Section: New Results

Application Domains

Material physics

EigenSolver

The adaptive vibrational configuration interaction algorithm has been introduced as a new method to efficiently reduce the dimension of the set of basis functions used in a vibrational configuration interaction process. 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. In the present work, the Hamiltonian is written as a sum of products of operators. The purpose of this paper is to study the properties and outline the performance details of the main steps of the algorithm. New parameters have been incorporated to increase flexibility, and their influence has been thoroughly investigated. The robustness and reliability of the method are demonstrated for the computation of the vibrational spectrum up to 3000 cm−1 of a widely studied 6-atom molecule (acetonitrile). Our results are compared to the most accurate up to date computation; we also give a new reference calculation for future work on this system. The algorithm has also been applied to a more challenging 7-atom molecule (ethylene oxide). The computed spectrum up to 3200 cm−1 is the most accurate computation that exists today on such systems. More details on this work can be found in [43], [21].

Dislocation

We have focused on the improvements of the parallel collision detection and of the accuracy in the force field computation in the OPTIDIS code.

• a 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;

• we observed that the force field computation depends on how the traversal of the segments list or boxes in the octree was done. New accurate formulas to remove this issue have been developed and we are implementing them in the code. They will be used in the Fast Multipole Method that we have developed previously.

Finally, 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

High performance simulation for ITER tokamak

Concerning the GYSELA global non-linear electrostatic code, the efforts during the period have concentrated on 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 is first to consolidate the parallel version of the gyro-average operator, in particular by designing a scalable MPI+OpenMP parallel version and 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.

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.

High performance simulation for 3D frequency-domain Maxwell's equations

We also recently developed a collaboration with NACHOS on the HORSE (High Order solver for Radar cross Section Evaluation) simulation code. The aim was to integrate the PaStiX solver, with low-rank compression technique, in a domain decomposition framework to solve 3D frequency-domain Maxwell's equations. The results are promising since we were able to reduce by two the factorization and the solve time for each subdomain. And we were also able to reduce by two the memory requirements thanks to our compression techniques. This would allow us to consider larger subdomains with the same memory constraints that currently limit the simulations.

High performance simulation for atmospheric chemistry

We worked on the development and tests of the Adaptative Semi-Implicit Scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the Ordinary Differential Equation systems associated with the time evolution of the species concentrations, ASIS adopts a one step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time stepping module to control the accuracy of the numerical solution. In 5 idealized box model simulations ASIS gives results similar to the higher order implicit schemes derived from the Rosenbrock’s and Gear’s methods and requires less computation and run time at the moderate precision required for atmospheric applications. When implemented in the MOCAGE CTM and the LMD Mars GCM the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the 10 concentrations of the species in aqueous phase in addition to gas phase chemistry.

More details on this work can be found in [19].