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dc.contributor.advisor Embree, Mark
dc.creatorSifuentes, Josef
dc.date.accessioned 2009-06-04T08:11:12Z
dc.date.available 2009-06-04T08:11:12Z
dc.date.issued 2006
dc.identifier.urihttps://hdl.handle.net/1911/17917
dc.description.abstract In this thesis we propose methods for preconditioning Krylov subspace methods for solving the integral equation formulation of the Helmholtz partial differential equation for modeling scattered waves. An advantage of using an integral formulation is that only the scattering obstacle is discretized and the outgoing boundary conditions are automatically satisfied. Furthermore, convergence is dictated by the wave number kappa with only a mild dependence on the discretization. However such methods are increasingly computationally expensive for increasing values of kappa. This cost is due to GMRES iteration counts that increase like O(kappa2), for a linear system that is dense with dimension N = O(kappa 4). GMRES is slow due to a small subset of the spectrum that is well separated, a part of which approaches the origin as kappa increases. The troublesome subset corresponds to low frequency eigenfunctions which can be approximated using coarse meshes. We propose a preconditioner based on deflating this subset of the spectrum which we evaluate by interpolating coarse mesh approximations of the spectrum. We show that for discretizations of less than one node per wavelength, we can effectively precondition the full problem over a sufficiently resolved mesh.
dc.format.extent 54 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
Physics
Electromagnetics
dc.title Preconditioning the integral formulation of the Helmholtz equation via deflation
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Physics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.identifier.citation Sifuentes, Josef. "Preconditioning the integral formulation of the Helmholtz equation via deflation." (2006) Master’s Thesis, Rice University. https://hdl.handle.net/1911/17917.


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