Section: Application Domains
Material physics
Participants : Bérenger Bramas, Olivier Coulaud, Aurélien Esnard, Pierre Fortin, Luc Giraud, Jean Roman.
Due to the increase of available computer power, new applications in nano science and physics appear such as study of properties of new materials (photovoltaic materials, bio and environmental sensors, ...), failure in materials, nanoindentation. Chemists, physicists now commonly perform simulations in these fields. These computations simulate systems up to billion of atoms in materials, for large time scales up to several nanoseconds. The larger the simulation, the smaller the computational cost of the potential driving the phenomena, resulting in low precision results. So, if we need to increase the precision, there is two ways to decrease the computational cost. In the first approach, we improve classical methods and algorithms and in the second way, we will consider a multiscale approach.
Many applications in material physics need to couple several models like quantum mechanic and molecular mechanic models, or molecular and mesoscopic or continuum models. These couplings allow scientists to treat larger solids or molecules in their environment. Many of macroscopic phenomena in science depend on phenomena at smaller scales. Full simulations at the finest level are not computationally feasible in the whole material. Most of the time, the finest level is only necessary where the phenomenon of interest occurs; for example in a crack propagation simulation, far from the tip, we have a macroscopic behavior of the material and then we can use a coarser model. The idea is to limit the more expensive level simulation to a subset of the domain and to combine it with a macroscopic level. This implies that atomistic simulations must be speeded up by several orders of magnitude.
We will focus on two applications; the first one concerns the computation of optical spectra of molecules or solids in their environment. In the second application, we will develop faster algorithms to obtain a better understanding of the metal plasticity, phenomenon governing by dislocation behavior. Moreover, we will focus on the improvement of the algorithms and the methods to build faster and more accurate simulations on modern massively parallel architectures.
Hybrid materials
There is current interest in hybrid pigments for cosmetics, phototherapy and paints. Hybrid materials, combining the properties of an inorganic host and the tailorable properties of organic guests, particularly dyes, are also of wide interest for environmental detection (oxygen sensors) and remediation (trapping and elimination of dyes in effluents, photosensitised production of reactive oxygen species for reduction of air and water borne contaminants). A thorough understanding of the factors determining the photo and chemical stability of hybrid pigments is thus mandated by health, environmental concerns and economic viability.
Many applications of hybrid materials in the field of optics exploit combinations of properties such as transparency, adhesion, barrier effect, corrosion, protection, easy tuning of the colour and refractive index, adjustable mechanical properties and decorative properties. It is remarkable that ancient pigments, such as Maya Blue and lacquers, fulfill a number of these properties. This is a key to the attractiveness of such materials. These materials are not simply physical mixtures, but should be thought of as either miscible organic and inorganic components, or as a heterogeneous system where at least one of the component exhibits a hierarchical order at the nanometer scale. The properties of such materials no longer derive from the sum of the individual contributions of both phases, since the organic/inorganic interface plays a major role. Either organic and inorganic components are embedded and only weak bonds (hydrogen, van der Waals, ionic bonds) give the structure its cohesion (class I) or covalent and ionocovalent bonds govern the stability of the whole (class II).
These simulations are complex and costly and may involve several length scales, quantum effects, components of different kinds (mineralorganic, hydrophilic and phobic parts). Computer simulation already contributes widely to the design of these materials, but current simulation packages do not provide several crucial functions, which would greatly enhance the scope and power of computer simulation in this field.
The computation of optical spectra of molecules and solids is the greatest use of the Time Dependent Density Functional Theory (TDDFT). We compute the ground state of the given system as the solution of the KohnSham equations (DFT). Then, we compute the excited states of the quantum system under an external perturbation  electrical field of the environment  or thanks to the linear theory, we compute only the response function of the system. In fact, physicists are not only interesting by the spectra for one conformation of the molecule, but by an average on its available configurations. To do that, they sample the trajectory of the system and then compute several hundred of optical spectra in one simulation. But, due to the size of interesting systems (several thousands of atoms) and even if we consider linear methods to solve the KohnSham equations arising from the Density Functional Theory, we cannot compute all the system at this scale. In fact, such simulations are performed by coupling Quantum mechanics (QM) and Molecular mechanic (MM). A lot of works are done on the way to couple these two scales, but a lot of work remains in order to build efficient methods and efficient parallel couplings.
The most consuming time in such coupling is to compute optical spectra is the TDDFT. Unfortunately, examining optical excitations based on contemporary quantum mechanical methods can be especially challenging because accurate methods for structural energies, such as DFT, are often not well suited for excited state properties. This requires new methods designed for predicting excited states and new algorithms for implementing them. Several tracks will be investigated in the project:

