TriMGRIT: An Extension of Multigrid Reduction in Time for Constrained Optimization

Robert Falgout (Lawrence Livermore National Laboratory)

Since clock speeds are no longer increasing, time integration is becoming a sequential bottleneck. The multigrid reduction in time (MGRIT) algorithm is an approach for creating concurrency in the time dimension that can be exploited to overcome this bottleneck and is designed to build on existing codes and time integration techniques in a non-intrusive manner. In this talk, we will discuss an extension of MGRIT for solving time-dependent constrained optimization problems. In the linear case, the MGRIT algorithm can be viewed as an approximate block cyclic reduction algorithm applied to a block lower bi-diagonal system. TriMGRIT extends this idea to block tri-diagonal systems such as those that arise in time-dependent constrained optimization. We will present a linear and a nonlinear algorithm applied to several model problems.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.