poly_rust：面向多面体方法的领域专用语言及Rust解释器

中文摘要 AI 辅助

本文介绍poly_rust，这是一个实现多面体方法领域专用语言的新软件库。多面体方法支持的网格比传统有限元方法所基于的网格通用得多，这可通过放弃全局函数空间，通过求解局部变分问题直接从自由度重构相关算子来实现，重构结果随后在全局变分公式中取代形函数。poly_rust提供了用与数学表述极为相似的语法表达多种多面体方法的功能，本文从基础用户视角综述该库的主要方面，并提供涵盖多个问题和方法的数值示例。

英文摘要

Background: Over the last two decades, considerable effort in the applied mathematics community has been devoted to the development of polytopal methods, i.e., numerical methods for partial differential equations that support meshes more general than those used by traditional finite element methods. Despite their flexibility and attractive mathematical properties, polytopal methods have a steep implementation curve and, to date, no easily accessible open-source software framework has been available for their systematic implementation. Methods: In this article, we introduce poly_rust, a new software library implementing a domain-specific language (DSL) specifically designed for polytopal methods. poly_rust provides high-level constructs for expressing a wide range of such methods using a syntax that closely mirrors their mathematical formulation, thereby substantially lowering the implementation barrier for both newcomers and experienced users. Results: The library facilitates the rapid implementation, testing, and comparison of polytopal discretizations, making these methods more accessible to researchers, applied scientists, engineers, and students. In our vision, this will foster their dissemination beyond the numerical analysis community and encourage their adoption by practitioners in a broad range of application fields. It will also contribute to reproducibility of results, as DSL files are text files that can be easily made available, stored, and exchanged. Conclusions: poly_rust introduces, to our knowledge, the first DSL specifically tailored to polytopal methods. By combining mathematical expressiveness, ease of implementation, and an open-source framework, it provides a common platform for developing, sharing, reproducing, and comparing polytopal schemes, with the ambition of becoming a reference tool for the wider scientific community.

发表机构

• Université de Montpellier（蒙彼利埃大学）

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