Applied Math Seminar: Stabilized Control Volume Finite Element Method for Drift-Diffusion Equations

Event Type: 
Seminar
Speaker: 
Kara Peterson
Event Date: 
Monday, February 6, 2017 - 3:30pm
Location: 
SMLC 356
Audience: 
Faculty/StaffStudentsAlumni/Friends

Event Description: 

Stabilized Control Volume Finite Element Method for Drift-Diffusion Equations

 
Predictive simulation of semiconductor devices depends on accurate numerical solutions of the drift-diffusion equations, which model the motion of electrons and holes. When discretizing the equations with a control volume finite element method (CVFEM) additional stabilization is required to enable robust solutions in the strong drift regime. In this talk I will provide an overview of the CVFEM and describe a new stabilization method that uses fluxes generated by solving the governing equations on mesh edges and lifting these edge fluxes into an element using curl-conforming basis functions. The resulting formulation can be thought of as a multi-dimensional extension to the classical Scharfetter-Gummel unwinding procedure that enables stable and accurate solutions on unstructured meshes. Results for standard advection-diffusion examples along with results from a Sandia semiconductor model for the coupled drift-diffusion equations will demonstrate the benefits of this stabilization approach. Extensions of the method, including a finite element implementation and a second-order version applied in a multi-scale CVFEM framework, will also be briefly discussed.