Abstract: We present a new implicit solver for a Boltzmann-Poisson system which models the evolution of electron densities in semiconductor devices. This system is difficult to solve numerically due to the high dimension of the phase space, the nonlocality of the collision operator, stiffness arising from collisions, and the potential wide range of time scales which necessitate implicit time integration.

Our main development is a new Schur complement formulation which poses the problem on a reduced dimension, and forms the basis of our new solvers. The reduced memory of the Schur complement enables acceleration of the iterative solvers using Anderson acceleration, which is a nonlinear extension of GMRES.

When collisions are strong, the problem becomes stiff, but the model limits to a lower dimensional drift diffusion equation. This lets us use a drift diffusion solver as an inexpensive preconditioner to the full kinetic model, which further accelerates the nonlinear solver.

Time permitting, we will discuss some preliminary work on a hybrid method which decouples the collided electrons from the free streaming electrons. The collided electrons, which are the source of stiffness, may be evolved on a coarser mesh to reduce execution time for similar accuracy.

Speaker Bio: Victor DeCaria received his PhD in Mathematics at University of Pittsburgh in 2019 working with William Layton. He is currently a postdoctoral researcher in the Computational and Applied Mathematics Group at Oak Ridge National Laboratory working with Cory Hauck. His research interests are computational fluid dynamics, partitioned and implicit-explicit timestepping methods, time adaptivity, and model reduction.

Host: Eirik Endeve, endevee@ornl.gov

About the Seminar: The Computational and Applied Math Seminar features talks by invited speakers, local mathematicians, and domain scientists working on problems of mathematical interest. The seminar is held weekly, every Thursday from 3:00pm-4:00pm. If you are interested in giving a seminar, please contact Eirik Endeve, endevee@ornl.gov. To subscribe to the CAM Seminar mailing list, please contact Kasi Arnold, arnoldkl@ornl.gov. To see the full list of previous and upcoming seminars, go to https://csmd.ornl.gov/events/9/seminars.

Last Updated: April 9, 2020 - 6:35 pm