FFCx code generation for expressions

The FEniCSx Form Compiler (FFCx) compiles the symbolic weak formulation of PDEs into C code.

Historically, its primary focus was on integral operators originating from weak forms. Using a quadrature rule it generated code to evaluate integrals. However, a number of applications appeared where symbolic UFL expressions not involving integrals needed to be compiled into C code—including interpolation into point-evaluation function spaces.

In this contribution a code generation for UFL symbolic expressions is described. Code generation and optimisation techniques of FFCx are briefly reviewed and improvements needed to compile C code for non-integral, tensor-valued expressions are described.

New functionality is demonstrated with several examples: efficient interpolation into Lagrange point-evaluation spaces and assembly of interpolation and other non-integral operators (discrete gradient, divergence, curl, etc.). Examples are prepared using the development version of FEniCSx.

It is believed that this extension to FFCx will be used in common practice by FEniCS users, improve their code performance and widen the applicability of the entire FEniCS package environment.