Publications - Jan Winkelmann

Submitted Paper

Non-linear Least-Squares optimization of rational filters for the solution of interior eigenvalue problems
Jan Winkelmann and Edoardo Di Napoli
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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Journal Article

ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems
Jan Winkelmann, Paul Springer and Edoardo Di Napoli
pp. 33, May 2018.
```
@article{Winkelmann2018:70,
    author = "Jan Winkelmann and Paul Springer and Edoardo {Di Napoli}",
    title  = "ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems",
    year   = 2018,
    pages  = 33,
    month  = may,
    url    = "https://arxiv.org/pdf/1805.10121"
}
```
Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take the form of correlations between the eigenvectors of consecutive problems, as is the case in many real-world applications, the potential benefit of exploiting them can be substantial. We present ChASE, a modern algorithm and library based on subspace iteration with polynomial acceleration. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree which further reduces the necessary FLOPs. ChASE is written in C++ using the modern software engineering concepts which favor a simple integration in application codes and a straightforward portability over heterogeneous platforms. When solving sequences of Hermitian eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits from the sequence's spectral properties and outperforms direct solvers in many scenarios. The library ships with two distinct parallelization schemes, supports execution over distributed GPUs, and it is easily extensible to other parallel computing architectures.
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Peer Reviewed Conference Publication

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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