2024/06/17 by Kwok, Felix, Tognon, Djahou N
#Distributed #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Parallel #and Cluster Computing (cs.DC)
paper · doi:10.48550/arxiv.2406.11478
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems. The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel. We then propose a preconditioner to speed up the convergence of GMRES in the special cases of the heat and wave equations. Numerical experiments are provided to illustrate the efficiency of our preconditioners.