experience with it? Would it be worth a try for someone who knows ANSYS and NASTRAN well?
> **weinzierl**: 我的职业生涯始于使用ANSYS和NASTRAN进行有限元建模和分析。有时我会想念这些日子。思考如何简化一个现实世界的问题，直到它可以用可用的计算手段解决，总是很有趣的。然后将四边形推几个小时，直到网格很好，这几乎有一种冥想的效果。但我不知道；我并不急于学习一种新的软件或语言<p> 令我惊讶的是，似乎还没有；那里没有太多动静。ANSYS似乎仍然是通用模拟和多物理场的领导者。NASTRAN仍然很受欢迎。仍然没有可行的开源解决方案<p> 唯一的新玩家似乎是COMSOL。有人有经验吗？对于熟悉ANSYS和NASTRAN的人来说，值得一试吗？
            
**kaonwarb**: I also studied FEM in undergrad and grad school. There&#x27;s something very satisfying about breaking an intractably difficult real-world problem up into finite chunks of simplified, simulated reality and getting a useful, albeit explicitly imperfect, answer out of the other end. I find myself thinking about this approach often.
> **kaonwarb**: 我还在本科和研究生阶段学习了有限元法。那里；将一个难以解决的现实世界问题分解为有限的简化模拟现实，并从另一端得到一个有用的（尽管明显不完美）答案，这是非常令人满意的。我发现自己经常思考这种方法。
            
**niraj-agarwal**: Predicting how things evolve in space-time is a fundamental need. Finite element methods deserve the glory of a place at the top of the HN list. I opted for &quot;orthogonal collocation&quot; as the method of choice for my model back in the day because it was faster and more fitting to the problem at hand. A couple of my fellow researchers did use FEM. It was all the rage in the 90s for sure.
> **niraj-agarwal**: 预测事物在时空中的演变是一项基本需求。有限元方法值得在HN列表中名列前茅。我选择了&quot；正交搭配”；作为我当年模型的选择方法，因为它更快，更适合手头的问题。我的几个同事确实使用了有限元法。毫无疑问，这在90年代风靡一时。
            
**pvg**: A 45 comment thread at the time <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=33480799">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=33480799</a>
> **pvg**: 当时有一个45条评论的帖子<A href=“https:&#x2F；news.ycombinator.com&#x2M；item？id=33480799”>https:&#x2F；news.ecombinator.com；项目？id=33480799</a>