An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

Understand

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used.

• They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method.
• In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE constrained optimization.
• In order to develop an efficient fully time-parallel algorithm we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and adjoint equations simultaneously.