ETNA - Electronic Transactions on Numerical Analysis
|
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
|
DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
|
ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Ronny Ramlau,
Bernadett Stadler
S. 256 - 275 doi:10.1553/etna_vol54s256 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol54s256
Abstract: Atmospheric tomography, i.e., the reconstruction of the turbulence profile in the atmosphere, is a challenging task for adaptive optics (AO) systems for the next generation of extremely large telescopes. Within the AO community, the solver of first choice is the so-called Matrix Vector Multiplication (MVM) method, which directly applies the (regularized) generalized inverse of the system operator to the data. For small telescopes this approach is feasible, however, for larger systems such as the European Extremely Large Telescope (ELT), the atmospheric tomography problem is considerably more complex, and the computational efficiency becomes an issue. Iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA) are a promising alternative. FEWHA is a wavelet-based reconstructor that uses the well-known iterative preconditioned conjugate gradient (PCG) method as a solver. The number of floating point operations and the memory usage are decreased significantly by using a matrix-free representation of the forward operator. A crucial indicator for the real-time performance are the number of PCG iterations. In this paper, we propose an augmented version of FEWHA, where the number of iterations is decreased by 50% using an augmented Krylov subspace method. We demonstrate that a parallel implementation of augmented FEWHA allows the fulfilment of the real-time requirements of the ELT. Keywords: adaptive optics, atmospheric tomography, inverse problems, augmented Krylov subspace methods Published Online: 2021/03/30 11:49:17 Object Identifier: 0xc1aa5576 0x003c53f1 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
|
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |