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Emans M.,Johann Radon Institute for Computational and Applied Mathematics | Emans M.,MathConsult GmbH
Journal of Computational Science | Year: 2011

We present an agglomeration approach for the solution of the coarse-grid problems in algebraic multigrid for coupled systems. Our implementation relies on an appropriate reordering of the variables of the merged systems. A benchmark from fluid dynamics, representing the important class of mixed elliptic-hyperbolic problems, is used to demonstrate that the performance of the suggested agglomeration scheme comes much closer to the desired behaviour of the ideal multigrid than that of alternatives described in the literature. © 2011 Elsevier B.V.


Shatokhina I.,Johannes Kepler University | Obereder A.,MathConsult GmbH | Ramlau R.,Johannes Kepler University
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2014

We present a fast wavefront reconstruction algorithm developed for an extreme adaptive optics system equipped with a pyramid wavefront sensor on a 42m telescope. The method is called the Preprocessed Cumulative Reconstructor with domain decomposition (P-CuReD). The algorithm is based on the theoretical relationship between pyramid and Shack-Hartmann wavefront sensor data. The algorithm consists of two consecutive steps - a data preprocessing, and an application of the CuReD algorithm, which is a fast method for wavefront reconstruction from Shack-Hartmann sensor data. The closed loop simulation results show that the P-CuReD method provides the same reconstruction quality and is significantly faster than an MVM. © 2014 SPIE.


Ramlau R.,Johannes Kepler University | Obereder A.,MathConsult GmbH | Rosensteiner M.,MathConsult GmbH | Saxenhuber D.,Johannes Kepler University
Inverse Problems in Science and Engineering | Year: 2014

The planned new generation of extremely large telescopes (ELT) requires highly efficient algorithms for its adaptive optics systems. Recently, a new iterative reconstruction approach for multi conjugate adaptive optics (MCAO) and multi object adaptive optics (MOAO) was introduced that computes the mirror corrections without the use of matrix-vector multiplications. The method splits the MCAO/MOAO problem into three subproblems – wavefront reconstruction, atmospheric tomography and mirror deformation – sequently. If an AO system uses laser guide stars, then the reconstruction methods have to be extended in order to consider the cone effect and the tip/tilt indetermination. For the reconstruction of an atmosphere with correct tip/tilt we assume that additional measurements from a tip/tilt sensor are available, and propose two iterative reconstruction methods for the atmosphere. In the first approach, the tip/tilt reconstruction is included into the atmospheric tomography, whereas in the second approach the tip/tilt is reconstructed separately and added to the atmosphere after the atmospheric tomography. Both algorithms are tested numerically. The reconstruction quality of our methods is evaluated for ELT. © 2014 Taylor & Francis.


Rosensteiner M.,MathConsult GmbH | Ramlau R.,Johannes Kepler University
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2013

We recently introduced the Kaczmarz algorithm for solving the atmospheric tomography problem in multiconjugate adaptive optics (MCAO). This iterative method solves the problem significantly faster than the standard matrix vector multiplication. We present the algorithm as well as an extension, which includes the effects of laser guide stars, such as the cone effect, tip/tilt indetermination, and spot elongation. We show that we can successfully cope with these effects and that the algorithm is suited for an MCAO system for the future generation of extremely large telescopes. © 2013 Optical Society of America.


Ramlau R.,Johannes Kepler University | Rosensteiner M.,MathConsult GmbH
Inverse Problems | Year: 2012

The planned new generation of extremely large telescopes requires highly efficient algorithms for its adaptive optics systems. We present a new reconstruction approach for multi-conjugate adaptive optics or multi-object adaptive optics that computes the mirror shapes without the use of matrix-vector multiplications. The method solves the involved subproblems - wavefront reconstruction, atmospheric tomography and determination of the mirror shapes - sequently. In this paper, we focus on highly efficient algorithms for the atmospheric tomography and the computation of the mirror shape. Finally, we estimate the complexity of the method and provide some numerical examples, including a comparison of our approach to the standard Tikhonov regularization and minimum variance reconstructors. © 2012 IOP Publishing Ltd.


Rosensteiner M.,MathConsult GmbH | Ramlau R.,Johannes Kepler University
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2012

Adaptive Optics systems for the new generation of extremely large telescopes require fast mathematical methods for the computation of the shape of the deformable mirrors. MCAO or MOAO systems use laser guide stars for the reconstruction of the turbulent atmosphere. However, measurements from laser guide stars contain no information on the tip/tilt of the incoming wavefronts. Assuming that additional tip/tilt measurements of wavefronts from natural guide stars are available, we present an iterative Kaczmarz reconstructor that computes the turbulent atmospheric layers from the wavefronts of both the laser and natural guide stars. We show in particular that the resulting algorithm meets the quality and speed requirements for ELTs. © 2012 SPIE.


Shatokhina I.,Johannes Kepler University | Obereder A.,MathConsult GmbH | Rosensteiner M.,MathConsult GmbH | Ramlau R.,Johannes Kepler University
Applied Optics | Year: 2013

We present a fast method for the wavefront reconstruction from pyramid wavefront sensor (P-WFS) measurements. The method is based on an analytical relation between pyramid and Shack-Hartmann sensor (SH-WFS) data. The algorithm consists of two steps-a transformation of the P-WFS data to SH data, followed by the application of cumulative reconstructor with domain decomposition, a wavefront reconstructor from SH-WFS measurements. The closed loop simulations confirm that our method provides the same quality as the standard matrix vector multiplication method. A complexity analysis as well as speed tests confirm that the method is very fast. Thus, the method can be used on extremely large telescopes, e.g., for eXtreme adaptive optics systems. © 2013 Optical Society of America.


Aichinger M.,Austrian Academy of Sciences | Aichinger M.,MathConsult GmbH | Aichinger M.,University Software Plus GmbH | Hernandez E.R.,CSIC - Institute of Materials Science
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here, we report calculations of the full spectrum of the single-particle Schrödinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential. © 2013 American Physical Society.


Rosensteiner M.,MathConsult GmbH
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2011

The Cumulative Reconstructor (CuRe)isanew direct reconstructor for anoptical wavefront from Shack-Hartmann wavefront sensormeasurements.Inthis paper, the algorithm is adapted to realistic telescope geometries and the transition from modified Hudgin to Fried geometry is discussed. After a discussion of the noise propagation,we analyze the complexity of the algorithm. Our numerical tests confirm that the algorithm is very fast and accurate and can therefore be used for adaptive optics systems of Extremely Large Telescopes. © 2011 Optical Society of America.


Rosensteiner M.,MathConsult GmbH
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2012

The Cumulative Reconstructor is an accurate, extremely fast reconstruction algorithm for Shack-Hartmann wavefront sensor data. But it has shown an unacceptable high noise propagation for large apertures. Therefore, in this paper we describe a domain decomposition approach to deal with this drawback. We show that this adaptation of the algorithm gives the same reconstruction quality as the original algorithm and leads to a significant improvement with respect to noise propagation. The method is combined with an integral control and compared to the classical matrix vector multiplication algorithm on an end-to-end simulation of a single conjugate adaptive optics system. The reconstruction time is 20n (number of subapertures), and the method is parallelizable. © 2012 Optical Society of America.

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