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A Gautschi time-stepping approach to optimal control of the wave equation
Institution:1. Dept. Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014, University of Jyväskylä, Finland;2. Dept. Mathematics and System Analysis, P.O. Box 11100, FI-00076, Aalto University, Finland;1. Metron, Inc., 1818 Library St., Reston, VA 20190, USA;2. School of Computing, National University of Singapore, 13 Computing Drive, COM1, Singapore 117417, Republic of Singapore;3. Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706-1325, USA;4. Department of Mathematics, School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Avenue, Nur-Sultan city, 010000, Kazakhstan;5. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, S17, Singapore 119076, Republic of Singapore
Abstract:A Gautschi time-stepping scheme for optimal control of linear second order systems is proposed and analyzed. Convergence rates are proved and shown to be valid in numerical experiments. The temporal discretization is combined with finite element and spectral based spatial discretizations, which are compared among themselves.
Keywords:Gautschi time-stepping  Optimal control  Wave equation  Trigonometric operators  Finite element and spectral methods
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