### Mathematics Colloquium

** Elbridge Gerry Puckett
**

University of California, Davis

**Title:** Recent Advances in Modeling Visco-Elastic-Plastic Flow Properties With
Particles in Geodynamic Computations

**Date:** Friday, November 12, 2021

**Place and Time:** Zoom, 3:05-3:55 pm

**Abstract.**

Combining finite element methods with particle methods is an important technique that is widely used in computational geodynamics to model mantle convection, lithosphere dynamics, crustal-scale modeling, and other geologic processes. In these applications particles are used to advect properties of the medium such as the location of material boundaries, density, components of stress, chemical composition, etc. However, replacing field-based descriptions of a material property by quantities that are only defined at the locations of the particles introduces numerical errors associated with the interpolation of the particle properties onto the finite element grid. Although these errors have previously been investigated, a complete understanding is still lacking. We will describe a class of high-order accurate interpolation algorithms, recent work showing that the (potentially) most useful member of this class requires an increasing number of particles per cell to obtain optimal accuracy in the limit as the grid size goes to zero, and a method to remove this requirement. We demonstrate the accuracy of these methods using several standard benchmarks from the computational geodynamics community. We will also describe a new algorithm for limiting the values of the properties in the interpolation step in order to eliminate the overshoot and undershoot that can result from the interpolation algorithm.