Kirby, Robert C.2015-05-222017-04-072015-05-222017-04-072015-052015-03-13May 2015http://hdl.handle.net/2104/9295Trace 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 modelled by a coupled system of complex elliptic partial differential equations for pressure and temperature. Solutions are approximated using the finite element method which we will show admits a continuous and coercive variational problem with optimal H¹ and L² error estimates. Numerically, the finite element discretization yields a skew-Hermitian dominant matrix for which classical algebraic preconditioners quickly degrade. We develop a block preconditioner that requires scalar Helmholtz solutions to apply but gives a very low outer iteration count. To handle this, we explore three preconditioners for the resulting linear system. First we analyze the classical block Jacobi and block Gauss-Seidel preconditions before presenting a custom, physics based preconditioner. We also present analysis showing eigenvalues of the preconditioned system are mesh-dependent but with a small coefficient. Numerical experiments confirm our theoretical discussion.application/pdfenBlock preconditioners. Finite element. Multi-physics. Thermoacoustics.Thesis2015-05-22Worldwide access.