FiniteEleme

FiniteEleme is an open-source software framework for finite element analysis and simulation. It provides a modular platform for formulating, discretizing, solving, and visualizing partial differential equation–based problems across engineering and physical sciences. The project emphasizes portability, extensibility, and performance, with the aim of supporting researchers and engineers in developing custom simulations and educational tools.

At its core, FiniteEleme comprises mesh data structures, element libraries, assembly routines, and solver backends. The mesh abstraction covers 2D and 3D domains with common element types such as triangles, quadrilaterals, tetrahedra, and hexahedra, including options for higher-order geometries. The framework translates variational forms into system matrices and vectors, applies boundary conditions, and supports both static and dynamic problems. It includes parallel execution support through MPI and multi-threading, and offers a Python interface alongside a performance-oriented C++ core for rapid prototyping and production use.

FiniteEleme covers linear and nonlinear material models and enables multiphysics couplings, including structural mechanics, heat transfer, and basic fluid-structure interaction. It provides a range of linear and nonlinear solvers, preconditioners, and time integration schemes, as well as post-processing hooks for extracting results. Interoperability with standard mesh and result formats—such as VTK, XDMF, and Exodus—facilitates integration with external visualization and workflow tools.

Developed by a distributed community of researchers and practitioners, FiniteEleme is released under an open-source license. The project maintains documentation, tutorials, API references, and a library of example problems to illustrate concepts and methods. Typical workflows include geometry and mesh creation, specification of variational forms, selection of element families and solvers, execution of simulations, and analysis of results.

FiniteEleme has been used in academic courses and research projects to compare numerical methods and to prototype new constitutive models. Its design emphasizes clarity and extensibility, making it a resource for both education and applied engineering studies.