Typically physicists or chemists consider spectral functions to build a basis (orbital functions) and all the computations are performed in a spectral way. Due to our background, we want to develop new methods to solve the system in the real space by finite differences or by wavelets methods. The main expectation is to construct error estimates based on for instance the gridsize $h$ parameter.

For a given frequency in the optical spectra, we have to solve a symmetric non Hermitian system. With our knowledge on linear solvers, we think that we can improve the methods commonly used (Lanczos like) to solve the system (see Section 3.3 ).

Improving the parallel coupling is crucial for large systems because the computational cost of the atomic and quantum models are really different. In parallel we have the following order of magnitude: one second or less per time step for the molecular dynamics, several minutes or more for the DFT and the TDDFT. The challenge to find the best distribution in order to have the same CPU time per time step is really important to reach high performance. Another aspect in the coupling is the coupling with the visualization to obtain online visualization or steerable simulations. Such steerable simulations help the physicists to construct the system during the simulation process by moving one or a set of molecules. This kind of interaction is very challenging in terms of algorithmic and this is a good field for our software platform EPSN .
Material failures
Another domain of interest is the material aging for the nuclear industry. The materials are exposed to complex conditions due to the combination of thermomechanical loading, the effects of irradiation and the harsh operating environment. This operating regime makes experimentation extremely difficult and we must rely on multiphysics and multiscale modelling for our understanding of how these materials behave in service. This fundamental understanding helps not only to ensure the longevity of existing nuclear reactors, but also to guide the development of new materials for 4th generation reactor programs and dedicated fusion reactors. For the study of crystalline materials, an important tool is dislocation dynamics (DD) modelling. This multiscale simulation method predicts the plastic response of a material from the underlying physics of dislocation motion. DD serves as a crucial link between the scale of molecular dynamics and macroscopic methods based on finite elements; it can be used to accurately describe the interactions of a small handful of dislocations, or equally well to investigate the global behavior of a massive collection of interacting defects.
To explore, i.e., to simulate these new areas, we need to develop and/or to improve significantly models, schemes and solvers used in the classical codes. In the project, we want to accelerate algorithms arising in those fields. We will focus on the following topics (in particular in the starting OPTIDIS ANRCOSINUS project in collaboration with CEA Saclay, CEA Iledefrance and SIMaP Laboratory in Grenoble) in connection with research described at Sections 3.4 and 3.5 .

The interaction between dislocations is long ranged ($O(1/r)$) and anisotropic, leading to severe computational challenges for largescale simulations. In dislocation codes, the computation of interaction forces between dislocations is still the most CPU time consuming and has to be improved to obtain faster and more accurate simulations.

In such simulations, the number of dislocations grows while the phenomenon occurs and these dislocations are not uniformly distributed in the domain. This means that strategies to dynamically construct a good load balancing are crucial to acheive high performance.

From a physical and a simulation point of view, it will be interesting to couple a molecular dynamics model (atomistic model) with a dislocation one (mesoscale model). In such threedimensional coupling, the main difficulties are firstly to find and characterize a dislocation in the atomistic region, secondly to understand how we can transmit with consistency the information between the two micro and meso scales.