Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decomposition

International audienceThe fine description of the mechanics and structure of materials atnanometric scale introduces some specific challenges related to the impressive numberof degrees of freedom required due to the highly dimensional spaces in whichthose models are defined. This is the case of quantum mechanics models, in whichthe wavefunction is defined in a space of dimension 3×Np, being Np the number ofparticles involved, that leads to the terrific curse of dimensionality. Despite the factthat spectacular progresses have been accomplished in the context of computationalmechanics in the last decade, the treatment of those models, as we describe in thepresent work, needs further developments