• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

• Legal notice
• Personal data

## 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

We have focused on the improvements of the parallel collision detection and the data structure in the OPTIDIS code [11].

• 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.