Numerical Analysis Seminar

Date: October 22, 2014

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Brian Brennan, Baylor University

Title: NUMERICAL ANALYSIS OF A MULTI-PHYSICS MODEL FOR TRACE GAS SENSORS

Abstract: Trace gas sensors are currently used in many applications from leak detection to national security and may some day help with disease diagnosis. These sensors are modeled by a coupled system of complex elliptic partial dierential equations for pressure and temperature. Solutions are approximated using the finite element method which we will show admits a continuous and coercive problem with optimal H1 and L2 error estimates. Numerically, the finite element discretization yields a skew-Hermitian dominant matrix for which classical algebraic pre conditioners quickly degrade. We develop a block preconditioner that requires scalar Helmholtz solutions to apply but gives a very low outer iteration count. We also present analysis showing eigenvalues of the preconditioned system are mesh-dependent but with a small coefficient. Numerical experiments confirm our theoretical discussion.