Interconnected Infinite-Dimensional systems for Heterogeneous Media (INFIDHEM): Scrimp

This archive is related to software developments proposed during the ANR-16-CE92-0028 project, entitled "Interconnected Infinite-Dimensional systems for Heterogeneous Media" (INFIDHEM) funded by the French National Research Agency (ANR) and the Deutsche Forschungsgemeinschaft (DFG). The focus is made on SCRIMP (Simulation and ContRol of Interactions in Multi-Physics), a Python project for the numerical approximation of boundary controlled partial differential equations (PDEs) using the port-Hamiltonian formalism. Within the INFIDHEM project, the main motivation behind the development of SCRIMP was to provide an easy-to-use framework for the numerical solution of infinite-dimensional port-Hamiltonian systems both for research and educational purposes. Numerical approximations with conforming or non-conforming finite element discretizations are handled through the popular finite element software FEniCS (https://fenicsproject.org/). Applications to various two- or three-dimensional model problems based on parabolic or hyperbolic partial differential equations are tackled. Several notebooks are provided to demonstrate the use of SCRIMP within this framework. Are available: * a README file related to the installation of FEniCS and dependencies, * a tutorial guide to SCRIMP "Numerical approximation of structure-preserving discretization of infinite-dimensional port-Hamiltonian systems: a tutorial guide to SCRIMP" by Andrea Brugnoli, Anass Serhani, Xavier Vasseur (tutorial.pdf), * Python and Notebook files related to SCRIMP.本归档文件关联的是ANR-16-CE92-0028项目中提出的软件开发成果，该项目由法国国家科研署（French National Research Agency, ANR）与德国研究基金会（Deutsche Forschungsgemeinschaft, DFG）资助，项目全称为“面向异构介质的互联无限维系统（Interconnected Infinite-Dimensional systems for Heterogeneous Media, INFIDHEM）”。本项目的核心研究对象为SCRIMP（多物理场交互模拟与控制，Simulation and ContRol of Interactions in Multi-Physics），这是一款基于Python的开源项目，用于采用端口哈密顿形式体系（port-Hamiltonian formalism）对边界受控偏微分方程（partial differential equations, PDEs）开展数值近似求解。在INFIDHEM项目框架下，开发SCRIMP的核心动机是为科研与教学场景提供一款易用的工具框架，用于求解无限维端口哈密顿系统的数值解。本项目依托主流有限元软件FEniCS（https://fenicsproject.org/），可支持协调与非协调有限元离散格式的数值近似计算。本项目覆盖了基于抛物型或双曲型偏微分方程的各类二维、三维模型问题的应用案例，并提供了多份演示Notebook文件，用于展示SCRIMP在该框架下的使用方法。本次归档包含以下可用资源：* 一份关于FEniCS及其依赖项安装的README文档；* 一份由Andrea Brugnoli、Anass Serhani、Xavier Vasseur撰写的SCRIMP教程《无限维端口哈密顿系统保结构离散的数值近似：SCRIMP教程指南》（tutorial.pdf）；* 与SCRIMP相关的Python脚本与Notebook文件。