Oak Ridge National Laboratory presents 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 (generalized minimal residual method).
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.
About the Speaker: Victor DeCaria is 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.