Reducing Memory Requirements in Scientific Computing and Optimal Control

Please always quote using this URN: urn:nbn:de:0297-zib-42695
  • In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps 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 typically are 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.

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Author:Sebastian Götschel, Christoph von Tycowicz, Konrad Polthier, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:compression; mesh compression; optimal control; trajectory storage
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Pxx Theory of data / 68P05 Data structures
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Pxx Theory of data / 68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]
94-XX INFORMATION AND COMMUNICATION, CIRCUITS / 94Axx Communication, information / 94A29 Source coding [See also 68P30]
Date of first Publication:2013/10/11
Series (Serial Number):ZIB-Report (13-64)
ISSN:1438-0064
Published in:submitted to "Multiple Shooting and Time Domain Decomposition Methods", Springer Series "Contributions in Mathematical and Computational Sciences"