Title: A Scalable Preconditioner for the Wigner-Poisson Equations

Speaker: Tim Kelley, North Carolina State University

Date/Time: Thursday, May 25, 2006, 9:30 – 10:30 am MDT

Location: Bldg. 899/1811 (videoconferenced to 915/S101 CA)

Brief Abstract: We analyze a preconditioner for the time-independent Wigner-Poisson equations for a resonant tunneling diode. This device is a nano-scale semiconductor which one hopes to use as a THz oscillator. A parameter study is needed to identify the operating regimes under which the device will oscillate. A critical part of this parameter study is the design of an effective preconditioner for the linearized problems which must be solved to compute Newton steps. The application of the preconditioner transforms the equations into a compact fixed point problem for the Wigner distribution. After discretization, the Jacobians of the discrete problem have mesh-independent eigenvalue clustering properties, which implies the mathematical scalability of the nonlinear solver. We present a numerical example of a continuation study which supports the theory. This is joint work with Matthew Lasater, Andy Salinger, Dwight Woolard, Greg Recine, and Peiji Zhao.

CSRI POC: Michael Parks, (505) 845-0512