Publications - Jan Winkelmann

Submitted Paper

  1. Non-linear Least-Squares optimization of rational filters for the solution of interior eigenvalue problems
    2017.
    Submitted to SIAM SIMAX.
    Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters based on a non-convex weighted Least-Squares scheme. When used in combination with the FEAST library, our filters out-perform existing ones on a large and representative set of benchmark problems. This work provides a detailed description of: (1) a set up of the optimization process that exploits symmetries of the filter function for Hermitian eigenproblems, (2) a formulation of the gradient descent and Levenberg-Marquardt algorithms that exploits the symmetries, (3) a method to select the starting position for the optimization algorithms that reliably produces effective filters, (4) a constrained optimization scheme that produces filter functions with specific properties that may be beneficial to the performance of the eigensolver that employs them.
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Peer Reviewed Conference Publication

  1. Parallel adaptive integration in high-performance functional Renormalization Group computations
    Julian Lichtenstein, Jan Winkelmann, David Sanchez de la Pena, Toni Vidovic and Edoardo Di Napoli
    Jülich Aachen Research Alliance High-Performance Computing Symposium 2016, Lecture Notes in Computer Science, Springer-Verlag, 2017.
    @inproceedings{Lichtenstein2017:360,
        author    = "Julian Lichtenstein and Jan Winkelmann and David {Sanchez de la Pena} and Toni Vidovic and Edoardo {Di Napoli}",
        title     = "Parallel adaptive integration in high-performance functional Renormalization Group computations",
        booktitle = "Jülich Aachen Research Alliance High-Performance Computing Symposium 2016",
        year      = 2017,
        editor    = "E. Di Napoli et. al.",
        series    = "Lecture Notes in Computer Science",
        publisher = "Springer-Verlag",
        url       = "https://arxiv.org/pdf/1610.09991v1.pdf"
    }
    The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body phenomena, such as high- temperature superconductivity or topological states of matter. In this work we present one of the latest realizations of fRG which makes use of an adaptive numerical quadrature scheme specifically tailored to the described fRG scheme. The final result is an increase in performance thanks to improved parallelism and scalability.
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