UFL Dual Spaces, a proposal

TL;DR

This paper proposes extending the Unified Form Language (UFL) to natively support dual spaces, addressing current limitations in representing dual objects and operators in finite element problems.

Contribution

It introduces a new approach to incorporate dual spaces as first-class types in UFL, enhancing its expressiveness for finite element analysis.

Findings

Sketches relevant mathematical foundations

Proposes language modifications for dual space support

Addresses limitations in current UFL implementation

Abstract

This white paper highlights current limitations in the algebraic closure Unified Form Language (UFL). UFL currently represents forms over finite element spaces, however finite element problems naturally result in objects in the dual to a finite element space, and operators mapping between primal and dual finite element spaces. This document sketches the relevant mathematical areas and proposes changes to the UFL language to support dual spaces as first class types in UFL.