Automated solution of differential equations

Differential equations are solved routinely by large computer programs, but the solution process is rarely automated. Each equation requires a different program and each such program requires a considerable amount of work to develop and maintain. The FEniCS project provides a set of tools that automate important aspects of the solution process, ultimately aiming at a complete automation of computational mathematical modeling, including the automation of discretization, discrete solution, error control, modeling and optimization. A key component of FEniCS is the FEniCS Form Compiler (FFC), which automates the discretization of differential equations by taking as input a variational problem in mathematical notation and generating highly efficient optimized low-level code for the evaluation of the corresponding discrete operator.