PolyDiM
C++ library for POLYtopal DIscretization Methods
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The PolyDiM library

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PolyDiM (POLYtopal DIscretization Methods) is a numerical library for solving partial differential equations (PDEs) using discretization techniques on general polytopal (polygonal and polyhedral) meshes.

The library is developed within the Numerical Analysis Group of the Department of Mathematical Sciences “Giuseppe Luigi Lagrange” (DISMA) at Politecnico di Torino, and is based on its long-standing research activity in numerical methods for PDEs.

Methods

The following methods have been implemented and tested:

  • FEM (Finite Element Method) - A widely used numerical method for solving partial differential equations (PDEs), which discretizes a continuous domain into smaller local subdomains (finite elements).
  • VEM (Virtual Element Method) - An advanced numerical method that extends FEM to general polygonal and polyhedral meshes, offering greater flexibility and high accuracy.

New numerical methods and extensions are continuously being developed and integrated into the library.

Features

The library's key features include:

  • High-order accuracy: supports arbitrary polynomial degrees for improved solution precision.
  • General mesh support: works natively with polygonal and polyhedral meshes.
  • Modular and extensible design: enables easy definition of custom PDE problems, meshes, and solvers.
  • Wide range of applications: suitable for linear and nonlinear elliptic problems, including Poisson, elasticity, Navier–Stokes equations, and coupled problems.

GeDiM

PolyDiM is tightly integrated with GeDiM, a geometry discretization library developed by the same authors.

GeDiM provides core functionality for computing geometric properties of mesh elements used in numerical simulations. It also includes tools for mesh generation, refinement, agglomeration, and a set of utilities and solvers for geometric processing in scientific computing.

External libraries

PolyDiM currently interfaces and exploits the following libraries:

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Installation Guide