POLYDIM: A C++ library for POLYtopal DIscretization Methods

TL;DR

PolyDiM is an open-source C++ library that facilitates polytopal discretization methods, especially the Virtual Element Method, for complex PDE problems in 2D and 3D, supporting advanced geometries and multiple interfaces.

Contribution

The paper presents PolyDiM, a modular, robust C++ library that supports advanced polytopal discretization techniques with features like multiple bases and stabilization strategies, integrated with GeDiM and accessible via MATLAB and Python.

Findings

Supports complex geometries including non-convex domains.

Provides interfaces for MATLAB and Python for broader accessibility.

Enables scalable scientific computing with efficient assembly procedures.

Abstract

This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support advanced numerical techniques, with a focus on the Virtual Element Method in both 2D and 3D settings. PolyDiM is designed to address a wide range of challenging problems, including those involving non-convex geometries, Discrete Fracture Networks, and mixed-dimensional coupling. It is integrated with the geometry library GeDiM, and offers interfaces for MATLAB and Python to enhance accessibility. Distinguishing features include support for multiple polynomial bases, advanced stabilization strategies, and efficient local-to-global assembly procedures. PolyDiM aims to serve both as a research tool and a foundation for scalable scientific computing in complex geometrical settings.