A Two-Grid-Approach to Identification and Control Problems for Partial Differential Equations
Both parameter identification and control problems for partial differential equations (PDE) can be treated by minimization of functionals the values of which depend on the unknown parameters or control functions. Each evaluation of these functionals requires an approximate solution of a boundary value or an initial boundary value problem (IBVP) for the PDE. To get an acceptable trade-off between accuracy and the amount of computation, we preferably use a coarse-grid-approximation of the IBVP for minimizing these functionals. Only at a few points of the parameter or control function space a fine-grid-approximation of the IBVP has to be calculated in order to reduce the systematic error created by the coarse grid.
This approach will be illustrated by the hand of parabolic equations, but it seems to be quite general even for large scale identification and control problems.
KeywordsControl Problem Coarse Grid Partial Differential Equation Initial Boundary Value Problem Radial Temperature Profile
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