Implementation of a distributed parallel in time scheme using PETSc for a Parabolic Optimal Control Problem
This work presents a parallel implementation of the Parareal method using Portable Extensible Toolkit for Scientific Computation (PETSc). An optimal control problem of a parabolic partial differential equation with known boundary conditions and initial state is solved, where the minimized cost function relates the controller $v$ usage and the approximation of the solution $y$ to an optimal known function $y^*$, measured by $|y|$ and $|y|$, respectively. The equations that model the process are discretized in space using Finite Elements and in time using Finite Differences. After the discretizations, the problem is transformed to a large linear system of algebraic equations, that is solved by the Conjugate Gradient method. A Parareal preconditioner is implemented to speed up the convergence of the Conjugate Gradien.(original abstract)
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