Numerical analysis of a multi-physics model for trace gas sensors.

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dc.contributor.advisorKirby, Robert C.
dc.creatorBrennan, Brian.
dc.date.accessioned2015-05-22T15:00:06Z
dc.date.accessioned2017-04-07T19:35:19Z
dc.date.available2015-05-22T15:00:06Z
dc.date.available2017-04-07T19:35:19Z
dc.date.created2015-05
dc.date.issued2015-03-13
dc.date.submittedMay 2015
dc.date.updated2015-05-22T15:00:07Z
dc.description.abstractTrace 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.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/2104/9295
dc.language.isoen
dc.rights.accessrightsWorldwide access.
dc.subjectBlock preconditioners. Finite element. Multi-physics. Thermoacoustics.
dc.titleNumerical analysis of a multi-physics model for trace gas sensors.
dc.typeThesis
dc.type.materialtext

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