Discrete-expansions for linear interpolation functions Original Research Article

Computational models of particle dynamics often exchange solution data with discretized continuum-fields using interpolation functions. These particle methods require a series expansion of the interpolation function for two purposes: numerical analysis used to establish the modelʹs consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid. This report presents discrete-expansions for two linear interpolation functions commonly used within triangular and tetrahedral cell geometries. Application of the linear discrete-expansions for numerical analysis and localization within particle methods is outlined and discussed.