We describe a block matrix iterative algorithm for solving a linearquadratic parabolic optimal control problem (OCP) on a finite time interval. We derive a reduced symmetric indefinite linear system involving the control variables and auxiliary variables, and solve it using a preconditioned MINRES iteration, with a symmetric positive definite block diagonal preconditioner based on the parareal algorithm. Theoretical and numerical results show that the preconditioned algorithm converges at a rate independent of the mesh size h, and has parallel scalability.
CITATION STYLE
Sarkis, M., Schaerer, C. E., & Mathew, T. (2008). Block diagonal parareal preconditioner for parabolic optimal control problems. In Lecture Notes in Computational Science and Engineering (Vol. 60, pp. 409–416). https://doi.org/10.1007/978-3-540-75199-1_52
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