## Section: Scientific Foundations

Keywords : multiscale schemes, molecular dynamics, parallelism and distributed computing (distributed computing, parallel computing).

### Schemes and algorithms for computational chemistry

Due to the increase of available computer power, new applications such as reaction paths, free energy computations, biomolecular dynamics simulations or failure material simulations are now commonly performed by chemists. These computations simulate systems up to several thousands of atoms, for large time scales up to several nanoseconds. The larger the simulation is, the smaller the computational cost of the potential driving the phenomena is, resulting in low precision results. To achieve realistic results, simulations need to include the environment surrounding the molecules, such as water and membranes, resulting in system sizes up to about several hundred thousands of atoms. Furthermore, simulating the aggregation of proteins, which is critical for biologists studying viruses, requires models of up to one million atoms, with a simulation time up to one millisecond. This implies that atomistic simulations must be speeded up by several orders of magnitude. To obtain this speed, numerical and parallel algorithms must be improved, as well as their implementations on distributed or parallel architectures.

We are currently focusing on several aspects of these problems.

First, we try to improve models and algorithms. To do this, we decrease the complexity of classical algorithms by introducing new approximations in the algorithms, in the model (this is the trick of linear scaling methods like the divide-and-conquer method), and by proposing new algorithms.

Second, we apply multiscale methods to decrease the number of atoms that are considered at the finest level (electronic or atomistic). To do this, we introduce a coarser model like continuum media to take into account the electrostatic effect of the environment, or an elasticity model for crystals. The difficulty here is to build an efficient scheme which couples the two different scales without any loss of precision.

Finally, an efficient implementation is necessary to reach the desired level of performance. For instance, we can rewrite our algorithms in the form of block computations, in order to use efficient computational routines such as BLAS vector-matrix operations, or to implement accurate load balancing strategies.

Another domain we are currently investigating is the development of parallel and distributed environments for coupling numerical codes, and for interactively steering numerical simulations in particular in the context of molecular dynamics.