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- Andreas Alvermann, Holger Fehske
- J. Comput. Physics
- 2011

The FEAST algorithm [5] is an algorithm aimed at solving generalized eigenvalue problems AX = BXΛ, where A,B are n×n matrices. In [4] we presented a short analysis of FEAST involving this eigenvalue problem. In the present work we focus on the real symmetric eigenvalue problem AX = XΛ, where A = A, XX = I and Λ is a diagonal matrix consisting of real… (More)

- Melven Röhrig-Zöllner, Jonas Thies, +6 authors Holger Fehske
- SIAM J. Scientific Computing
- 2015

Block variants of the Jacobi-Davidson method for computing a few eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm when it comes to computing multiple or clustered eigenvalues. In practice, however, they are typically avoided because the total number of matrix-vector operations increases. In this paper we… (More)

The Kernel Polynomial Method (KPM) is a wellestablished scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show… (More)

- L Bakemeier, A Alvermann, H Fehske
- Physical review letters
- 2015

We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period-doubling bifurcations that leads to chaos and state the experimentally observable signatures in the optical spectrum. In addition to… (More)

- Andreas Alvermann, Achim Basermann, +10 authors Gerhard Wellein
- Euro-Par Workshops
- 2014

The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution. The project pursues a coherent co-design of all software layers where a holistic performance engineering process guides code development across the classic boundaries… (More)

- A Alvermann, D M Edwards, H Fehske
- Physical review letters
- 2007

We study the interplay of collective dynamics and damping in the presence of correlations and bosonic fluctuations within the framework of a newly proposed model, which captures the principal transport mechanisms that apply to a variety of physical systems. We establish close connections to the transport of lattice and spin polarons, or the dynamics of a… (More)

- A Alvermann, H Fehske
- Physical review letters
- 2009

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which… (More)

- Andreas Pieper, Moritz Kreutzer, +5 authors Gerhard Wellein
- J. Comput. Physics
- 2016

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with high-order filter polynomials obtained from a regularized Chebyshev expansion of a window function. After a… (More)

- Moritz Kreutzer, Andreas Pieper, Georg Hager, Gerhard Wellein, Andreas Alvermann, Holger Fehske
- 2015 IEEE International Parallel and Distributed…
- 2015

The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the Eigen value density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization potential and feasibility of peta-scale heterogeneous CPU-GPU implementations of the KPM. At the node level we show… (More)