Work Package 1 – High-dimensional and large-scale problems in molecular simulation

This Work Package focuses on developing and analyzing new numerical methods and algorithms for molecular simulation problems leading to solving linear and nonlinear systems of equations and eigenvalue problems, that are characterized by high dimensionality, large ranks (for tensor problems), and extreme scale. The goal is to have algorithms that are numerically sound, are able to exploit massive parallelism in both space and time, through deterministic or stochastic approaches, minimize the communication, and as a by-product, also reduce the energy consumption of the simulation. An important goal of this work package is to create a tensor library that deals with high-dimensional problems and is scalable on massively parallel machines.

In more details, our research focuses on: 

• Communication avoiding algorithms for problems arising in molecular simulations and in particular tensor operations,
• A framework for tensor computations, to deal with problems that feature high-dimensionality, but also possibly large ranks. This will be applied in particular to address the accurate and efficient description of strong electron-correlation effects.
• Solving linear and non-linear systems of equations and eigenvalue problems ubiquitous in electronic structure calculation.
• Parallelization in space and time for time-dependent problems.
• Stochastic methods, to efficiently sample high-dimensional multimodal measures in order to evaluate averages with respect to these measure.