Computing Derivatives for PETSc Adjoint Solvers using Algorithmic Differentiation

Understand

Most nonlinear partial differential equation (PDE) solvers require the Jacobian matrix associated to the differential operator.

• In PETSc, this is typically achieved by either an analytic derivation or numerical approximation method such as finite differences.
• For complex applications, hand-coding the Jacobian can be time-consuming and error-prone, yet computationally efficient.
• Whilst finite difference approximations are straight-forward to implement, they have high arithmetic complexity and low accuracy.