Time- and memory-efficient representation of complex mesoscale potentials
For computational nanomechanics researchers, it offers a universal method to handle complex mesoscale potentials, though the demonstration is limited to a single example.
The paper applies tensor train cross approximation to efficiently represent van der Waals potentials between complex-shaped bodies (e.g., carbon nanotubes) in a compact tensor form, enabling memory- and time-efficient mesoscale modeling.
We apply the modern technique of approximation of multivariate functions - tensor train cross approximation - to the problem of the description of physical interactions between complex-shaped bodies in a context of computational nanomechanics. In this note we showcase one particular example - van der Waals interactions between two cylindrical bodies - relevant to modeling of carbon nanotube systems. The potential is viewed as a tensor (multidimensional table) which is represented in compact form with the help of tensor train decomposition. The described approach offers a universal solution for the description of van der Waals interactions between complex-shaped nanostructures and can be used within the framework of such systems of mesoscale modeling as recently emerged mesoscopic distinct element method (MDEM).