Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods

TL;DR

This paper introduces a new class of interpolants for lattice functions, providing essential theoretical tools for analyzing atomistic and multiscale models in materials science.

Contribution

It develops a general framework for (quasi-)interpolants on Bravais lattices, crucial for multiscale analysis of atomistic and continuum methods.

Findings

Established key properties of the interpolants

Provided technical results for multiscale analysis

Facilitated rigorous analysis of atomistic models

Abstract

We introduce a general class of (quasi-)interpolants of functions defined on a Bravais lattice, and establish several technical results for these interpolants that are crucial ingredients in the analysis of atomistic models and atomistic/continuum multi-scale methods.