Lymph: discontinuous poLYtopal methods for Multi-PHysics differential problems

We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. 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 article 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 article, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, the elastodynamics system, and a multi-physics problem coupling poroelasticity and acoustic equations. 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.