Medusa: A C++ Library for solving PDEs using Strong Form Mesh-Free methods

TL;DR

Medusa is a flexible C++ library that facilitates the implementation and comparison of strong form mesh-free methods for solving PDEs, supporting experimentation with different algorithms and applications in elasticity and fluid flow.

Contribution

It introduces a modular library design that abstracts core mesh-free components, enabling researchers to easily develop, test, and compare various methods.

Findings

Provides flexible implementation of mesh-free methods

Demonstrates application in elasticity and fluid flow problems

Includes performance benchmarks

Abstract

Medusa, a novel library for implementation of strong form mesh-free methods, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection and stencil weight computation. Many different algorithms exist for each part and the possible combinations offer a plethora of possibilities for improvements of solution procedures that are far from fully understood. As a consequence there are still many unanswered questions in mesh-free community resulting in vivid ongoing research in the field. Medusa implements the core mesh-free elements as independent blocks, which offers users great flexibility in experimenting with the method they are developing, as well as easily comparing it with other existing methods. The paper describes the chosen abstractions and their usage, illustrates aspects of the philosophy and design, offers some executions time benchmarks and demonstrates the application of the library on cases from linear elasticity and fluid flow in irregular 2D and 3D domains.