Making automatic differentiation truly automatic: coupling PETSc with ADIC

Despite its name, automatic differentiation (AD) is often far from an automatic process. Often one must specify independent and dependent variables, indicate the derivative quantities to be computed, and perhaps even provide information about the structure of the Jacobians or Hessians being computed. When AD is used in conjunction with a toolkit with well-defined interfaces, however, many of these issues can be dealt with automatically. We describe recent research into coupling the ADIC automatic differentiation tool with PETSc, a toolkit for the parallel numerical solution of PDEs. This research leverages the interfaces and objects of PETSc to make the AD process very nearly invisible.