Abstract
Partial differential equations (PDE) are indispensable to describe complex processes. PDE constrained parameter estimation is still a prevailing topic of research. The increase in computation time with increasing complexity of the problem is one of the main problems. With the application of multiple shooting, the number of required derivatives for the generalized Gauss–Newton method rises rapidly. We introduce a method to overcome this challenge. By using directional derivatives the computational effort can be reduced to the minimal number. We demonstrate our methods with help of the heat equation.
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Kircheis, R., Körkel, S. (2015). Parameter Estimation for High-Dimensional PDE Models Using a Reduced Approach. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds) Multiple Shooting and Time Domain Decomposition Methods. Contributions in Mathematical and Computational Sciences, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-23321-5_5
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DOI: https://doi.org/10.1007/978-3-319-23321-5_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23320-8
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