We present the library \texttt{lymph} for the finite element numerical discretization of coupled multi-physics problems. \texttt{lymph} is a Matlab library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the paper is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting -- when necessary -- key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the paper, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, and the elastodynamics system. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e. geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters.

翻译：本文介绍了用于耦合多物理场问题有限元数值离散的lymph库。lymph是一款基于高阶不连续伽辽金方法（PolyDG）在多面体网格上进行空间离散，并结合合适有限差分时间推进格式求解偏微分方程的Matlab库。本文旨在通过描述该库的安装、输入/输出数据及代码结构来介绍lymph，并在必要时重点说明与该方法相关的关键实现环节。同时提供了逐步实施和求解泊松问题的用户指南。在论文最后部分，我们展示了针对多个微分问题（即泊松问题、热传导方程及弹性动力学系统）的计算结果。通过这些算例，我们验证了该方法的收敛特性，并凸显其几何灵活性、高阶精度及对异质物理参数的鲁棒性等主要优势。