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## Section: New Results

### Application Domains

#### Material physics

##### EigenSolver

The adaptive vibrational configuration interaction algorithm has been introduced as a new eigennvalues method for large dimension problem. It is based on the construction of nested bases for the discretization of the Hamiltonian operator according to a theoretical criterion that ensures the convergence of the method. It efficiently reduce the dimension of the set of basis functions used and then we are able solve vibrationnal eigenvalue problem up to the dimension 15 (7 atoms). This year we have worked on three main areas. First, we extend our shared memory parallelization to distributed memory using the message exchange paradigm. This new version should allow us to process larger systems quickly. To target the eigenvalues relevant for chemists, i. eigenvalues with an intensity. This requires calculating the scalar product between the smallest eigenvalues and the dipole moment applied to an eigenvector to evaluate its intensity. In addition, to get closer to the experimental values, we introduced the Coriolis operator into the Hamiltonian. A paper is being written on these last two points.

##### Dislocation
• The new collision detection algorithm to reliably handle junction formation for Dislocation Dynamics using hybrid OpenMP + MPI parallelism has been developed. The enhanced precision and reliability of this new algorithm allows the use of larger time-steps for faster simulations. Hierarchical methods for collision detection, as well as hybrid parallelism are also used to improve performance;

• A new distributed data structure has been developed to enhance the reliability and modularity of OPTIDIS . The new data structure provides an interface to modify safely and reliably the distributed dislocation mesh in order to enforce data consistency across all computation nodes. This interface also improves code modularity allowing the study of data layout performance without modifying the algorithms.

#### Co-design for scalable numerical algorithms in scientific applications

##### A geometric view of biodiversity: scaling to metagenomics

We have designed a new efficient dimensionality reduction algorithm in order to investigate new ways of accurately characterizing the biodiversity, namely from a geometric point of view, scaling with large environmental sets produced by NGS (∼105 sequences). The approach is based on Multidimensional Scaling (MDS) that allows for mapping items on a set of n points into a low dimensional euclidean space given the set of pairwise distances. We compute all pairwise distances between reads in a given sample, run MDS on the distance matrix, and analyze the projection on first axis, by visualization tools. We have circumvented the quadratic complexity of computing pairwise distances by implementing it on a hyperparallel computer (Turing, a Blue Gene Q), and the cubic complexity of the spectral decomposition by implementing a dense random projection based algorithm. We have applied this data analysis scheme on a set of ${10}^{5}$ reads, which are amplicons of a diatom environmental sample from Lake Geneva. Analyzing the shape of the point cloud paves the way for a geometric analysis of biodiversity, and for accurately building OTUs (Operational Taxonomic Units), when the data set is too large for implementing unsupervised, hierarchical, high-dimensional clustering.

##### High performance simulation for ITER tokamak

Concerning the GYSELA global non-linear electrostatic code, a critical problem is the design of a more efficient parallel gyro-average operator for the deployment of very large (future) GYSELA runs. The main unknown of the computation is a distribution function that represents either the density of the guiding centers, either the density of the particles in a tokamak. The switch between these two representations is done thanks to the gyro-average operator. In the previous version of GYSELA, the computation of this operator was achieved thanks to a Padé approximation. In order to improve the precision of the gyro-averaging, a new parallel version based on an Hermite interpolation has been done (in collaboration with the Inria TONUS project-team and IPP Garching). The integration of this new implementation of the gyro-average operator has been done in GYSELA and the parallel benchmarks have been successful. This work is carried on in the framework of the PhD of Nicolas Bouzat (funded by IPL C2S@Exa ) co-advised with Michel Mehrenberger from TONUS project-team and in collaboration with Guillaume Latu from CEA-IRFM . The scientific objectives of this work are first to consolidate the parallel version of this gyro-average operator, in particular by designing a scalable MPI+OpenMP parallel version and by using a new communication scheme, and second to design new numerical methods for the gyro-average, source and collision operators to deal with new physics in GYSELA. The objective is to tackle kinetic electron configurations for more realistic complex large simulations. This has been done by using a new data distribution for a new irregular mesh in order to take into account the complex geometries of modern tokamak reactors. All these contributions have been validated on a new object-oriented proptotype of GYSELA which uses a task based programming model. The PhD thesis of Nicolas Bouzat has been defended on December 17, 2018.

In the context of the EoCoE project, we have collaborations with CEA-IRFM . First, with G. Latu, we have investigated the potential of using the last release of the PaStiX solver (version 6.0) on Intel KNL architecture, and more especially on the MARCONI machine (one of the PRACE supercomputers at Cineca, Italia). The results obtained on this architecture are really promising since we are able to reach more than 1 Tflops using a single node. Secondly, we also have a collaboration with P. Tamain and G. Giorgani on the TOKAM3X code to analyze the performance of using PaStiX as a preconditioner. Since a distributed memory is required during the simulation, the previous release of PaStiX is then used. Some difficulties regarding the Fortran wrapper and some memory issues should be fixed when we will have reimplemented the MPI interface in the current release.

##### Numerical and parallel scalable hybrid solvers in large scale calculations

Numerically scalable hybrid solvers based on a fully algebraic coarse space correction have been theoretically studied within the PhD thesis of Louis Poirel defended on November 28, 2018. Some of the proposed numerical schemes have been integrated in the MaPHyS parallel package. In particular, multiple parallel strategies have been designed and their parallel efficiencies were assessed in two large application codes. The first one is Alya developed at BSC, that is a high performance computational mechanics code to solve coupled multi-physics / multi-scale problems, which are mostly coming from engineering applications. This activity was carried out in the framework of the EoCoE project. Thye second large code is AVIP jointly developed by CERFACS and Laboratoire de Physique des Plasmas at École Polytechnique for the calculation of plasma propulsion. For this latter code, part of the parallel experiments were conduced on a PRACE Tier-0 machine within a PRACE Project Access.