Abstract
Optimal control problems constrained by partial differential equations arise in a multitude of important applications, such as in Engineering, Medical and Financial research. They arise also in microstructure analyses.
They lead mostly to the solution of very large scale algebraic systems to be solved. It is then important to formulate the problems so that these systems can be solved fast and robustly, which requires construction of a very efficient preconditioner. Furthermore the acceleration method should be both efficient and cheap, which requires that sharp and tight eigenvalue bounds for the preconditioned matrix are available. Some types of optimal control problems where the above hold, are presented.
With the use of a proper iterative aceleration method which is inner product free, the methods can be used efficiently on both homogeneous and heterogeneous computer architectures, enabling very fast solutions.
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Acknowledgement
The work of Owe Axelsson is supported by The Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II), project “IT4Innovations excellence in science - LQ1602” and by the project BAS-17-08, “Microstructure analysis and numerical upscaling using parallel numerical methods, algorithms for heterogeneous computer architectures and hi-tech measuring devices”.
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Axelsson, O. (2021). A Survey of Optimal Control Problems for PDEs. In: Dimov, I., Fidanova, S. (eds) Advances in High Performance Computing. HPC 2019. Studies in Computational Intelligence, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-55347-0_32
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DOI: https://doi.org/10.1007/978-3-030-55347-0_32
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