INTEGRATING A LINEAR INTERPOLATION FUNCTION ACROSS TRIANGULAR CELL BOUNDARIES Page: 2 of 19
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Integrating a Linear Interpolation Function
Across Triangular Cell Boundaries
J. Renae Wiseman, Mathematics Department
U. S. Air Force Academy, Colorado Springs, CO 80841
Jerry S. Brock, Applied Physics Division
Los Alamos National Laboratory, Los Alamos, NM 87545
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 model's
consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid.
This report presents discrete-expansions for a linear interpolation function commonly used within
triangular cell geometries. Discrete-expansions, unlike a Taylor's series, account for interpolation
discontinuities across cell boundaries and, therefore, are valid throughout a discretized domain.
Verification of linear discrete-expansions is demonstrated on a simple test problem.
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WISEMAN, J. R. & BROCK, J. S. INTEGRATING A LINEAR INTERPOLATION FUNCTION ACROSS TRIANGULAR CELL BOUNDARIES, article, April 1, 2000; New Mexico. (digital.library.unt.edu/ark:/67531/metadc719526/m1/2/: accessed December 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.