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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. Source


Kasumba H.,Johann Radon Institute for Computational and Applied Mathematics | Kunisch K.,University of Graz | Laurain A.,TU Berlin
Interfaces and Free Boundaries | Year: 2014

A bilevel shape optimization problem with the exterior Bernoulli free boundary problem as lower-level problem and the control of the free boundary as the upper-level problem is considered. Using the shape of the inner boundary as the control, we aim at reaching a specific shape for the free boundary. A rigorous sensitivity analysis of the bilevel shape optimization in the infinite-dimensional setting is performed. The numerical realization using two different cost functionals presented in this paper demonstrate the efficiency of the approach. © European Mathematical Society 2014 Source


Emans M.,Johann Radon Institute for Computational and Applied Mathematics | Emans M.,IMCC GmbH | Liebmann M.,University of Graz
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

We explore a GPU implementation of a Krylov-accelerated algebraic multigrid (AMG) algorithm with flexible preconditioning. We demonstrate by means of two benchmarks from an industrial computational fluid dynamics (CFD) application that the acceleration with multiple graphics processing units (GPUs) speeds up the solution phase by a factor of up to 13. In order to achieve good performance for the whole AMG algorithm, we propose for the setup a substitution of the double-pairwise aggregation by a simpler aggregation scheme skipping the calculation of temporary grids and operators. The version with the revised setup reduces the total computing time on multiple GPUs by further 30% compared to the GPU implementation with the double-pairwise aggregation. We observe that the GPU implementation of the entire Krylov-accelerated AMG runs up to four times faster than the fastest central processing unit (CPU) implementation. © 2013 Springer-Verlag. Source


Piotrowski Z.P.,National Water Research Institute | Matejczyk B.,Johann Radon Institute for Computational and Applied Mathematics | Marcinkowski L.,University of Warsaw | Smolarkiewicz P.K.,European Center for Medium Range Weather Forecasts
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

Effective preconditioning lies at the heart of multiscale flow simulation, including a broad range of geoscientific applications that rely on semi-implicit integrations of the governing PDEs. For such problems, conditioning of the resulting sparse linear operator directly responds to the squared ratio of largest and smallest spatial scales represented in the model. For thin-spherical-shell geometry of the Earth atmosphere the condition number is enormous, upon which implicit preconditioning is imperative to eliminate the stiffness resulting from relatively fine vertical resolution. Furthermore, the anisotropy due to the meridians convergence in standard latitude-longitude discretizations becomes equally detrimental as the horizontal resolution increases to capture nonhydrostatic dynamics. Herein, we discuss a class of effective preconditioners based on the parallel ADI approach. The approach has been implemented in the established high-performance all-scale model EULAG with flexible computational domain distribution, including a 3D processor array. The efficacy of the approach is demonstrated in the context of an archetypal simulation of global weather. © Springer International Publishing Switzerland 2016. Source


Su M.,Nankai University | Winterhof A.,Johann Radon Institute for Computational and Applied Mathematics
IEEE Transactions on Information Theory | Year: 2010

We combine the concepts of the p-periodic Legendre sequence, the (q-1)-periodic Sidelnikov sequence and the two-prime generator to introduce a new p(q-1)-periodic sequence called LegendreSidelnikov sequence. We show that this new sequence is balanced if p=q. For an arbitrary odd prime p and an arbitrary power q of an odd prime with gcd (p,q-1)=1 we determine the exact values of its (periodic) autocorrelation function and deduce an upper bound on its aperiodic autocorrelation function showing that it is small compared to its period. © 2006 IEEE. Source

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