DOLFIN: Automated Finite Element Computing

TL;DR

DOLFIN is a library that automates finite element PDE solutions by translating high-level mathematical descriptions into efficient code, integrating mesh handling and linear algebra for high performance.

Contribution

It introduces novel automated code generation techniques for finite element methods, combining expressiveness with computational efficiency.

Findings

Supports near-mathematical notation for variational forms

Automatically generates and compiles low-level code

Provides object-oriented interfaces in C++ and Python

Abstract

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.