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Thursday, March 05, 2020
12:00 PM - 1:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

Computational physics models for nonlocal problems, particle tracking, and solid mechanics

Giacomo Capodaglio
Florida State University

The talk is an overview of three computational physics projects that have in common the use of the finite element method (FEM) to perform numerical simulations. I will begin discussing some recent advances in the modeling of nonlocal diffusion processes with interface. Nonlocal problems are characterized by a type of interaction that is not limited to points that are in direct contact with each other, and long range communication can occur. Nonlocal interface models differ considerably from their local counterpart and therefore call for an appropriate treatment. The proposed formulation relies on an energy minimization approach inspired by a similar strategy used for elliptic partial differential equations, and aims at guaranteeing well-posedness and consistency. Numerical results are obtained to gain further insight on the problem. Second, I will present a particle tracking algorithm designed for parallel finite element applications, i.e. when the finite element mesh is shared among different processes. The algorithm has been designed to work effectively with meshes that possess curved edges as well as non-planar faces, and it is shown to scale reasonably well with the number of processes. Perfect scalability with the number of particles is obtained, and the accuracy is consistent with the use of a Runge-Kutta 4 time stepping scheme. Next, I will discuss the coupling of the material point method (MPM) with the FEM for the simulation of the interaction between two solid bodies. The coupling is motivated by the properties of the two methods under different deformation regimes. The proposed approach is inspired by the ALE method for fluid-structure interaction and relies on a monolithic coupling obtained attaching the MPM grid to the FEM body. In this way, contact search and detection algorithms are avoided because the bodies are treated as a single continuum. Numerical simulations are performed to investigate the reliability and robustness of the coupling procedure.

Host: Mark Petersen