Unified Framework for Finite Element Assembly

TL;DR

This paper introduces UFC, a universal interface for finite element assembly that simplifies implementation, enhances flexibility, and supports various finite element methods without external dependencies.

Contribution

The paper presents UFC, a novel, general interface for finite element assembly that is independent of mesh and linear algebra components, supporting diverse methods.

Findings

Supports a wide range of finite element problems.

Enables implementation independence from mesh and linear algebra.

Released as public domain software.

Abstract

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.