Fellow members of the math department,

The information for this week's CAM seminar is below.

Best,
Abner

Date and Time: W 4/14 @ 4:45pm

Zoom: https://tennessee.zoom.us/j/91531216657

Speaker: Victor DeCaria

Affiliation: ORNL

Title: A new implicit solver for semiconductor models


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, 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 correction to the full
kinetic model, which further accelerates the nonlinear solver.

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