# Research

The SLQM carries on several research projects in three distinct categories:

- Development and maintenance of numerical libraries tailored to computational tasks emerging from Materials Science simulation software;
- Design and implementation of high-performance algorithms targeting specific simulation codes in the broad area of quantum materials;
- Development of new mathematical and computational models aimed at improving performance, accuracy and scalability of simulations within a methodological framework.

## Projects

**Robust methods for achieving self-consistency in large-scale ab-initio quantum mechanical calculations**

Density Functional Theory is a powerful theory to calculate quantum mechanical properties of materials. In metallic systems of larger size, though, charge fluctuates between regions within the metal (known as charge sloshing) and the number of iterations necessary to achieve convergence, if it converges at all, increases dramatically. As part of this project we develop and implement preconditioners that extend the existing mixing models, ensure convergence and improve the its total rate.

Contact: *Miriam Hinzen*

**Inverse design of functional hetero-interfaces in photovoltaic applications **

The PVnegf code, recently developed at the Forschungszentrum Jülich IEK-5 institute is at the base of this project. The first objective is to improve PVnegf flexibility and accuracy by introducing several mathematical and algorithmic optimizations. Concurrently the plan is to blueprint a number of design principles targeting specific features for a given desired functionality. The end result of the project will be the identification of core features opening a path towards the surgical design of complex hetero-interfaces which can then be compared against the outcome of experimental tests.

Contact: *Sebastian Achilles*

**Optimized Solver for Sequences of Sparse Eigenvalue Problems arising in ab initio Computations**

DFT simulations yield a sequence of eigenvalue problems, where only a small part of the spectrum is required. Spectrum-slicing eigensolvers promise an additional level of parallelism over more traditional solvers. Research efforts include the optimization of rational filter functions for accelerating subspace iteration. Future research will include slice placement for better performance and load-balancing.

Contact: *Jan Winkelmann*

**Linear-Scaling Green's Function-based Density Functional Theory - KKRnano**

Greensfunction based DFT requires linear solvers and is advantages to be defined in real-space as there, we can exploit the Kohn-nearsightedness principle. KKRnano is a implementation of Greensfunction-based DFT aimed towards large systems (100,000 atoms and larger). With nearsightedness, it scales linearly with the number of atoms and parallelises well onto hundred thousands of nodes. In order to increase its efficiency, we are currently working on improving the electrostatics solver and porting the custom linear solver for block-sparse matrices to GPUs.

Contact: *Paul Baumeister*

**Real-space grid based Density Functional Theory - juRS**

A key ingredient to density functional theory is the evaluation of the exchange-correlation functional. Due to its non-linearity, the input electron density must be defined in real-space. This forces any DFT method to transform at least the density into a real-space representation. De facto, the most common plane-wave based DFT methods extensively use FFTs to transform into real-space for the application of the potential operator to Kohn-Sham states. Real-space grid based DFT goes one step beyond and avoids all Fourier transforms by representing also the kinetic energy operator on the real-space grid. Its Laplacian is approximated with high-order finite differences. The localised stencils allow for a good scalability when parallelising large problems in a domain-decomposition fashion.

Contact: *Paul Baumeister*

**Data Compression for the Projector Augmented Wave method**

The Projector Augmented Wave method like older pseudopotential methods allows to properly describe the scattering properties of the atomic nuclei screened by the core electrons. Due to its separable form, the potential operator contribution from each atom is a low-rank operator and can, therefore, be applied by projection to a set of states localised around the nucleus. These states need to be stored in memory and loaded on demand. Using tensor compression methods, we aim to find a basis set that allows to reduce the requirements on memory capacity and bandwidth in order to accelerate DFT codes like GPAW and juRS.

Contact: *Paul Baumeister*

**Juelich Numerical Library (JuNLib) **

In Materials Science, like in many other scientific domains making use of scientific computing simulations, numerical libraries play a fundamental role. SLQM develops and implements modern algorithms into numerical linear algebra libraries tailored to heterogeneous computing architectures and modular supercomputers.

Contact: *Edoardo Di Napoli*

**Joint Laboratory on Extreme Scale Computing (JLESC) project**

The JLESC project deals with the customization and integration of the Chebyshev Accelerated Subspace Eigensolver (ChASE), recently developed at JSC, into the BSE Jena code developed and maintained at the University of Urbana-Champaign. The aim is to facilitate the computation of the desired lowest eigenpairs of large dense eigenproblems on massive many-cores architectures.

Contact: *Edoardo Di Napoli*

**Applying Machine Learning methods to Lathanides orthophosphates **

Orthophosphates of lanthanides (LnPO_{4}) are particularly interesting for their applications in forming ceramics matrices that are used in the nuclear waste management to store safely large amounts of radioactive material. One of the most important thermodynamic features of composite materials are the enthalpies of formation. Such property are not quite easy to measure especially for compounds with high-temperature melting points. We plan to retrieve enthalpies of formation using Machine Learning techniques on the available set of data for lathanides orthophosphates in their pure phases.

Contact: *Edoardo Di Napoli*