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Reducing memory requirements in scientific computing and optimal control. (English) Zbl 1337.65052

Carraro, Thomas (ed.) et al., Multiple shooting and time domain decomposition methods. MuS-TDD, Heidelberg, Germany, May 6–8, 2013. Cham: Springer (ISBN 978-3-319-23320-8/hbk; 978-3-319-23321-5/ebook). Contributions in Mathematical and Computational Sciences 9, 263-287 (2015).
Summary: In high accuracy numerical simulations and optimal control of time-dependent processes, often both many timesteps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which are typically double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.
For the entire collection see [Zbl 1333.65003].

MSC:

65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49M25 Discrete approximations in optimal control
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