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Optimal control of the principal coefficient in a scalar wave equation
- Source :
- Applied Mathematics and Optimization 84 (2021), 2889-2921
- Publication Year :
- 2019
-
Abstract
- We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for the coefficient-to-solution mapping for discontinuous coefficients. We additionally consider a so-called "multi-bang" penalty that promotes controls taking on values pointwise almost everywhere from a specified discrete set. Under additional assumptions on the data, we derive an improved regularity result for the state, leading to optimality conditions that can be interpreted in an appropriate pointwise fashion. The numerical solution makes use of a stabilized finite element method and a nonlinear primal-dual proximal splitting algorithm.
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Journal :
- Applied Mathematics and Optimization 84 (2021), 2889-2921
- Publication Type :
- Report
- Accession number :
- edsarx.1912.08672
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00245-020-09733-9